Error Rate for Peak-Limited Coherent Binary Channels

An exponential-type bound on error rate Pefor peaklimited binary coherent channels operated at low signal-to-noise ratio (SNR) is presented. The bound depends exponentially only on the first and second moments of the channel output and serves to justify, in part, the use of SNR calculations for error-rate performance. It is assumed that the receiver outputVis given by a simple sum ofn( = [TW])identically distributed, independent random variables wi, each of which is decomposable into the sum of two independent random variables ziand ηi, i.e.,wᵢ = zᵢ+ηᵢ. The ziare peak limited byBz,|zᵢ| ≤ Bz, whereas ηiare normal (0, σ²). The zirepresent the output of a peak-limited channel and the ηirepresent any post channel receiver thermal noise (which may be zero,σ² = 0). For example, the zimay represent the output of a bandpass-limited satellite repeater, with an interference input in addition to the desired signal, and ηithe front-end noise in a receiving ground station. No assumption as to the channel-limiting characteristic or interference model, other than stated above, is made. Defining α as the ratio[Ew]²/var w(i.e., twice the receiver input average SNR) and β as the ratioBz²/var w(i.e., twice the receiver input peak SNR), then forα < 1,Pₑ < e-nμμ=α/2(1-α)- {γ³}{6} eγγ= √αβ, i. e., twice the geometric mean of average and peak SNR. If all odd moments ofzhave the same sign then a larger μ is obtained:μ=α/2(1-α)-{γ⁴}{24}e^{γ²}/28Upper bounds on the size of α and β are provided to guaranteeμ > 0. An example of a captured limiter that exhibits SNR suppression effects on the error rate is presented.