Energy Detection of ASK With Receive Diversity in Nakagami- m Fading

Consider a single-input multiple-output (SIMO) 1 ×Nsystem in independent and identically distributed (i.i.d.) flat fading with fully noncoherent detection ofL-level one-sided amplitude-shift keying (ASK) symbols using an energy detection receiver. Let Фi(·) denote the conditional cumulative distribution function (c.d.f.) of the normalized received signal energy, conditioned on theith ASK symbol, that is, theith conditional c.d.f., fori= 1, . . . ,L. For this SIMO system, the symbol error probability (SEP) is analytically represented in terms of theLconditional c.d.f.s and theL− 1 detection thresholds. For the particular situation of i.i.d. Nakagami-mfading withm> 1, an analytical expression for theith conditional c.d.f. is obtained. In the cases of finitemandm→ ∞, high signal-to-noise ratio (SNR) approximations of the detection thresholds are derived. Under the high SNR condition with first level zero, the approximate optimal amplitude levels that minimize the SEP subject to a total energy constraint are shown to be in geometric progression for finitemand in arithmetic progression form→ ∞. Furthermore, for i.i.d. Nakagami-mfading withNmas a positive integer, a closed form expression for theith conditional c.d.f. is presented. Numerical results show the accuracy of the high SNR approximations.