Effective Capacity of $L_p$ -Norm Diversity Receivers Over Generalized Fading Channels Under Adaptive Transmission Schemes

This paper presents novel moment generating function (MGF)- and characteristic function (CHF)-based frameworks for the EC performance analysis of a generic <inline-formula> <tex-math notation="LaTeX">$L_{p}$ </tex-math></inline-formula>-norm diversity combining scheme under adaptive transmission policies. The considered system operates over generalized fading channels, a maximum delay constraint and under various channel state information (CSI) conditions. Depending upon the operational CSI, four policies are studied, namely: i) Constant power with optimal rate adaptation (ORA); ii) Optimal power and rate adaptation (OPRA); iii) Channel inversion with fixed rate (CIFR); and iv) Truncated CIFR (TIFR). The <inline-formula> <tex-math notation="LaTeX">$L_{p}$ </tex-math></inline-formula>-norm diversity is a generic diversity structure which includes as special cases various well-known diversity schemes, such as equal gain combining (EGC), maximal ratio combining (MRC) and amplify-and-forward (AF) relaying. Under the ORA and OPRA policies, we derive single integral expressions for evaluating the EC of <inline-formula> <tex-math notation="LaTeX">$L_{p}$ </tex-math></inline-formula>-norm diversity reception directly from the MGF or the incomplete MGF of the Signal-to-Noise-Ratio (SNR) at the receiver, respectively. For the EC performance evaluation of the EGC and AF relaying systems operating under the OPRA policy, a CHF-based approach, which is computationally more efficient as compared to the MGF-based approach, is further presented. It is shown that the EC for the CIFR and TIFR policies can be directly evaluated from the MGF or the CHF of the SNR at the receiver, respectively. For the ORA policy, a novel analytical approach for the asymptotic EC performance analysis is also developed and evaluated, revealing how important system operation parameters affect the overall system performance. The mathematical formalism is validated with selected numerical and equivalent simulation performance evaluation results, thus confirming the correctness of the proposed analytical methodology.