(2.19) per degrees of freedom (DOF), where is the noise power spectral density. According to the Nyquist sampling theory, DOF is 2W. Therefore, the channel capacity is bits per second. The C=2WR channel capacity in bits/s is given by [101]: (2.20) Consequently SE is given by: (2.21) Consequently EE is: (2.22) As a result, the SE-EE relation can be expressed as: (2.23) (2.24) From (2.24), it can be shown that decreases monotonically with R. With max =1/(ln2) as and R→0, min = 0 as [101]. The results obtained from (2.24) assume an infinite size of information block R →∞ and infinite number of DOF. In the finite case the behaviour will be different. In practice the EE bounds from the information-theoretic analysis might not be achieved in practical systems due to performance loss of capacity-approaching channel codes e.g. Turbo codes, imperfect knowledge of the CSI, the performance of the synchronization subsystem and transmission associated electronic circuit consumption [101]. When considering the circuit power EE needs to be re-defined as information bits per unit energy i.e. not just the transmitted energy, where additional circuit power, Pc, needs to be included: (2.25) The EE-SE trade-off is shown in Figure 2.10. In particular, circuit power will break the monotonic relation between SE and EE. If circuit power is considered it will turn the curve into a bell shape. Figure 2.10 EE/SE trade-off in AWGN
(2.19) per degrees of freedom (DOF), where is the noise power spectral density. According to the Nyquist sampling theory, DOF is 2W. Therefore, the channel capacity is C=2WR bits per second. The channel capacity in bits/s is given by [101]: (2.20) Consequently SE is given by: (2.21) Consequently EE is: (2.22) As a result, the SE-EE relation can be expressed as: (2.23) (2.24) From (2.24), it can be shown that decreases monotonically with R. With max =1/(ln2) as R→0, and min = 0 as R →∞ [101]. The results obtained from (2.24) assume an infinite size of information block and infinite number of DOF. In the finite case the behaviour will be different. In practice the EE bounds from the information-theoretic analysis might not be achieved in practical systems due to performance loss of capacity-approaching channel codes e.g. Turbo codes, imperfect knowledge of the CSI, the performance of the synchronization subsystem and transmission associated electronic circuit consumption [101]. When considering the circuit power EE needs to be re-defined as information bits per unit energy i.e. not just the transmitted energy, where additional circuit power, Pc, needs to be included: (2.25) The EE-SE trade-off is shown in Figure 2.10. In particular, circuit power will break the monotonic relation between SE and EE. If circuit power is considered it will turn the curve into a bell shape. Figure 2.10 EE/SE trade-off in AWGN
PhDThesisWithCorrections.docx