Error rate performance of narrowband multilevel CPFSK signals

Abstract

The paper presents a relatively simple method for analysing the effect of IF filtering on the performance of multilevel FM signals. Using this method, the error rate performance of narrowband FM signals is analysed for three different detection techniques, namely limiter-discriminator detection, differential detection and coherent detection followed by differential decoding. The symbol error probabilities are computed for a Gaussian IF filter and a second-order Butterworth IF filter. It is shown that coherent detection and differential decoding yields better performance than limiter-discriminator detection and differential detection, whereas two noncoherent detectors yield approximately identical performance. 1 Introduction Among many recent papers which investigated the performance of narrowband digital FM signals [1-6], the most important, perhaps, is Pawula's work [2] on limiter-discriminator (LD) detection of narrowband binary FM signals. An observation originally made by Cartier [1] that only the intersymbol interference (ISI) caused by bits adjacent to the bit being detected is significant, when the time-bandwidth product (BT) of the IF filter is restricted to a certain range, has been extended by Pawula for simplifying the analysis of binary FM signals.Although his analysis was intended for LD detection, it has later been shown to be easily amenable for determining the performance of several other detection techniques, including differential detection [3,4]. The objective of this paper is to extend Pawula's analytical approach for evaluating the performance of narrowband multilevel FM signals when detected using three symbol by symbol detection techniques. In a recent paper Korn [6] has presented numerical results for LD detection of multilevel FM signals using an alternative approach. As in the case of binary FM signals, considering the ISI caused by adjacent symbols and employing Fourier series expansion technique, we present a method for determining the performance of M-ary continuous phasefrequency-shift-keyed (CPFSK) signals when the effect of the receiver IF filter is taken into account. However, in contrast to the binary case, where only one term of the Fourier series expansion of a two-bit pattern is needed for numerical computation, the M-ary case requires approximately five to ten terms of a similar Fourier series expansion. We have not succeeded in reducing this number any further without forgoing accuracy. In any case, a digital computer is required for obtaining numerical results, and therefore we believe that the relatively large number of terms required does not hinder the applicability of our analysis. The extension of previous work on binary FM to the M-ary case in this paper is based on the key observation that ISI 'spilling' into the adjacent signalling intervals decays within the first half of each of the adjacent interval. Apparently, this observation does not simplify the analysis in the binary case any further, but considerably simplifies the analysis in the M-ary case. The restricti...