Analysis of the exponential linear pulse in baseband digital communication systems

In digital communication systems the use of filters that fulfill the first Nyquist criterion (Nyquist-I), guarantees that a sequence of pulses will not be affected by inter-symbol interference (ISI) if the receiver samples signals at optimum and uniformly spaced instants. In this manuscript the Nyquist-I pulse, called exponential linear pulse (ELP), is evaluated in the time and frequency domain using different evaluation tools and compared with other existing pulses. The eye diagram is simulated in presence of time sampling errors and the approximated average bit error rate (BER) is computed considering the ideal and truncated version of the pulses. Finally, the spectral energy distribution and spectral regrowth of the pulses are presented for comparison purposes. Numerical results show that the ELP outperforms other existing pulses in terms of the eye diagram opening and BER, evaluated for various symbol timing errors and roll-off factors. However, the good performance of the ELP in the time domain is at the expenses of introduction of out-of band radiation compared to the traditional Raised Cosine pulse; therefore, a trade-off between BER and out-of-band radiation exists.