Multi-Level Signaling With Noncoherent SIMO Over a Rayleigh Channel

Multi-level signaling for a single-input multiple-output system over a Rayleigh fading channel with noncoherent detection is considered. The decision rule for the optimum noncoherent receiver, that has features of both noncoherent amplitude-shift keying (ASK) and noncoherent frequency-shift keying (FSK) receivers, is derived. Using a characteristic function approach, a closed form expression for the union bound on the symbol error probability (SEP) is obtained; this serves as an approximation for the SEP under the condition of high signal-to-noise ratio (SNR). A new M-ary signaling scheme, termed amplitude-frequency keying (AFK), which uses M-a amplitude levels and N-f orthogonal tones such that M=M-a(Nf), is presented, and its diversity order as well as a closed form high SNR approximation for its SEP is obtained. The advantages of AFK over ASK and FSK schemes are shown through numerical results.