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

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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> and the ASK-data-symbol-scaled channel norm estimate to the power of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>. 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha \lt 2$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha =2$ </tex-math></inline-formula>. Numerical results illustrate the performance variation of this receiver with respect to system parameters.