Performance of $p$-Norm Detector in AWGN, Fading, and Diversity Reception

Performance analysis of the p-norm detector to date has been limited to ad hoc approximations, non-fading channels and Rayleigh fading. To overcome these limitations, we develop several analytical/numerical solutions for the detection probability Pd and the false alarm probability Pf , which are necessary to specify the receiver operating characteristic curves of the p-norm detector. First, for non-fading channels (additive white Gaussian noise only), the moment generating function (MGF) of the decision variable is derived in two forms: (i) closed-form for even-integer p and (ii) series-form for arbitrary p. To evaluate Pd and Pf , a numerical method utilizing the Talbot inversion is developed for case (i), and an infinite series expansion with convergence acceleration based on the ε-algorithm is derived for case (ii). As an alternative to MGF-based analysis, a Laguerre polynomial series is also used to derive new Pd and Pf approximations. Second, series-form MGF-based Pd expressions are derived for κ-μ and α-μ fading channels. Third, for antenna diversity reception, new p-law combining (pLC) and p-law selection (pLS) schemes are proposed. The performance of these combiners with the p-norm detector is derived for Nakagami-m fading and is compared to that of the classical maximal ratio combining (MRC) and selection combining (SC). Interestingly, both pLC and pLS perform similarly to SC at low signal-to-noise ratio (SNR) but outperform it at relatively high SNR, with pLC performing closer to the optimal MRC. Numerical results are presented to verify the derived results and to provide further insights.