Suboptimum Energy Detection Receiver Using Channel Norm Estimate for SIMO in Rayleigh Fading With Multi-Level ASK

Abstract

A single-input multiple-output system in flat Rayleigh fading, with pilot-symbol-aided least squares channel norm estimate based energy detection of one-sided multi-level amplitude-shift keying (ASK) data symbols, is considered. A suboptimum minimum distance (SMD) receiver is presented; it minimizes, over all ASK data symbols, the square of the difference between the received signal vector norm to the power of a real-valued non-zero parameter $\alpha $ and the ASK-data-symbol-scaled channel norm estimate to the power of $\alpha $ . For the SMD receiver, a closed form expression for the exact SEP is derived using a characteristic function approach. Furthermore, analytical methods of optimizing the ASK levels by SEP minimization, with high signal-to-noise ratio, large number of receive diversity branches, and one pilot symbol, are obtained for $\alpha \lt 2$ and $\alpha =2$ . Numerical results illustrate the performance variation of this receiver with respect to system parameters.