Detection of a PSK signal transmitted through a hard-limited channel

Abstract

Abstract-This paper considers the problem of the detection of a binary phase-modulated carrier which has been transmitted along with noise through a hard-limiting repeater, corrupted by additional noise, and demodulated by cross correlation and sampling at the receiver. Three equivalent expressions are obtained for the error probability of the receiver output. Two of these expressions take the form of an infinite series involving either confluent hypergeometric functions or modified Bessel functions. A third form allows representation of the error probability in terms of Rice's le function. In the special case where the signalto-noise ratios Pi^ and p2^ at the limiter and receiver inputs are equal, the error probability is simply Pe = iexp i-pi^).Asymptotic expressions for the error probability for large and small signal-to-noise ratios are also derived. The error probability is found to be smaller than that of a linear system for all practical values of limiter and receiver input signal-to-noise ratios. The optimum repeater nonlinearity is investigated and is shown to be a limiter at such signal-to-noise ratios.

A Modified Monte-Carlo Technique for the Simulation of Satellite Communication Systems.

“…In fact, for BPSK with no ISI, the expression Q 2 (e) is seen to be identical to that derived by can be taken from some of the curves developed in [16].…”

“…QM(e) is taken as an expectation over v and, after some algebraic manipulations, is found to be very similar in form to that given in [16]. In fact, for BPSK with no ISI, the expression Q 2 (e) is seen to be identical to that derived by can be taken from some of the curves developed in [16].…”

“…In their earliest work [27] (the first to be written, although not the first to be published), Ekanayake and Taylor present what is, essentially, just an extension of the work of Jain and Blachman [16] to M-ary systems with ISI. Like Jain and Blachman, the authors assume that the transponder nonlinearity is an ideal hard-limiter.…”

“…Some use the rationale that since the uplink S/N is typically much larger than that of the downlink then the effect the uplink noise has on the probability of error is so slight as to be insignificant and can be safely ignored. Others assume that the uplink noise may be significant and compute an "equivalent" downlink noise power using some simple algorithm in a manner vaguely similar to the work of Jain and Blachman (16] or Lyons (15]. In short, the semianalytical method is comprised of the retention of the "building block" analytical models of Monte Carlo simulation, the use of several short sequences as input to replace that random or partially random signal, and the analytical treatment of the thermal noise as if it were all downlink and thus easily handled in a deterministic manner..…”

“…[ been presented by the preceding papers [14]- [16]. Obviously, the next step in the analysis of this kind of wideband system is the consideration of a more realistic type of transponder nonlinearity.…”