Digital Communications with Emphasis on Data Modems

APPENDIX C DETECTION OF SIGNALS IN NOISE

C.1 INTRODUCTION

This appendix evaluates the detection and false‐alarm characteristics for the reception of single and multiple pulses using coherent and noncoherent processing techniques. The performance of the square‐law envelope detector is contrasted with that of the linear detector, and it is shown that the detection characteristics of the two techniques are nearly the same for sufficiently high signal‐to‐noise ratios (SNRs). The practical result of this observation is that the relatively straightforward analysis involving square‐law detection can be used to establish the performance of linear detectors under a wide variety of applications involving combining several received pulses. The classical work of Marcum and Swerling is used to characterize the detection and false‐alarm performance with multiple‐pulse combining in slow and fast fading Rayleigh environments. Although this appendix derives most of the results from radio detection and ranging (radar) signal detection applications, the analysis and statistical characteristics are directly applicable to communication systems analysis involving signal presence detection, waveform acquisition, diversity combining, and spread‐spectrum signal detection.

In Section C.2, the statistical performance is examined for coherent pulse integration and detection. In radar applications [1–3], coherent combining is referred to as predetection integration and generally applies to the combining ...