Design Criteria for Noncoherent Gaussian Channels with MFSK Signaling and Coding

Abstract

This paper presents data and criteria to assess and guide the design of modems for coded noncoherent communication systems subject to practical system constraints of power <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</tex> , bandwidth <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W</tex> , noise spectral density N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> , coherence time T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> , and number of orthogonal signals <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> . Three basic receiver types are analyzed for the noncoherent multifrequency-shift keying (MFSK) additive white Gaussian noise channel: hard decision, unquantized (optimum), and quantized (soft decision). Channel capacity and computational cutoff rate R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">comp</inf> are computed for each type and presented as functions of the predetection signal-to-noise ratio <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ST/N_{0}</tex> and the number of orthogonal signals <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M = 2TW</tex> . This relates the channel constraints of power, bandwidth, coherence time, and noise power to the optimum choice of signal duration <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T \leq T_{c}</tex> and signal number <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> .