Numerous systems for digital communications are known and transmit digital data using a-variety of techniques. The particular technique used by a system determines how data is encoded in a transmitted signal and how the data may be decoded by a receiver of the transmitted signal. Regardless of the particular technique used, it is generally necessary for the receiver of the transmitted signal to reconstruct a clock signal corresponding to a clock signal by which the information was sent. Reconstructing the correct clock is sometimes complicated by the fact that the information in the transmitted signal may be valid at only one instant in the clock cycle.
In general, digital communications systems send information in units called symbols. For each symbol, a band-limited waveform is transmitted. These waveforms are transmitted at a certain rate (the symbol rate) by the system. However, because the waveforms are band-limited, they typically have a duration of much longer than one symbol period. Thus, at any particular time, a signal sent by the system is the sum of a large number of these waveforms. However, as long as the transmitted waveforms have periodic zero crossings at the symbol rate, it is still possible to decode the symbols. Decoding of the symbols becomes a matter of determining when to sample the transmitted signal so that the transmitted signal includes only the information from one symbol, or, at the least, so that the interference from the other symbols is minimized. In other words, to decode a symbol, a receiver must generate a symbol clock for sampling the transmitted signal at times which minimizes interference from other symbols.
When a transmitted waveform has periodic zero crossings at the symbol rate, the transmitted signal contains the waveform of only one symbol at a particular time during a symbol period. For example, if the waveform for a symbol, s, is s*h(t), and the symbol rate is one symbol every T seconds, then the transmitted signal, x, is given by the following equation: EQU x(t)=.SIGMA.s(i)*h(t-iT) (1)
If the waveform has periodic zero crossings at the symbol rate, then h(t) is such that: EQU h(t)=0 for t=n*T (n=integer&lt;&gt;0) (2)
Then, at the times t=nT, the transmitted signal, x(t), contains only contributions from one symbol, s(n). By sampling the transmitted signal at these times, the symbols may be correctly decoded.
The problem of symbol clock recovery may be further complicated by the fact that the transmitted signal may still contain some of the carrier during decoding of the symbols. More particularly, instead of receiving the transmitted signal, x(t), the receiver may receive the signal, x(t)*exp(-jwt+p), where w and p are unknown and possibly varying.
Previous implementations of digital communications systems solve the symbol clock recovery problem in different ways. Typically, the solution involves some feature of the specific system. For example, some systems start up with, or periodically insert, known symbol patterns. Receivers for these systems "look" for the known pattern and use that information to "sync up" a local oscillator which generates the symbol clock sample times. Receivers in other systems look for particular zero crossings of the transmitted signal and generate the timing data therefrom. A disadvantage to most current systems is that their receivers depend on some characteristic of the particular communication scheme to generate a symbol clock. Hence, the receivers will not work if employed for a different communication scheme. One object of the present invention, therefore, is to provide a technique for generating a symbol clock that is compatible with a very large number of different communications systems.
In at least one digital communications system, the receiver contains a phase detector which looks at the magnitude of the real and imaginary parts of the transmitted signal at times 1/4 of a symbol period away from a symbol clock sample time. The phase detector is used to synchronize a synthesized clock signal to the symbol rate of the transmitted signal. However, since such a system does not compare the magnitude of the transmitted signal itself before and after a symbol clock sample time, its phase detector is affected by any carrier that is left in the transmitted signal and may be inaccurate. An example of such a system is the STEL-2110A chip manufactured by Stanford Telecom.
The present invention is based on principles described in the attached appendix A, a paper entitled "Clock Recovery Phase Detector". As is derived in the appendix, the expected value of the magnitude squared of the transmitted signal varies sinusoidally with a period of the sample rate. This sinusoid has a maximum at the correct sample times and a minimum 1/2 way between the correct sample times. Therefore, the correct sample times of the symbol clock can be found by locating the maximums of the squared magnitude of the transmitted signal.
In accordance with the present invention, the problem of symbol clock recovery is solved by providing a phase detector for synchronizing a symbol clock with the maximums of the squared magnitude of the transmitted signal. The phase detector compares the squared magnitude of the transmitted signal at times spaced an equal fraction of a symbol clock period away from symbol clock sample times and produces a phase error signal proportional to the difference between the magnitude squared of the transmitted signal at such times. For example, a phase detector according to the present invention may sample the transmitted signal at times one quarter and three quarters of a symbol period before a symbol clock sample time. The phase error signal generated by the phase detector may be expressed mathematically as follows: EQU phase error=.vertline.x(t-T/4).vertline..sup.2 -.vertline.x(t-3T/4)/.sup.2( 3)
where .vertline.X.vertline..sup.2 means the magnitude squared, or x times the complex conjugate of x; t is a symbol clock sample time; and T is the symbol period.
The comparison of magnitudes squared allows the phase detector to determine if the symbol clock frequency is synchronized with the symbol rate of the transmitted signal. If the magnitude squared of the transmitted signal at these times is equal, the symbol clock is synchronized. If the magnitude squared at these times differs, the symbol clock is out of phase. By connecting the phase detector in a phase-locked loop configuration with the symbol clock generator, the phase error signal can serve as a feedback signal for adjusting the frequency of the symbol clock to be synchronous with the symbol rate of the transmitted signal.
The phase detector described above has two drawbacks: (1) the gain of the phase detector is related to the level of the transmitted signal, and (2) because of the magnitude squared function, twice as many bits of precision are needed in the calculation as compared with a straight magnitude based system. Thus, to function adequately, some form of automatic gain control would be necessary to keep the level of the transmitted signal constant. However, another modification to the phase detector eliminates both these problems. The modified phase detector takes the logarithm of the magnitude of the transmitted signal at times spaced an equal fraction of a symbol period away from the sample times rather than the magnitude squared. Thus, the phase error signal may be expressed as follows: EQU phase error=log(.vertline.x(c-T/4)I)-log(.vertline.x(c-3T/4).vertline.)(4)
where the vertical bars (.vertline..vertline.) denote magnitude, and the log may be in any convenient base. The advantage of using the logarithm of the magnitude function rather than the magnitude squared function is that the phase error signal is not dependent on the gain of the transmitted signal. Also, the logarithm function decreases the number of bits of precision required in the phase detector. A further advantage to using the logarithm function instead of the magnitude squared function is that the signal to noise ratio is increased.
Additional features and advantages of the invention will be made apparent from the following description of the preferred embodiment, which proceeds with reference to the accompanying drawings.