The effects of bandlimiting on the performance of digital communication systems

The effects of bandlimiting on the performance of various digital transmission systems corrupted by additive white Gaussian noise are analyzed using two methods, the averaging method and the series expansion method. The results from both methods agree. The performance of an ideal bandlimited NRZ (Non-Return- to-Zero) baseband transmission system is examined using correlation detection and sampling. The explicit expression for the degradation of the signal and the intersymbol interference as a function of system parameters is derived. The average, lower bounds and upper bounds of the probabilities of bit-error are computed for both detectors. It is shown that the correlation detector performs better than the sample detector for BT>0.6 and worse for BT=0.5. A Split-Phase baseband system is also analyzed following the same steps used for analyzing the NRZ system. It is shown that a Split-Phase baseband system requires less than twice as much bandwidth as the NRZ system to have the same probability of bit-error for the same value of signal- to-noise ratio using the correlation detector. An NRZ baseband system using Gaussian filters is also analyzed employing correlation detection. It is found that the system introduces more intersymbol interference and performs poorly compared to the ideal bandlimited NRZ system. The effects of bandlimiting on the performance of modulation the Phase-Shift-Keying (PSK) System, the Amplitude-Shift-Keying (ASK) System, and the Frequency-Shift-Keying (FSK) System are analyzed assuming a correlation receiver and using ideal filters as well as correlation detection. The explicit expression for the degradation of the signal and the intersymbol interference as a function of bandwidths of the filters, signal-to-noise ratio and carrier frequencies is given. It is found that the aliasing effect can be neglected if the carrier frequency is more than three times the bit rate. It is also found that PSK requires 3 db less on an average power basis than ASK. If the spacing between the two carrier tones in FSK is less than three times the bit rate, FSK shows a better performance than that of ASK. The optimum setting of the tone spacing of FSK is shown to be equal to the bit rate. However, PSK always gives the best performance. Thus for a coherent system, PSK should always be used. Finally, a tapped-delay-line (TDL) filter is introduced at the receiver of the NRZ baseband system in conjunction with the correlation detector as an intersymbol eliminator. On an average probability of bit-error basis, and using only three taps, it is demonstrated that the performance of this system is near optimum.