text:
Equalization technique for compensating for degradation to the transmission of digitally modulated signals
An equalization technique for the compensation of degradation caused by multipath Rayleigh fading channels to the transmission of digitally modulated signals such as π/4 Differential Quadrature Phase Shift Keying (DQPSK) modulated signals. The technique is applicable to both linear and nonlinear transversal equalizers. Based on the Method of Projection onto Convex Sets (POCS), the technique is realized in an iterative form. The convergence speed of equalization depends on the magnitude of a look-back parameter, and is comparable to the speed of recursive least square based equalizers. The computational complexity of the technique also is variable and is adaptable to the convergence speed requirements. For achieving convergence speeds as recursive least square techniques, the computational load required of the presented equalization is of the order of the load required of the recursive least square techniques, but its program implementation is exceedingly simpler. At the same time the code size, memory and power consumption requirements are lower.
Kostic, Zoran (Tinton Falls, NJ)
AT&T Corp. (Murray Hill, NJ)
375/229, 708/323
H04B3/10; H03H15/00; H03H17/00; H03H21/00; H04B7/005; H04L25/03; H04L27/01; (IPC1-7): H03H7/30
375/11, 375/14, 364/724.2, 333/28R
5311546 Carrier phase recovery for an adaptive equalizer 1994-05-10 Paik et al. 375/14
5297166 Method and apparatus for decision feedback equalization with reduced convergence time 1994-03-22 Batruni 375/14
5268930 Decision feedback equalizer 1993-12-07 Sendyk et al. 375/13
5237588 Automatic equalizer 1993-08-17 Tanaka et al. 375/11
5175747 Equalizer 1992-12-29 Murakami 375/14
5164727 Optimal decoding method and apparatus for data acquisition applications of sigma delta modulators 1992-11-17 Zakhor et al. 341/143
5157690 Adaptive convergent decision feedback equalizer 1992-10-20 Buttle 375/14
5119401 Decision feedback equalizer including forward part whose signal reference point is shiftable depending on channel response 1992-06-02 Tsujimoto 375/14
5097482 Method and apparatus of decision feedback equalization for multipath digital communication 1992-03-17 Serizawa et al. 375/12
EP0467412 1992-01-22 375/14 Line equalizer for digital signals.
GHEBRETINSAE, TEMESGHEN
P. V. D. WILDE (AT&T BELL LABORATORIES 600 MOUNTAIN AVE. P. O. BOX 636, MURRAY HILL, NJ, 079740636, US)
1. A method of equalizing a channel degraded received signal to compensate for channel degradations in the received signal, the method comprising the steps of:
sampling the received signal for obtaining a plurality of received signal samples;
generating a set of equation lines from the plurality of received signal samples, the equation lines being indicative of a common value solution used in determining values for coefficients for use in an equalizer;
iteratively examining each one in the set of equation lines, the examining step examining a new equation line only after each one in a subset of previously examined equation lines in the set is reexamined; and
iteratively computing coefficients for achieving adaptive convergence of the coefficients in the equalizer with the received signal.
2. The method of claim 1 wherein the iteratively examining step further includes the step of limiting the equation lines being reexamined in the subset to a number M of equation lines in the subset, the number M identifying M most recently examined equation lines in the subset.
3. The method of claim 2 wherein the generating step further includes the step of providing a training signal, the training signal providing a plurality of training signal samples for combining with the received signal samples.
4. The method of claim 3 further comprising the step of adjusting the received signal samples to be equivalent to the training signal samples, the adjusting step compensating for degradations in the received signal.
5. The method of claim 2 wherein the generating step further includes the step of providing an error signal having a magnitude indicative of a convergence speed required for providing a specific level of adaptive convergence for the coefficients in compensating for degradations in the received signal.
6. The method of claim 5 further comprising the step of varying the number M in response to the change in magnitude of the error signal.
7. The method of claim 6 wherein the number varying step causes the number M to increase in magnitude when the convergence speed required for achieving the specific level of adaptive convergence of the coefficients is high and decrease in magnitude when the convergence speed required for achieving the specific level of adaptive convergence of the coefficients is low.
8. An equalizer circuit for performing equalization on a channel degraded received signal to compensate for channel degradations in the received signal, the circuit comprising:
means for sampling the received signal for obtaining a plurality of received signal samples for use in the equalizer circuit;
means for generating a set of equation lines from the plurality of received signal samples, the equation lines being indicative of a common value solution used in determining values for coefficients for use in the equalizer circuit;
means for iteratively examining each one in the set of equation lines, the examining means examining a new equation line only after each one in a subset of previously examined equation lines in the set is reexamined; and
means responsive to the examining means for iteratively computing coefficients for achieving adaptive convergence of the coefficients in the equalizer circuit with the received signal.
9. The circuit of claim 8 wherein the examining means further includes means for limiting the equation lines being reexamined in the subset to a number M of equation lines in the subset, the number M identifying M most recently examined equation lines in the subset.
10. The circuit of claim 9 wherein the generating means further includes means for generating a training signal, the training signal providing a plurality of training signal samples for combining with the received signal samples.
11. The circuit of claim 10 further comprising adjusting means responsive to the coefficient computing means for adjusting the received signal samples in the receive signal to be equivalent to the training signal samples being provided in the training signal, the adjusting means compensating for degradations in the received signal.
12. The circuit of claim 9 wherein the generating means further comprises means for providing an error signal having a magnitude indicative of a convergence speed required for providing a specific level of adaptive convergence for the coefficients in compensating for degradations in the received signal.
13. The circuit of claim 12 further comprising means for varying the number M in response to the change in magnitude of the error signal.
14. The circuit of claim 13 wherein the means for varying the number M causes the number M to increase in magnitude when the convergence speed required for achieving the specific level of adaptive convergence of the coefficients is high and decrease in magnitude when the convergence speed required for achieving the specific level of adaptive convergence of the coefficients is low.
15. A method of equalizing a channel degraded received signal to compensate for degradations in the received signal, the method comprising the steps of:
iteratively examining each one in the set of equation lines, the examining step examining a new equation line only after each one in a subset of previously examined equation lines in the set is reexamined;
selecting an initial value for a look-back depth parameter B for use in determining the subset of previously examined equation lines, the selected value for the parameter B being indicative of a level sufficient for achieving a selected level of adaptive convergence of the coefficients with the received signal; and
16. The method of claim 15 further comprising the steps of:
providing an error signal indicative of the level of adaptive convergence of the coefficients with the received signal; and
selecting a subsequent value for the parameter B in response to a change in value of the error signal, the change in error signal being indicative of a change in the degradations in the received signal and the subsequently selected value for the parameter B being indicative of a level sufficient for achieving the selected level of adaptive convergence of the coefficients with the received signal.
17. The method of claim 16 wherein the value for the parameter B increases in magnitude when the level of adaptive convergence of the coefficients for compensating for degradations in the signal is high and decreases in magnitude when the level of adaptive convergence of the coefficients for compensating for degradations in the signal is low.
18. The method of claim 17 wherein the iteratively examining step includes the step of limiting the equation lines being reexamined in the subset to a number M of equation lines in the subset, the number M being reflective of the assigned value B for identifying M most recently examined equation lines in the subset.
19. An equalizer circuit for performing equalization on a channel degraded received signal to compensate for channel degradations in the received signal, the circuit comprising:
means for sampling the received signal for obtaining a plurality of received signal samples;
means for iteratively examining each one in the set of equation lines, the examining means examining a new equation line only after each one in a subset of previously examined equation lines in the set is reexamined;
means for selecting an initial value for a look-back depth parameter B for use in determining the subset of previously examined equation lines, the selected value for the parameter B being indicative of a level sufficient for achieving a selected level of adaptive convergence of the coefficients with the received signal; and
means for iteratively computing coefficients for achieving adaptive convergence of the coefficients in the equalizer circuit with the received signal.
20. The circuit of claim 19 further comprising:
means for providing an error signal indicative of the level of adaptive convergence of the coefficients with the received signal; and
means for selecting a subsequent value for the parameter B in response to a change in value of the error signal, the subsequently selected value for the parameter B being indicative of a level sufficient for achieving the selected level of adaptive convergence of the coefficients with the received signal.
21. The circuit of claim 20 wherein the value for the parameter B increases in magnitude when the level of adaptive convergence of the coefficients for compensating for degradations in the signal is high and decreases in magnitude when the level of adaptive convergence of the coefficients for compensating for degradations in the signal is low.
22. The circuit of claim 21 wherein the iteratively examining means includes means for limiting the equation lines being reexamined in the subset to a number M of equation lines in the subset, the number M being reflective of the assigned value B for identifying M most recently examined equation lines in the subset.
1. Technical Field
This invention relates to equalization systems for use in digital communications and more specifically to an equalization system for compensating for undesirable degradations that occur to signals in communication channels.
2. Description of the Prior Art
Digital communication systems which employ digitally modulated signals are increasingly being used in wireless and cellular applications. While propagating through a communication channel, these digitally modulated signals incur degradations in the form of intersymbol interference, fading and noise. These undesirable degradations on the signal are generally compensated for through use of equalization provided by equalizers in receivers employed in the digital communication systems.
The operation of conventional equalizers is well known and described, for example, by S. U. Quereshi in an article entitled Adaptive Equalization, Proceedings of the IEEE, Vol. 73, pages 1349-1387, September 1985. Two types of equalizer structures are most often used, transversal filters and Viterbi structures. Transversal filters consist of tap delay lines through which the received digitally modulated signals are shifted and the output of every tap is multiplied by a different coefficient. The output of the transversal filter based equalizer is the summation of all of the outputs from the taps multiplied by the coefficients. A part of transversal equalizers is a coefficient adaptation process which adjusts the coefficients such that the output of the equalizer is a signal without intersymbol interference degradation.
Viterbi equalizers are fundamentally different from transversal equalizers. Viterbi equalizers detect the sequence of the received signal for obtaining the maximum likelihood estimate of the sequence of the transmitted signal. The trellis, which is used for Viterbi equalization, represents all possible sequences of the transmitted signal. In operation, the Viterbi equalizer identifies a path through the trellis, this path representing the most likely sequence of the transmitted signal.
The properties of radio propagation through multipath fading channels, and the limitations of receiver technology impose a number of requirements on equalizers which attempt to compensate for degradations that occur to digitally modulated signals while in these channels. Traditional equalization structures and coefficient adaptation methods have disadvantages. By way of illustrative example, a numeration of the most often used equalizers and some particular disadvantages of these equalizers is provided. Linear transversal equalizer structures have noise inversion problems. Decision feedback equalizer (DFE) structures with least mean squares (LMS) coefficient adaptation have slow coefficient convergence. DFE structures with recursive least squares (RLS) adaptation have high computational complexity and are numerically unstable. Lattice equalizer structures are computationally complex. Tap-jamming based transversal equalizers are characterized by memory inefficient block processing and high computational complexity. And maximum likelihood sequence estimation (MLSE) equalization techniques have a high computational complexity and a need to have good channel estimates. Also, these MLSE equalization techniques are sensitive to phase errors and have high memory requirements.
As apparent from the above, various techniques of equalization are known and have been used to date. These techniques are, however, either computationally complex or are limited in performance in some manner. It is therefore desirable that equalization techniques not only be capable of satisfactory performance but also be computationally simple. With an increased need for portable communication terminals, such as digital cellular telephones and cordless telephones, there is an increased need for this type of equalization technique. The availability of such a technique advantageously would allow, for example, power consumption to be conserved in these portable communication terminals which, while in their normal operating environment, receive all operating power from a battery usually contained within the terminal.
An improved technique for equalizing a received signal which is degraded by propagating through a multipath fading communication channel is provided, in accordance with the invention. In the operation of the technique, a separate equation is generated from the combination of each sample in the received signal, a desired signal value (or estimated signal value) and a measured signal estimation error. Each equation is examined for generating an increasingly improved approximation of a common value solution for use in determining the values of coefficients employed in an equalizer.
In one aspect of the invention, equalization of the degraded received signal is achieved in the equalizer through use of a look-back depth parameter. This selectable parameter determines the number of previously examined equations which are reexamined prior to examining an equation generated using the most recently received signal sample. Since only those equations that must be reexamined are stored in memory, the memory requirements for this technique are significantly less than those required by other equalization techniques.
In another aspect of the invention, flexibility in selecting and adaptively varying the value of the look-back depth parameter is provided. Through use of the measured signal estimation error, the technique variably adapts the value of the look-back depth parameter. Optimal equalizer complexity and performance in compensating for channel degradation effects are thus achieved through the selection of an optimum value for the look-back depth parameter. Being able to configure the equalizer in this manner results in significant savings in power consumption and memory requirements while being able to achieve the desired convergence speed for the selected application.
BRIEF DESCRIPTION OF THE DRAWING
This invention and its mode of operation will be more clearly understood from the following detailed description when read with the appended drawing in which:
FIG. 1 is a block diagram representation of functions performed in a digital receiver such as a cellular telephone;
FIG. 2 is a flow-chart representation of the basic POCS equalization operation;
FIG. 3 is a Hyperplane representation of equalizer equations for the 2-dimensional case;
FIG. 4 is a illustration of the LMS based iterative solution of the set of equations;
FIG. 5 is an illustration of the Doherty (RAP) based iterative solution of the set of equations;
FIG. 6 is an illustration of the POCS based iterative solution of the set of equations;
FIG. 7 is a fractionally spaced decision feedback equalizer;
FIGS. 8, 9 and 10 show performance comparisons in terms of convergence speed between various equalization techniques; and
FIG. 11 is a table which summarizes a comparison between the POCS technique and other equalization techniques.
With reference to FIG. 1 there is shown a high level block diagram representation of functions performed, for example, in a digital cellular telephone terminal. The equalization technique of this invention may be readily employed in such a digital cellular telephone. A signal received over antenna 101 is received in an IF/RF components block 102. In this block 102, a conversion from radio frequencies to baseband frequencies of the received signals is performed. Also since this block contains a transmitter, which provides signals for transmission over the antenna, a conversion from baseband frequencies to radio frequencies is performed as well in this block 102.
Receive signals from the block 102 are coupled to a modem 110 in which a number of digital signal processing functions illustrated by blocks 111 through 118 are performed. Each of these processing functions are well known and found as parts of traditional modems.
One particular important function in the modem 110 is the equalizer 115, which performs compensation of channel degradations that occur during the transmission of digitally modulated signals. Although this equalizer function is known, improving its performance in terms of reducing its complexity, power consumption, code size (ROM size requirement) and storage memory size (RAM size requirements) is desirable and has been achieved in accordance with the present invention. An equalizer suitable for use as equalizer 115 is shown in FIG. 7 and described in detail later herein.
Connected to the modem 110 is a speech codec 121 that performs a conversion which changes the digitally encoded speech received from the modem 110 into an analog speech waveform and vice versa. Connected to the speech codec 121 is a user interface 122 which enables a user to control and use the cellular telephone terminal.
Referring next to FIG. 2, them is shown a simplified flow diagram illustrating the operation of equalizer 115 in providing equalization to a channel degraded receive signal, in accordance with the invention. Coefficient adaptation is achieved through a process which is based on the Method of Projection onto Convex Sets (POCS) realized iteratively using the least mean squares procedure. The process is initialized at step 201 where the initializing parameter, the value for the equation K in memory, is set to zero. From this step 201, the process advances to step 202 where a new sample along with a new desired signal, or a new computed estimate of the signal is entered and used for the subsequent processing steps. From step 202, the process advances to step 203 where the equation formed by previously entered values is put into memory. In steps 204, 205, 206, as well as in any additional intermediate steps (not illustrated), previously stored equations are recomputed with new estimates of coefficients. In decision 207 the process determines if all input samples have been used. If not, then the equation indexed with k-B is removed from memory in step 208, the value for the equation k is incremented by one in step │209, and the process is restarted at step 202. If in decision 207, it is determined that all inputs have been used the process is exited.
An equalization problem can be expressed by the following vector/matrix equation d=Xc+e, (1)
where d is the vector of desired symbols/estimated symbols (training mode/decision directed mode), X is the matrix of received symbols, c is the vector of equalizer coefficients, and e is the error vector. Equivalently this equation can be written as ##EQU1## where XKH is conjugated and transposed vector xk. In the case of the linear transversal equalizer vector xk represents the set of symbols present in the transversal filter at time k. Parameter L denotes the processing size of the filter and N stands for the number of the taps in the filter. Any two adjacent vectors xk and xk+1 in the equalization problem are obtained by shifting the data through the filter, feeding new data point and discarding the oldest data point. The equation (1) can be geometrically represented as a set of intersecting hyperplanes.
With reference to FIG. 3, there is shown a graphical illustration of intersecting hyperplanes for a two-dimensional case. This graphical illustration represents a set of ten equations for a simple two coefficient (tap) equalizer: ##EQU2##
The task of equalization is to find c so as to minimize some error criterion. The least-square solution which minimizes ∥e∥ is given by c=[XH X]-1 XT d. (4)
The inverse of the matrix XH X does not necessarily exist or it can be unstable because of the properties of the data. It is therefore desirable to find some other regularized inversion c=X d which does exists and is stable at the same time. It is observed that the POCS based iterative procedure satisfies these requirements.
Each one of the set of ten equations shown in FIG. 3 is built from one desired sample value and two input signal values. Ideally all the equations should intersect in a single point, but due to distortion and noise that is not the case. The goal of any equalization method is to obtain a common solution to all the equations which is represented in the figure by a generally common intersection. A process of examining or solving the set of equations may be represented by a trajectory which starts at an initial signal estimate marked by 0, in FIG. 4, 5 and 6, and ends when all equations have been solved. Different equalization methods use different coefficient adaptation procedures and their solution trajectories differ.
With reference next to both FIGS. 4 and 5, there are shown solution trajectories for two known equalization techniques. In FIG. 4, a trajectory for LMS or RLS coefficient based adaptations is shown. Each equation in these FIGS. is represented by a single line.
A simple approximation to the stochastic gradient solution of the set of equations is given by a LMS adaptive expression ck+1 =ck +μ[dk -ckH xk ]xk, k=1, 2, . . . , L. (5)
The major problem of this method is its slow convergence. In the LMS technique every data vector xk and the corresponding equation or hyperplane is used only once in arriving at the solution.
In a paper by J. F. Doherty et al., entitled A fast method for Regularized Adaptive Filtering, in Digital Signal Processing, Vol. No. 2, pp. 14-26, 1992, an iterative procedure based on the normalized LMS was investigated. Doherty proposed using the LMS adaptation repetitively on the same set of equations, in a block processing fashion which can be represented by ##EQU3## when proper indexing is specified. Here j=(mod)i, and the sequence in which indices change is specified by (i,j) for i=1, . . . , L×I where I is the number of times that one equation is reused. The way in which the equations are reused is illustrated in FIG. 5. This FIG. thus shows an equalization technique which visits every equation line more than once. It is observed that every equation (line) is revisited for the next time only after all equations have been visited once. By way of comparison to the equalization technique shown in FIG. 4, a better solution to the set of equations is obtained through the equalization technique shown in FIG. 5. (The closer the last solution is to the intersection point, the better the overall solution).
Referring next to FIG. 6, there is shown a graphical illustration of an equalization technique which operates in an iterative routine and requires low computational complexity coefficient adaption, in accordance with the invention. The equalization technique specifies when and how many particular equations are reused in the process. The analytical expression for the POCS based iterative process is ##EQU4##
In this process a parameter B is introduced which defines a look-back depth. More specifically, it specifies how many previous equations are revisited and used for the iterative coefficient computation prior to using a new equation (data point). The solution trajectories for this process are shown in the graphical illustration provided in FIG. 6. And this process may be performed by the routine described by the flow chart shown in FIG. 2. Stated differently, the look-back depth parameter B determines a subset of previously examined equations lines, a number M being reflective of the assigned value B for identifying M most recently examined equation lines in the subset.
The equalization technique disclosed herein is a recursive and adaptive improvement over the block processing technique described by Doherty et al., in Digital Signal Processing Vol. No. 2, pp.14-26, 1992. Other relevant work addressing cyclical equalization has been reported by K. H. Mueller et at. in an article entitled Cyclic Equalization--A new Rapidly Converging Equalization Technique for Synchronous Data Communication, The Bell System Technical Journal, Vol. 534, pp.369-406, February 1975.
In solving the equalization equation, in accordance with the invention, the POCS based technique effectively performs regularized inversion, and avoids the problem of least-square solutions related to inverting rank deficient and ill-conditioned matrices. D. C. Youla et al., in an article entitled Image Restoration by the Method of Convex Projections Part 1--Theory, IFFF Trans. Medical Imaging, Vol. MI, pp. 81-94 October 1982, shows that POCS-based equalization can be represented in a form of regularized iterative pseudo inversion.
This can be shown by the following cl =Hcl-1 +d (9)
where H=Pk Pk-1 . . . Pk-LV+1, ##EQU5## Here V=B+1.
Further manipulation leads to the representation of these equations in a pseudo-inverse form as set forth in K. Tanabe in an article entitled Projection Method for Solving a Singular System of Linear Equations and its Application in Numer. Math., Vol 17, pp.203-214, 1971. This form is cl =Gl d (12)
with singular values ##EQU6## The POCS process is regularized through the iteration index 1. Small singular values are inverted with the taper, zero singular values are inverted to zeros. The smaller the singular values, the more they are attenuated. Data structures do not influence convergence properties.
FIG. 7 is an equalizer operably in accordance with the principles of the present invention. The equalizer structure is of the decision feedback type. The object of the adaptation technique disclosed herein is to adapt coefficients so that an input digital signal (x) provided at the input of the equalizer on line 701 is compensated for channel degradations before being provided as an output digital signal (y) over an output line 702. With every time step the input signal propagates through taps 703,704, 705 one at a time. Taps 703, 704, 705 delay the signal for a fractional amount of symbol time T, which is equal to T/f (By having T/f the equalizer becomes a fractionally spaced decision feedback equalizer). At every time instance signal samples present at nodes 706, 707,708 and 709 are respectively multiplied at multipliers 710, 711,712 and 713 with coefficient values C1, C2, C3 and C4, and summed in adder 714. Simultaneously, the signal at the output 702 (in the decision directed mode) or signal d (in the training mode) as chosen by switch 729 and denoted by r is multiplied by coefficient value C5 in multiplier 723 or propagates through the tap 721 and is multiplied with coefficient value C6 in multiplier 722. These two signals are then summed up in the summer 724. Outputs of the summers 7 14 and 724 are summed up in summer 725 once per signal sample period T. In detector 726, the signal is detected by being appropriately thresholded. The output of the detector provides the output signal, y.
The coefficients are computed in a coefficient adaptation processor block 728. This processor block 728 may be implemented through the use of a microcomputer containing ROM, RAM and through use of the proper coding. Such a microcomputer is know in the art and is readily available from semiconductor manufactures such as Signetics, Intel, AMD and AT&T.
The inputs to processor block 728 are a measured estimation error signal e which is obtained from the block 727; vector x generated by the set of x signals currently present at nodes 706, 707, 708, 709, 731 and 732; and the signal r. While operating in the training mode of equalization, signal r is equal to the known training signal d, which is provided as an input to the equalizer for a predetermined number of symbols. In the American Digital Cellular Communication System (IS-54), for example, the training period is 14 symbols long. While operating in the decision directed mode of equalization, signal r is equal to the estimated signal y at the output of the equalizer. In processor block 728, the coefficient values are computed as specified in the simplified flow diagram shown in FIG. 2 and as specified in greater detail using the POCS procedure defined in equation (7). After the coefficient values are computed, these values are used in multipliers 710, 711, 712, 713, 722 and 723. This procedure is repeated for each new input sample x appearing on line 701.
The differences between the RAP technique proposed by Doherty and the technique disclosed herein, in accordance with the invention, may be visualized simply by comparing FIGS. 5 and 6. The beneficial differences are numerous, however, and are set forth for highlighting the advantageous features of this improved equalization technique. First, the POCS technique does not require that all of the equations be revisited in every step of the iterative procedure. Second, since only a few previous equations have to be revisited by the POCS technique, it is not required that all equations be stored in memory. The number of equations that have to be stored in the memory for the POCS technique is determined by the look-back depth B. The significance of this operation is that the memory required for storing the equations that need to be reused is equal to L/B in the general case. In the particular case of American Digital Cellular IS-54, the number of equations that need to be stored for POCS procedure is approximately two times smaller than the memory needed for the RAP technique. Third, the POCS technique provides flexibility in choosing and adaptively varying the look-back depth parameter. The POCS technique can adapt the value of the look-back depth parameter based on the measurement of the system's signal estimation error and accomplish convergence in approximately the same time needed by the frame structure of the protocol. This assures that there are no computations wasted. In the particular case of the American Digital Cellular IS-54, the convergence with POCS can be accomplished in approximately 14 symbols used for the training mode of the equalizer.
Properties of the equalizer disclosed herein are:
Rapid equalizer coefficient convergence (comparable to RLS convergence);
Low computational complexity coefficient adaptation (comparable or linearly increased from LMS methods);
Low power consumption in digital processing or ASIC implementations;
Numerical stability for fixed-point implementations;
Minimal program-code size (the same as LMS methods);
Minimal RAM-memory size; and
Controllability of the equalizer computational complexity.
One application of the technique is in the American Digital Cellular Communication System (IS-54) in which the performance has been verified. The results of the performance when operating in this system are shown in FIGS. 8, 9 and 10. The modulation used in this system is π/4 DQPSK, bit rate is 48.6 kb/s, and symbol rate is 24.3 kbaud. The multipath Rayleigh fading channel has been used where allowed Doppler spread was up to 80 Hz, the separation between multipath components was up to one symbol time, and equal to 41 microseconds. Automatic gain control and when necessary baseband carrier recovery were used in the receiver.
FIG. 8 presents a comparative performance in terms of convergence speed between an equalizer based on the RLS coefficient adaptation technique and the equalizer based on the POCS coefficient adaptation technique disclosed herein. The value presented at the abscissa is the time and the values presented at the ordinate are the magnitude of the error signal e. The maximal error values are different for the RLS and POCS techniques illustrated in this figure. This figure has been obtained by simulating the communications channel and relevant modem blocks. In this simulation the Doppler spread of the channel is equal to 10 Hz and the multipath characteristics are such that the second path is 1/8 symbol away from the first multipath component and it has the same average power. It should be observed that the duration of the peaks, during which the equalizers based on the RLS and POCS are in the 14 symbol long training mode (where the coefficients are converging), are about the same. This verifies that POCS based equalization achieves the desired convergence speed.
FIG. 9 presents a comparison between the convergence speed of an equalizer based on the RLS coefficient adaptation technique and the convergence speed of the equalizer based on the POCS coefficient adaptation technique disclosed herein. The value presented at the abscissa is the time and the values presented at the ordinate are the magnitude of the error signal e. The figure has been obtained by simulating the communications channel and relevant modem blocks. In this simulation the Doppler spread of the channel is equal to 15 Hz and the multipath characteristics are such that the second path is 1/4 symbol away from the first multipath component and it has the same average power. It can be seen that the duration of the peaks during which equalizers are converging are about the same. This verifies that POCS based equalization achieves the desired convergence speed under described channel conditions. It can also be seen that POCS converges as fast as RLS, and that POCS does not have an occurrence of extremely low values of the errors as shown in this Figure. This appears to suggests that the POCS technique is more stable.
FIG. 10 presents a comparison between the convergence speed of an equalizer based on the RLS coefficient adaptation technique and the convergence speed of the equalizer based on the POCS coefficient adaptation technique disclosed herein. The value presented at the abscissa is the time and the values presented at the ordinate are the magnitude of the error signal e. Note that the maximal error values are different for RLS and POCS techniques in this figure. The figure has been obtained by simulating the communications channel and relevant modem blocks. In this simulation the Doppler spread of the channel is equal to 30 Hz and the multipath characteristics are such that the second path is 3/7 symbol away from the first multipath component and it has the same average power. It is shown that the duration of the peaks during which the equalizers are converging are about the same. This verifies that POCS based equalization achieves the desired convergence speed under described channel conditions.
A summary of the comparison between POCS technique and other equalization techniques is provided in the table shown in FIG. 11. In this table, the advantages of the POCS in terms of computational simplicity, power savings and memory requirements are shown. The table presents approximate computational complexity, RAM memory requirements and code size (ROM memory) requirements. LMS processing requirements are taken as a point of reference for RAM memory size and code size. Values in parentheses refer to normalized versions of RAP and POCS (versions presents herein).
Various modifications of this invention are contemplated and may obviously be resorted to by those skilled in the art without departing from the spirit and scope of the invention as hereinafter defined by the appended claims.
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"It was his decision", Coach Brett Brown said. "Tonight is not really an outlier, it's been sort of progressive".
Fultz played about 15 minutes, in the 123-104 win over the Nuggets, which is right around the minutes Brown had in mind for him. Colangelo added that the team would likely seek out additional "garbage time" opportunities. "I'm not sure I have the answer. Knowing what I know and seeing what I've seen, and understanding how special that kid is from a human being standpoint, it's a good day".
Fultz entered the game with 2 minutes 54 seconds remaining in the first quarter to thunderous applause at Wells Fargo Center in Philadelphia and, after turning the ball over on his first trip up the court, he settled down and scored his first points since October with an easy layup. But Fultz - whose awkward shooting form made him a punchline in the National Basketball Association - fired an airball later in the quarter.
So, he played, played well but not flawless (one airball and three blocked shots), but most importantly-he survived. But the improvement has come without any help from Fultz. "Once I stepped on the floor, it felt great just to be back out there with my brothers". Burke tried to keep pace (six points on 3-of-4 shooting) but didn't have enough.
Fultz shot 5-of-13 from the field, including this nice pull-up jumper late in the game. The 6-foot-4 guard out of Washington just may have a significant impact after all in the postseason.
The Sixers players were similarly happy with the rookie's return.
Philadelphia fell behind by eight points at half-time, but charged ahead in the third quarter, outscoring Denver 34-15. Paul Milsap chipped in 16 points.
Sixers: Waived G James Young.
For the Nuggets, Will Barton led the way with 25 points followed by Jamal Murray with 17 points.
The last New York Knick to have a 40-point game was Kristaps Porzingis this past November when he dropped 40 on the Indiana Pacers.


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Q: Support For Elastic Beanstalk on LocalStack I am rather new to LocalStack and I am finding it to be extremely useful.  The LocalStack GitHub page does not list Elastic Beanstalk as a supported service.  Is there any information on whether this will be rolled out anytime soon?

A: Elasticbeanstalk automatically creates the infrastructure necessary to deploy and run your application in the cloud. For example. it creates EC2 instances, load balancer etc for you.
if you look at localstack, it supports the standalone services such IAM, S3, Dynamodb etc. Therefore I don't think the localstack will ever support elasticbeanstalk as a service.
If you want to simulate running the elasticbeanstalk application locally,  you can try running the following the eb cli command. It will run the application in docker.
eb local run

redpajama_set_name: RedPajamaStackExchange


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Why is this image so small?
This image is presented as a "thumbnail" because it is protected by copyright. The Brooklyn Museum respects the rights of artists who retain the copyright to their work.
Henri Matisse (French, 1869-1954). [Untitled] (Headpiece for the Poem "L'Après-Midi d'un Faune"), 1932. Etching on wove paper, Sheet: 13 x 9 3/4 in. (33 x 24.8 cm). Brooklyn Museum, Carll H. de Silver Fund, 36.67.14. © artist or artist's estate (Photo: Brooklyn Museum, 36.67.14_PS2.jpg)
Henri Matisse (French, 1869-1954). [Untitled] (Headpiece for the Poem "L'Après-Midi d'un Faune"), 1932. Etching on wove paper, Sheet: 13 x 9 3/4 in. (33 x 24.8 cm). Brooklyn Museum, Carll H. de Silver Fund, 36.67.14. © artist or artist's estate (Photo: Brooklyn Museum, CUR.36.67.14.jpg)
[Untitled] (Headpiece for the Poem "L'Après-Midi d'un Faune")
PORTFOLIO/SERIES accompanies the book "Poésies de Stéphane Malarmé"
ARTIST Henri Matisse, French, 1869-1954
MEDIUM Etching on wove paper
DIMENSIONS Sheet: 13 x 9 3/4 in. (33 x 24.8 cm) (show scale)
MARKINGS Stamped verso lower right in brown ink: "Brooklyn Museum, Brooklyn, N.Y."
COLLECTIONS European Art
ACCESSION NUMBER 36.67.14
STATE First state
CREDIT LINE Carll H. de Silver Fund
RIGHTS STATEMENT © artist or artist's estate
Copyright for this work may be controlled by the artist, the artist's estate, or other rights holders. A more detailed analysis of its rights history may, however, place it in the public domain. The Museum does not warrant that the use of this work will not infringe on the rights of third parties. It is your responsibility to determine and satisfy copyright or other use restrictions before copying, transmitting, or making other use of protected items beyond that allowed by "fair use," as such term is understood under the United States Copyright Act. For further information about copyright, we recommend resources at the United States Library of Congress, Cornell University, Copyright and Cultural Institutions: Guidelines for U.S. Libraries, Archives, and Museums, and Copyright Watch. For more information about the Museum's rights project, including how rights types are assigned, please see our blog posts on copyright. If you have any information regarding this work and rights to it, please contact copyright@brooklynmuseum.org.
CAPTION Henri Matisse (French, 1869-1954). [Untitled] (Headpiece for the Poem "L'Après-Midi d'un Faune"), 1932. Etching on wove paper, Sheet: 13 x 9 3/4 in. (33 x 24.8 cm). Brooklyn Museum, Carll H. de Silver Fund, 36.67.14. © artist or artist's estate (Photo: Brooklyn Museum, 36.67.14_PS2.jpg)
IMAGE overall, 36.67.14_PS2.jpg. Brooklyn Museum photograph, 2010

redpajama_set_name: RedPajamaCommonCrawl


President Cyril Ramaphosa has been vocal about issues facing Eskom. From its debt, its administrative issues and load-shedding, Ramaphosa has moved to alleviate concerns.
Since taking up office, Ramaphosa has vowed to fix some of the county's troubled state-owned entities, including the debt-ridden Eskom.
Here are four quotes from Ramaphosa on the Eskom crisis.
In an opinion piece written for the Sunday Times, Ramaphosa said that moves were being made to make Eskom more "efficient".
"We are redesigning and repositioning Eskom for the future. This is not about 'privatising' Eskom but separating and balancing operations to make the entity far more efficient. State-owned enterprises must be fully self-sufficient and able to fulfil their developmental and economic roles. This therefore requires that those consuming services, including electricity, must pay for them."
"Restoring energy security for the country is an absolute imperative. We are giving detailed attention to the crisis and challenges that our electricity company, Eskom, faces."
Ramaphosa reassured investors at the Mining Indaba in Cape Town amid concerns over Eskom's stability.
"We're confronted by the Eskom challenge once again, but this time around we are taking steps to address the challenge in terms of the processes that we are involved in."


Many people today believe that the metal bed frame brown room essentials will go only with substantial space. The truth is that a bedding vanity with tops are sometimes a good furniture for modest bedding as long since you may choose the right layout. You have to center on the big event. Before believing about cosmetic variable of this vanity, you ought to continue to keep your focus about the job. Opt for the vanity tops that accompanies effective layouts like powerful storage, electrical lighting installation in the upper area, mirror, and faucet setup. In the event the vanity has plenty of functions, you can lower another furniture that perform similar role to bargain together with the constrained distance.
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metal bed frame brown room essentials has a personal place in most folks to beautify the bedding. Sea glass also can find in jewelry. It has several sort of comfortable shade such as for example kelly-green, clear, and brown. I thinkthe sea-glass stone is almost much like crystal because it is very beautiful. Inside this period, the sea glass accessories additionally influence into bedding equipment. They have lots of kind of bedding add-ons that formed with ocean glass.


SHUTi is currently available only to participants in approved clinical trials and to those with subscriptions or pre-paid certificates.
If you are looking to purchase SHUTi for your individual use or a clinician referred you to SHUTi and gave you a clinician code for a discount, this program is not available for consumer purchase as of October 12, 2018. We apologize for any inconvenience this may cause.
However, if you would like to register to be part of an upcoming clinical trial using CBT for insomnia, please click the interest button below (3rd column).
SHUTi is only available to residents/citizens of the USA, Canada, Australia, and New Zealand.
I'm part of an approved Clinical Trial.
I have a pre-paid and pre-approved certificate or code with which to register for a subscription to SHUTi.
I would like to receive information on being part of an upcoming clinical trial using CBT for Insomnia.
If you are 55 years of age or older and are interested in participating in a trial by the University of Virginia and funded by the National Institutes of Health, click this button to learn more!


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New! FoodID's Kevin Lo in Science Magazine – "Raised without Antibiotics" Label Claims Lack Integrity
Are factory farms adding to the risk of deadly epidemics?
Farming April 2, 2020
Viveca Morris, executive director of the Law, Ethics & Animals Program at Yale Law School, argues that diseases like Covid-19 are a consequence of the way we are treating animals and their habitats. This includes factory farms where animals live in conditions that are "hotbeds for viral and bacterial pathogens". The same animals are fed medically important antibiotics creating the conditions for antibiotic resistant infections to develop. This put people at great risk of deadly viral epidemics. Preventing further outbreaks requires a "radical changes to business as usual".
"We pack most of the world's livestock animals, for all or part of their lives, into crammed living conditions that are hotbeds for viral and bacterial pathogens, and then we lace their feed with the world's most medically important antibiotics, creating perfect conditions for antibiotic-resistant pathogens to develop. The public pays the price in the form of drug-resistant UTI and MRSA infections… and increased risk of deadly viral epidemics…"
Are you passionate about food safety? Want to keep up to date on meat testing and the use of antibiotics in livestock production? Sign-up to receive notifications for articles we've been reading and company updates on our journey to build a future where everyone knows what's in their food.
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text:
化学工程与生物工程学院英文网
ZJU
Leadship
Finanical Aid
Labs/Centers
A recombinant vaccine against COVID-19 developed by alumni Wei Chen approved for clinical trials
Publisher:钱礼光Time:2021-04-06View:65
Since arriving in Wuhan, China, the team led by Wei Chen, a member of Chinese Academy of Engineering, the College of Chemical and Biological Engineering's alumni of 1988, has focused on emergency scientific research in vaccine development. On March 16, a recombinant vaccine against COVID-19 developed by Wei Chen's research group is approved for clinical trials.
Since their arrival in Wuhan in January 26, Wei Chen has combined with local leading enterprises, based on the experience of successful research and development of Ebola Vaccine, to launch the research on pharmacy, pharmacodynamics, pharmacology and toxicology of New Coronavirus vaccine against time and time. It has completed the design of new crown vaccine, the construction of recombinant virus species and the production of GMP,and the safety, effectiveness evaluation and quality review of vaccine of the third party. Last night, the new crown vaccine developed by academician Chen Wei's team passed the clinical research registration review and was approved for clinical trial.
Wei Chen said "In accordance with international norms and domestic laws and regulations, the vaccine has been prepared for mass production with safety, effective and controllable quality." in an exclusive interview with CCTV.
Add:38 Zhe-da Road, Hangzhou, Zhejiang Province, P.R. China
E-mail:zjuche@zju.edu.cn
Copyright © 2020 College of Chemical and Biological Engineering, Zhejiang University


Like a primeval volcanic eruption frozen in time, Glacier spectacularly freezes logs of burnt timber in Crystalline Acrylic. The ice cold smooth appearance contrasts with the charred remains of the rugged timber, like mixing fire and ice.
The dining table features four beams of timber encased in acrylic, set atop two large timbers also in acrylic. The spectacular bubbling finish is uniquely different on each piece. Relaxed and casual dining, perfect for storytelling around the table.
Special Note: Each piece is unique and made individually, therefore patterns and extent of bubbles within the acrylic may vary.


RCW 65.12.300: Indexes and files—Forms.
The registrar of titles, under the direction of the court, shall make and keep indexes of all duplication and of all certified copies and decrees of registration and certificates of titles, and shall also index and file in classified order all papers and instruments filed in his or her office relating to applications and to registered titles. The registrar shall also, under the direction of the court, prepare and keep forms of indexes and entry books. The court shall prepare and adopt convenient forms of certificates of titles, and also general forms of memorials or notations to be used by the registrars of titles in registering the common forms of conveyance and other instruments to express briefly their effect.


We provide leading experts, with domestic and international experience and deep technical knowledge, who are able to work independently and take initiative and propose effective technical and financial solutions.
VNTower is professionally capable of project management and construction management in accordance with international standards. We build work procedures based on ISO 9001-2008 standards and the application of modern information technology.


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Home›Trustee›CPS Energy accepts nominations for a new board of directors
CPS Energy accepts nominations for a new board of directors
Applications are now available to serve the northwest side of CPS Energy's service area.
SAN ANTONIO – CPS Energy says it has started looking for a new board. The five-member board of directors will work together to oversee the utility's electricity and natural gas systems strategies and policies, their website says.
"Each member of the Board of Directors strives to support the company's customers who reside within its official 1,500 mile service area. This area covers Bexar County and parts of seven surrounding counties. To achieve better geographic coverage and clarity, the board selection process is aligned on four quadrants. in Bexar County, "explains CPS Energy.
Their website describes the following for their application process:
In the search for a new trustee, the person will be selected in quadrant 1. See the area highlighted in blue on the map. Director Edward Kelley currently resides in Quadrant 1. His last term as director will end on January 31, 2022.
Each of the four directors can serve two five-year terms. In addition, the fifth member of Council is the Mayor of San Antonio, who is an ex-officio member. This is important because the City of San Antonio owns CPS Energy.
Aligned with the geographic area of Quadrant 1, San Antonio City Council Districts 7 and 8, and parts of Districts 1, 6 and 9. Residents can find out which CPS Energy quadrant they reside in by entering their address on the website by CPS Energy.
Council members must be US citizens. With the exception of the mayor, each trustee receives an annual remuneration of $ 2,000. Regular meetings are typically held on the last Monday of each month at 1 p.m. in the company's boardroom on the first floor of its corporate headquarters, located at 500 McCullough Ave, San Antonio, TX 78215.
Additional time requirements for Trustees include special board meetings, quarterly committee meetings and, as required, group and individual working sessions as well as public consultation sessions and various other events..
You can apply for this position on the Board here. You can also visit the head office of CPS Energy. You can also call (210) 353-3212 or email [email protected]
The deadline for submitting applications will be Wednesday, August 31 at 5 p.m.
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This town offers interest-free loans of up to $ 40,000 for first-time homebuyers
Airtel prepays Rs 15,519 crore at DoT to clear all deferred liabilities for 2014 spectrum: The Tribune India
What week: who do you represent? PUSD reflects on regional elections | New


text:
Karen Hawkins ist der Name folgender Personen

* Karen Hawkins (Leichtathletin) (* 1957), US-amerikanische Sprinterin
 Karen Hawkins (Schriftstellerin), US-amerikanische Schriftstellerin

redpajama_set_name: RedPajamaWikipedia


Here | psKINETIC - Transformation & automation. Intelligently Delivered.
Here (formerly Brighton and Hove Integrated Care Service – BICS) is an NHS organisation that improves patient experiences by working innovatively and collaboratively with GPs, clinicians and other health partners. The organisation has pioneered Referral Management based on peer review and education. This work has led to better care for patients and delivered substantial cost savings.
The team from Here has won a number of awards, including Excellence in Healthcare Business Intelligence 2013 hosted by the journal ehealth Insider. The judges found Here's IT solutions to be the winner in helping staff make better decisions for patients.


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Portland Arts & Lectures Seating
View Order / Checkout
← Back to full calendar
Pop-up: Steph Cha
When:November 9, 2019 @ 11:30 am - 11:45 am
Steph Cha pops-up in the Portland Art Museum galleries with her novel, Your House Will Pay.
Cha is paired with the artwork Stars and Bars by Hank Willis Thomas; found in the Hank Willis Thomas special exhibit, on the 1st floor of the Portland Art Museum. Please reference the Portland Art Museum Map to find this location.
A powerful and taut novel about racial tensions in Los Angeles, following two families—one Korean-American, one African-American—grappling with the effects of a decades-old crime
In the wake of the police shooting of a black teenager, Los Angeles is as tense as it's been since the unrest of the early 1990s. But Grace Park and Shawn Matthews have their own problems. Grace is sheltered and largely oblivious, living in the Valley with her Korean-immigrant parents, working long hours at the family pharmacy. She's distraught that her sister hasn't spoken to their mother in two years, for reasons beyond Grace's understanding. Shawn has already had enough of politics and protest after an act of violence shattered his family years ago. He just wants to be left alone to enjoy his quiet life in Palmdale.
But when another shocking crime hits LA, both the Park and Matthews families are forced to face down their history while navigating the tumult of a city on the brink of more violence.
← Pop-up: Graham Annable
Pop-up: Cat Winters →


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Steven J. Wangsness says
Life itself is full of little digressions. Stripping away the "unessential" leaves half the story untold. At least for some kinds of books. In a mystery, such as I wrote, or some other genre sort of fiction, I'd agree about stripping away the useless junk. But if all books become commodities, I can't help thinking we're losing something important.
Terry Odell says
My current WIP has my crit partners asking whether I'm digressing too much from the mystery plot. However, I'm a reader who enjoys watching characters develop, and learning new things along the way, so I hope there are others out there.
I do try to make sure that my digressions still touch upon the forward progress of the story.
And, interestingly, I've been reading a lot of blog posts lately about adding depth to stories by NOT sticking too tightly to the main plot points.
I don't have anything to add other than to completely agree with you. I thought about listing everything you said that I thought was spot-on, but I'd basically be summarizing it, which seems redundant. 🙂
Chris Lunda says
The earth around J. D. Salinger's grave is trembling…
Emily Carpenter says
Oh no, Moby Dick is your favorite? And I was liking you sooo much…..
Kidding. It nearly killed me in high school and I've never had the guts to revisit it. Sorta like that mean girl I hope I never run into again.
Annalise Green says
I think that "stripping away the unnecessary stuff" is like most writing advice – a good rule of thumb but when applied mechanically and rigorously without insight to the why, it can be abused. People's definitions of unnecessary stuff can vary. People's definitions of digressions can vary.
Carmen Webster Buxton says
It always seemed to me that books changed as the world changed. Readers of Victorian novels who read for entertainment WANTED long passages about the setting or the characters' feelings because they had no movies, TV, or Internet as alternate distractions. They expected a book to take days to read. If they read MOBY DICK, it was partly because they wanted to know what life was like on a whaling ship. Modern books are (for the most part) written for modern times and compete with video games and HBO. That's not to say we can't still enjoy older books, but it does mean we will notice the difference when we read them.
Doug says
To bring together a couple of points made in the article: even in its time, Moby-Dick was scorned for its digressions.
According to Wikipedia (fount of all knowledge on the Web), Melville "was shocked and bewildered at the scathing reviews [Moby-Dick] received. Instead of bringing him the literary acclaim which he sought, this master-work started a slide toward literary obscurity in his lifetime."
Wikipedia cites one of the reviews, "The idea of a connected and collected story has obviously visited and abandoned its writer again and again in the course of composition."
Actually…in reality….Wikipedia is a corporate evil. And takes off very important truths from its site when they don't want that power getting in the hands of the masses. I wont even choose to click on it anymore since I know now what their up to.
Michael A. Lewis says
Self-publishing is re-opening the door to unique self-expression.
With corporate publishing, content and style is controlled by those who seek the greatest profit through quantity rather than quality. Get it in, get it out on the shelves, move on to the next. Keep those titles moving, slap a new cover on a proven title, get it back on the shelves.
Now the author is in control, as much as the author desires. Content and style are a function of the author's vision. "Readability" depends on the audience, which need not be large for the author to be "successful." Success is measured in the writer/reader contact, not advances and royalties.
Writers can be freed once again from the necessity to become authors; we can write what we want, in a length and complexity appropriate to the story and the storyteller, and still reach an appreciative audience.
The medium is irrelevant; it's the words, sentences and paragraphs that are paramount.
Digressions tend to make people think..and some readers don't want to do that. They want to be entertained. 'Don't make me think, just serve it up!' It's one of the reasons that literary writing only appeals to a certain type of reader. I love Dickens stories, but find his run-on sentences ponderous at times.
I'm reading 'Tender is the Night' by F.S. Fitzgerald and it does digress but to useful purpose. Not all classics are enjoyable, but MANY written in the 20th century have staying power.
I'm not sure with our flooded book market (of trad, indie and selfpubs) if that can be said of most current books.
My faves – scifi and mystery also have their forms of digressions, but much less so in the new books. With digression you can get layers, without it, you skim on the top.
I say yes, we are stripping our modern books, and not always to good purpose.
Ellen Etc says
There's so much content coming down the pipestream, readers need "curators" of one kind or another. Editors, publishers, and bookstores used to hold that role. The question is, who are the curators that people turn to now for advice on what to read? How does one discover a new writer that one enjoys?
The evil downside of self-publishing is that so many people sink so much money into self-publishing outfits. Many of those companies make their profits from the unedited writer's naive dreams, misleading them about the effectiveness of such package deals as "an email campaign" that promises to send 5,000 marketing emails. I know one writer who sold exactly 2 copies of his book from the vanity press's 5,000 emails.
The editor/publisher/bookstore route used to assure a minimum competence and saleability for a book. When people insist on "creative control," too often it means "my self-indulgence."
Interesting post. I think traditional publishing is so focused on being cost-effective that the word count seems VERY important, and that means that many digressions are axed. I think you are allowed to digress if you are an established, best-selling author, but otherwise–no.
You raise a good point that self-publishing may allow people more leeway. Done well, digressions can make a book richer. Obviously, done badly, they can make it a hot mess.
Matthew J. Beier says
When writing books now, this is at the forefront of my mind. If I'm not addicted to my story on every page, I feel as if it isn't good enough. I end up slaving away to make it both comfortably paced (i.e. fast, in this day and age) and true to my vision, which can be extremely frustrating. Just last week, I had one of those "doubting my entire future in publishing" nights, because my current project just wasn't grabbing me the way I wanted it to. Much of it ended up having to do with cutting some unnecessary stuff, and this week, the book looks better. So, in this case, cutting was a blessing.
Still, I don't think this is a black and white issue. It depends on the writing, the story, the characters, and the overall vision. Amazing writers can make every word feel necessary. Thus, While I can love short and sweet books like The Hunger Games, some of my favorite reading experiences have been on the longer side: Many books by Stephen King, Atlas Shrugged, Harry Potter, The Poisonwood Bible, The Time Traveler's Wife, The Girl With The Dragon Tattoo, etc.
Like Carmen said above, books change as the world changes. It will be interesting to observe the progression, especially now that playing fields have evened out a bit!
Nathan, sometimes your blog is just what I need to make me feel better about the state of things. Thanks.
"Digression is the soul of wit." Ray Bradbury
Alexa O says
I love this post, and I think about this question a lot.
Books that are ONLY plot are sadly lacking. To further your food metaphor, they're like icing without cake–the icing may be your favorite part, but without the cake, it's just going to leave you feeling sick.
On the other hand, self-indulgent diversions simply aren't a benefit to fiction.
Maybe the trick is that the "diversions" have to not really be diversions at all. True character-building and world-building are essential to a plot. A reader has to know a character in order to care that he might die, or to believe that he would dive off a bridge to avoid the police and that he's a strong enough swimmer to survive. Such elements can be introduced through darling diversions. I think.
Either that, or a writer has to be so damn good that readers fall in love with the diversions.
daniel t. radke says
I recently waded into the self-publishing pool, so this has been on my mind a lot lately.
I'm against completely eliminating all non-plot-essential items. I think it takes realism out of the work, and it can make the story formulaic.
For instance, if you see a romantic comedy at the theater, not only do you know that male character will do something heroic at the end to win the female's heart, depending on what happens in the first twenty minutes, you might even be able to guess the fashion in which he'll do it (if the male lead has cold feet about marriage and he's self absorbed, he'll sacrifice a beloved part of himself, like his job, and propose marriage).
I agree that if you show a gun then it needs to be shot, but what if you show ten guns? Do they all need to be fired by plot's end?
Huntress says
In my distant past (youth), I read Tom Jones, loved it, and thought it was the best book ever.
But now, when I started re-reading it, I lost interest after the first five pages. Impatience and the age of the sound bite took its toll.
SLC says
I love the part where you take down Dickens (who got paid by the word – and it shows) and then laud Melville. While a stripped-down Moby Dick might well suit audiences better – after all, the nonessential stuff gets scrapped in every film/tv version – the book would lack a certain something without those extra parts, and not just heft.
Kathryn Rose says
It's interesting to see what grabs you about Moby Dick because it's the exact same thing that turned me off that book: I loved the story, but the extra prose felt like a text book to me (I'm not terribly interested in how to properly tie a knot or the science of catching a whale). Art is subjective, which is a great thing. As for whether stripping away the unessential is good, I remember reading one author (Vonnegut? Can't remember) who argued that everything we write should reveal character or further the plot. I think there's some truth to that.
janesadek says
I'm a fan of old school. Life is not texting. It's the "digressions" that make you love the characters and get caught up in the world. Just being carried along with a bunch of characters I barely know in a wild ride to "the end" is unsatisfying to me. I keep reading what supposed to the latest and greatest, but I'm left feeling like someone who was only invited to the wedding, while everyone else has been to the rehearsal dinner and will attend the reception.
Andrew Leon says
I love Moby Dick. It's the only book I've ever taken the time to sit down with and mark up. I mean, I grew up believing not to mark up books, but I decided that I was going to do that with Moby Dick and highlighted and made notes and all kinds of things.
I don't think it's an improvement that people don't write that way anymore. It's different, but it's not an improvement. Per se.
Mr. D says
Imo, digressions are cool if they're well written and entertaining. Even better if they're very well written and very entertaining.
Backfence says
I like a little meat in a story. A book shouldn't be judged by word count, but whether each word COUNTS!
Liam, Head Phil says
I dearly hope digressions become more commonplace. At least, I hope there are more important scenes disguised as digressions. A conversation in which an idea is planted in a character's head could be viewed as irrelevant, though that idea sparks one of the most important plot twists in the story. In the quest to destroy the irrelevant, some writers have instead gone to the bare minimum: when they don't have enough information to work with, they just reference a scene that wasn't part of the book. That sort of thing gets irksome. "Suddenly it all became clear to Bob. Two years ago, when he had been driving home, a stray cat with ears and whiskers shaped respectively like cancerous rodents and low-budget fireworks had appeared in front of his car– then abruptly disappeared into thin air. And Dr. Evil was standing right where the cat had vanished!" When the author has to say "Oh, and that works because…" it's annoying. The reader should have all of the information already, even if it means digressing slightly.
Books, analogous with film, have different audiences for different experiences. There is resurgence in the "slow burn" film category that was the hallmark of '60s and '70s. The same can be said of new novels today, where just getting into the plot takes a little effort and the plot itself may be fairly elusive.
This slow style leaves much more room for imagination and for picking out the details that make the experience interesting and worthwhile. A few extra pages of character study, a few more pages to paint the scene, a few pages of author musings that add thought-provoking nuance to the story. Using the film example, you could cut both 2001 and the Godfather down to less than 90 minutes and keep the pace. However, think of all you would lose, the texture, the emotion, the buildup.
Mirka Breen says
You could be called No Nostalgia Nathan. Good for you. 'Life isn't what it used to be and never was' is a good motto, because we can't go back.
But I'm not quite there with you. The efficient writing/story telling, while a must in commercial writing, isn't that absolute when it comes to the truly literary. Think of Jeffrey Eugenides' books, or even the HP volumes. Riveting but not every point stripped to bare essentials.
Leisurely prose was perfect for an age of fewer discretionary distractions. We gained, but we have lost also.
Elisa Nuckle says
I think some meandering isn't a bad thing, but nowadays that character development looks a little different. It seems like characters need to be developed in the motion of the plot, that readers want both at once without slowing the pace. At least that's what I've noticed in fantasy and science fiction, though fantasy does tend to meander more than other genres. Science fiction can, too.
Thomas Pluck says
I disagree. I feel like most of my favorite books were written almost twenty years ago, and many of today's feel rushed and empty.
There have been some very spare masterpieces like James Sallis's DRIVE, but I'm loving James Lee Burke's 450+ page Feast Day of Fools so far. He'd have a lot of fun shopping that around as a new writer today.
Dearth of Reason says
What you say also applies to music. Our Mozart-level symphonies are sneaking past us today as scores for films. Listen closely to the music for Dances With Wolves, Lord of the Rings, and Harry Potter and you will see what I mean. Today our audiences value smaller bites, but even in wider varieties they taste no less sweet.
And, as a teardrop of hope to all, there are many writers today who are still telling the whole story to delight their readers. George RR Martin, Neal Stephenson, and Rowling (the final four HP books) are good examples. The HP movies missed out on a lot of depth because many funny and poignant subplots could not be condensed onto the screen.
s.r.sheldon says
The notion that people read authors like Dickens and Proust as a kind of vegetable that's good for you is so, i don't know, tiresome, I guess. Maybe just ignorant. People who read Dickens and Proust's books love them, they experience overwhelming pleasure reading them (with their huge works they can wallow in pleasure), they read them slowly for each word and image (and the insanity of their visions. Who is more insane than Dickens and Proust?).
(And this notion is particularly hysterical coming from a writer's blog, from people ostensibly interested in character, and yet without the imagination to imagine someone who loves to read something dense, and crazy, and wildly excessive. Is it that hard? You probably meet people like that every day.) (Hey, how about poetry? Do we have a condescending theory about all those nutty people who love poetry? Often there is no plot or characters. Poetry must really, really, really suck! I mean, can't we try to understand the other people we share this planet with even a little bit?)
I happen to love the excess of Dickens and Proust's visions. Their worlds teem uncontrollably with people, places, feeling, stories, ideas, smells, visions, energy, food, humor, meaning, and on and on. In other words: Life. And when I put the book down, I see clearer this world in all it's teeming craziness. My vision opens up. (And if you don't like excess, if you want to strip everything down to only what's absolutely essential, why do you read at all? Reading isn't 'essential', millions of people do fine without it. You can live on bread and water. We can 'live' without Love or music or Joy or Meaning. Edit everything unessential out!)
(By the way, I'm sure there's some people who see Proust's digressions and false-starts not as bad writing but as the exotic architecture of a building to get lost in. Or some crazy exotic garden. To some people 'mysteries' that are immediately solved aren't interesting at all, they are boring. Yes, some people prefer to preserve the mystery.)
Ruth Harris says
What I miss in much new fiction—and perhaps what you call digression—is the social/cultural/historical context in which the characters act & react. I don't mean large chunks of "background" bulldozed in but people, after all, reflect their time & place.
The 60's were different from the 80's. The Lehman collapse era was different from the internet bubble years. Good, readable, entertaining fiction should include the mood, texture and tenor of time & place in characters' lives. Just steering characters thru the "plot" isn't really very interesting. At least not to me.
Heather Hawke says
I too have mixed feelings. Those digressions often contain the truly individual and creative parts. I am reminded of a book published recently, a real page-turner – I stayed up 'till 3 AM to finish. Must be a great book, right? Now a couple of months later, I can't for the life of me remember much about it.
s.r.-
I never said I don't love Dickens and Proust. Ignorant is a strong word to throw around.
Sarah Stegall says
"…books that are quirky and strange and digressive will also be out there too."
Received opinion in literary circles (aka Academia) is that editor Maxwell Perkins created a masterpiece out of a mass of rambling prose that was Thomas Wolfe's original manuscript for "Look Homeward, Angel". A few years ago, some scholars pieced together Wolfe's original submission, and re-issued it as "O Lost" (Wolfe's original title). As it turns out, "O Lost" is a helluva lot better read than "Look Homeward", which is itself widely hailed as superb. So what does that tell us? That traditional editing, especially during those "golden years", was actually focused on weeding out all that extra prose, those digressions, those distractions. Yet the very appeal of Wolfe's writing is that flood of poetry that is his narrative style. Plot? Who needs a plot when we can wallow in the fabulous description, the stream-of-consciousness narration, the evocative characterization? What Perkins did was turn an original and creative work into a standard work that matched other works in the field. Maybe that was good for sales, but it wasn't very good for Wolfe, his reputation, or the generations to come who will possibly be confused by his very different works.
Wolfe is often wild, out of control, drowned in "excess". He's an acquired taste, but once acquired, an unforgettable, unshakeable one. And how much would we have lost, if he had been persuaded to strip everything down to "plot"?
There are many writers out there with many visions, and readers who will now, thanks to the Internet, be able to find that writer who speaks to them. And may not give a damn about plot.
I don't know that Perkins was necessarily wrong though either. It's easy to look back on choices like that and infer that Wolfe would have been better off without Perkins' meddling, but who's to say Wolfe would have enjoyed the reputation he has today if he were left to his own devices?
We grant writers a whole lot of leeway once they've established a reputation, and we're more patient with them. Even if we might see the greater genius in the original work, we're viewing it through the prism of years distant where we will afford Wolfe greater latitude because of his reputation.
This is partially why just about every literary writer out there started off with a relatively mainstream work stylistically to establish themselves before branching off into uncharted waters. See also this post: https://nbrans.wpengine.com/2010/08/writers-authority-and-keith-hernandez.html
I agree, sorry. I guess I was reading, and responding to, your post in the light of an overall attitude I always get, which drives me crazy! That I'm really reading them out of serious, dour, academic, no-fun motivations. Like I like taking bitter medicine or something! I just want people to understand (sniff)! I'll be more careful next time!
s.r.
No worries, I agree that people should definitely still read those works and there's so much to love in them. I find it difficult to do so with my Internet-molded brain, but I still really enjoy them. I hope people will continue to challenge themselves.
I keep hearing how self-publishing will open up the world to the quirky and strange and digressive. But I see many (not all) self-publishers urging each other to just write fast, write a lot, get it out there. The self-published books that are doing well seem to be the same kinds of books that do well in the Big 6 world: action and romance.
It's true that a self-publisher can put out a quirky, digressive work now with a lower upfront investment of money. On the other hand, it might not get even the championing that today's traditionally-published literary fiction gets from places like NPR, book clubs, etc., and it might not find many readers.
I can't help thinking that just as there is no Golden Era in the past, there isn't one in the future either. Every era has its pluses and minuses. A high-concept page-turner will always have a bigger audience than a thoughtful, slower-paced story, but when the latter catches on it might be more long-lasting. In any era.
Some classics of the past hold up remarkably well (Jane Austen springs to mind). On the other hand, I find D.H. Lawrence unreadable now.
Naja Tau says
Nathan! I am soooo happy/thankful that someone is also thinking about these things.
Please forgive my snobbery- I recognize it all too well, but as a fellow Moby Dick fan who can't get enough of Ahab and was willing to hear all kinds of information about why a whale needs to be classified scientifically as a fish in order to get to Ahab and Queequeg, I have been sooooo miserably disappointed with most contemporary bestsellers. Ugh!!!
Although it's so easy to digest books like Hunger Games, Harry Potter, Twilight, Dexter, etc… and those are all books I love obsessively (Harry Potter 2 is in my backpack right now) those bestsellers are all, literally, on a 12-year-old reading level.
On my SAT's, I was in the 97th percentile. That upsets me very much- because I am a total airhead. I did not even remember what a percentile is, so I had to Google the definition. That tells me that most people can't understand and enjoy serious literature and absorb complex ideas in writing.
Reading a book like Hunger Games is like mind-popcorn. Fun! I loved the book. It was great. Very inventive. But man. I feel so hollow and shallow by the end of it.
Give me Ahab. I'm so sick of speedy plots. I want to pick up a book and get to know someone, like Mrs. Dalloway or Blanche DuBois. When I read, I want to feel spiritually renewed- feel intimate. I want to feel like I had a conversation with an adult. You can do that with a spare writer like Hemingway, but dang… I'm getting so disappointed so consistently with the new books I've been picking up. And I'm also super disappointed with the lack of deep conversation about contemporary literature.
*gets off soap box*
Man. This post's turned me into one of those internet ranters. *closes ears in oven door like Dobby the House Elf, in order to punish herself*
neal says
This is a really interesting idea, the idea of "digression" coming back with self-publishing.
But, while I also cite Moby-Dick as one of my all-time favorite books (and I use it as a benchmark against which I rate other books on my blog), we should also remember that IT barely got published. Doug touches on this. It's not like people recognized Melville for the genius he was…in fact, American critics thought Moby-Dick was one of the most self-indulgent, uninteresting pieces of crap they'd ever read. It only got published because Melville had written a few other popular conventional novels first.
It's also worth noting that a lot of Melville's other stories, many of them short stories, (Benito Cereno, Bartleby the Scrivener, Billy Budd) were very different structurally than Moby-Dick. Melville did what he did in Moby-Dick because it fit a specific effort at a specific moment in literary life. But he was both fighting the publishing industry with the effort, and he was also doing something out of the ordinary for his own oeuvre.
I hardly think Rowling, Stephenson, or Martin compare with Melville. But I'd suggest that Salman Rushdie writes with a richness and breadth that verges on Melville's discursiveness. I've not read Wallace, but I'd believe that. Perhaps Pynchon as well. Susanna Clarke's Jonathan Strange is nowhere near as insightful as the rest of these, but I think it offers and interesting level of digressiveness (a word?) that people seemed to really latch on to.
It strikes me that there are still novels that try to do what Moby-Dick did…it's just that you'd rarely see that sort of stuff on the best-sellers lists.
Caleb says
"Books won't have to be readable in order to find their audience."
That, my friends, is the greatest Nathan quote ever (but only because I've decided to take it wildly out of context in my mind.)
Robert Treskillard says
One advantage of the internet is that you can post that "digressive, cut material" as freebies for your fans, without costing a dime. Sure, it might not be edited fully, but I would think the fans would like it anyway.
My first novel, which is coming out next February has a lot of material like that (I cut 50,000 words before finding a publisher), and I'll be giving the best parts away on my website.
As a screenwriting student, I got so used to stripping everything down that Stephen King's "Salem's Lot" was a delicious shock to the system. Digressions galore!
Susan Kaye Quinn says
I can't possibly cheer this post loudly enough via blog comment! Have you read Midnight's Tale (the literary short story from the POV of a goat, which is utterly charming and currently at #704 on Paid Kindle)? It's a fantastic example of literature I probably would never have heard up, much less read, prior to self-publishing enabling it's worldwide distribution at the touch of a button.
Taylor Napolsky says
There is too much general emphasis on stripping down novels and yet modern audiences seem to value all types of books.
Plenty of aforementioned authors are more prolix and many popular authors are also sparse.
50 Shades is a perfect example of cut-cut-cut. Like two pages into that book you are in an office with Christian.
I think audiences have a wide variety of tastes, and authors of all styles get more-or-less represented, though the NYT bestsellers list does tend to favor the plot-oriented stuff.
But Stieg sure gave us an example of how long-winded books can be hits, didn't he? With his grocery lists of items the characters bought.
I suppose the real key is to be excellent at the style you choose. Get good at what you do, and I'm a firm believer that you will get your work out there.
P J O'Leary says
My biggest argument against this is Terry Pratchett and his Discworld series. Those books are filled with pointless asides, anecdotes and digressions on his imaginary world and it's history. But those are often some of the funniest parts of the books. And he's able to do them without detracting from the main story.
Of course, Sir Terry is a great writer and even he has improved as the series has progressed. So I'd avoid the N=1 fallacy, and say it is possible, but not easy. So use them sparingly and only where they actually improve the book. Because there are plenty of examples of it failing.
Susanna Calkins says
Great post! I've thought about a lot of these things too. Not so much about digression–but I think I see a similar quality in those oft-repeated admonitions not to use adverbs, or words for 'said' other than said. But the arbiter of 'good' writing seems to be changing as the publishing community continues to change.
I went from writing super sparse to adding more details. These things enrich the reading experience. Books that are too slimmed down read almost like screen plays.
Thanks for this post! I love how you weighed both sides of the conflict. To me, I think there's room for both. I like to read my intense, deep, dark reads and break them up with quick-paced, easily-digestible fiction. If I read too much of one or the other, I get bored and irritated. I'm not a person who enjoys reading series straight through or one book after another by the same author. At the moment I'm reading four books (well three, since I finished one yesterday): A Lovely, Indecent Departure by Steven Gilbert (stripped-down, contemplative debut of a child custody dispute), The Sense of an Ending by Julian Barnes (which won the 2011 Man Booker Prize), The Night Eternal by Guillero del Toro and Chuck Hogan (the third and final in a vampire thriller trilogy), and Of Moths and Butterflies by V.R. Christensen (a Jane Austen-esque historical romance). So really, I love to read all over the map. It keeps me on my toes, keeps me learning from everywhere and everything.