Construction of new ISI-free pulses using a linear combination of two polynomial pulses

Abstract

This paper deals with the design of inter-smybol interference free pulses having reduced sensitivity to time synchronization errors. A new improved Nyquist filter is proposed and investigated. Its impulse response is obtained from a linear combination of new Nyquist pulses with different asymptotical decay rates. Error probability results show that the proposed filter outperforms other existing filters. The proposed scenarios aimed at demonstrating the feasibility of the concept.

Sinc Exponential ISI-Free Pulse with Better Performance

“…The obtained results are tabulated in Table II. Note that in general the sub-optimum SEP has the smallest error rates, for different roll-off factors and timing offsets, compared to the RC, the pulses proposed in [8] (r(t), q(t), and v(t)), the PFE [11], as well as the IPLCP. This behaviour is consistent with the wider eye opening of the SEP.…”

“…The trend is the same for other roll-off factors and values of β and γ. Consequently, robustness against ISI, a larger eye opening, and smaller PAPR are expected by implementing the SEP in single carrier systems [9], [13], [14]. The prior implies that the undesired effects of jitter will be diminished, and the suboptimum SEP will be less sensitive to timing-sampling errors, resulting in a lower BER [1], [2], [7], [8].…”

“…In the expression g k = p (kT + η), p(t) is the ISI-free pulse evaluated. The parameters used to make the truncated Fourier series converge comply with the parameters used in previously reported manuscripts [3], [4], [8], [11]. These parameters are given in Table I.…”

“…The BER in the presence of time-sampling errors was determined for the sub-optimum SEP, RC, as well as other recently proposed pulses. The families of Nyquist-I pulses proposed in [8] (r(t), q(t), and v(t)) are one of the newest families of pulses found in the literature. Further, the recently proposed PFE [11] is also evaluated, as well as the improved parametric linear combination pulse (IPLCP) [3], and the sinc parametric linear combination pulse (SPLCP) [4].…”

“…Further, the proposed pulses in [1] subsume previous ISI-free pulses as special cases, such as the RC pulse, among others. In [7], a family of ISI-free polynomial pulses is derived, whereas in [8] new families of Nyquist-I pulses are proposed using a linear combination of two polynomial pulses. Other ISIfree linear combination pulses have also been proposed in [2] and [9].…”