Channel Norm-Based Energy Detection With Diversity Reception for Amplitude-Shift Keying in Rayleigh Fading

Optimum and suboptimum energy detection receivers with diversity reception in Rayleigh fading, that only require limited channel state information based on the channel norm, are introduced. The importance of these channel norm based energy detection (CNBED) receivers is that they achieve the same diversity order as that of a coherent receiver. Furthermore, their performance degradation when compared to a coherent receiver can be made sufficiently low by appropriate choice of parameters. Due to their performance and the low complexity of energy detection, the CNBED techniques have potential applications to internet of things. Analysis of the CNBED receivers is performed for multi-level amplitude-shift keying (ASK). For the optimum receiver, an analytical approximation of the symbol error probability (SEP) as a sum of univariate integrals involving averaging of Gaussian
$Q$
-functions is derived. For the suboptimum receiver, closed form expressions for the exact SEP and for the approximate SEP under the condition of high signal-to-noise ratio (SNR) are obtained; in addition, using asymptotic approximations, expressions for the optimal ASK transmit levels with high SNR and large number of receive diversity branches, that minimize the SEP subject to an energy constraint, are found. Numerical results are provided to demonstrate the performance of the receivers.