Two-ray (TR) fading model is one of the fading models to represent a worst-case fading scenario. We derive the exact closed-form expressions of the generalized moment generating function (G-MGF) for the TR fading model, which enables us to analyze the numerous types of wireless communication applications. Among them, we carry out several analytical results for the TR fading model, including the exact ergodic capacity along with asymptotic expressions and energy detection performance. Finally, we provide numerical results to validate our evaluations.

This paper derives highly accurate and effective closed-form formulas for the average upper bound on the pairwise error probability (PEP) of the multi-carrier index keying orthogonal frequency division multiplexing (MCIK-OFDM) system with low-complexity detection (i.e., greedy detection) in two-wave with diffuse power (TWDP) fading channels. To be specific, we utilize an exact moment generating function (MGF) of the signal-to-noise ratio (SNR) under TWDP fading to guarantee highly precise investigations of error probability performance; existing formulas for average PEP employ the approximate probability density function (PDF) of the SNR for TWDP fading, thereby inducing inherent approximation error. Moreover, some special cases of TWDP fading are also considered. To quantitatively reveal the achievable modulation gain and diversity order, we further derive asymptotic formulas for the upper bound on the average PEP. The obtained asymptotic expressions can be used to rapidly estimate the achievable error performance of MCIK-OFDM with the greedy detection over TWDP fading in high SNR regimes.

In this paper, we analyze the best relay selection scheme for the soft-decision-and-forward (SDF) cooperative networks with multiple relays. The term `best relay selection' implies that the relay having the largest end-to-end signal-to-noise ratio is selected to transmit in the second phase transmission. The approximate performances in terms of pairwise error probability (PEP) and bit error rate (BER) are analyzed and compared with the conventional multiple-relay transmission scheme where all the relays participate in the second phase transmission. Using the asymptotics of the Fox's H-function, the diversity orders of the best relay selection and conventional relay scheme for the SDF cooperative networks are derived. It is shown that both have the same full diversity order. The numerical results show that the best relay selection scheme outperforms the conventional one in terms of bit error rate.

To assess the performance of maximum-likelihood (ML) based Nakagami m parameter estimators, current methods rely on Monte Carlo simulation. In order to enable the analytical performance evaluation of ML-based m parameter estimators, we study the statistical properties of a parameter Δ, which is defined as the log-ratio of the arithmetic mean to the geometric mean for Nakagami-m fading power. Closed-form expressions are derived for the probability density function (PDF) of Δ. It is found that for large sample size, the PDF of Δ can be well approximated by a two-parameter Gamma PDF.

Space-time block coding is an attractive solution for improving quality in wireless links. In general, the multiple-input multiple-output (MIMO) channel is correlated by an amount that depends on the propagation environment as well as the polarization of the antenna elements and the spacing between them. In this paper, asymptotic performance and exact symbol error probability (SEP) of orthogonal space-time block code (STBC) are considered in spatially correlated Rayleigh fading MIMO channel. We derive the moment generating function (MGF) of effective signal-to-noise ration (SNR) after combining scheme at the receiver. Using the MGF of effective SNR, we calculate the probability density function (pdf) of the effective SNR and derive exact closed-form SEP expressions of PAM/PSK/QAM with M-ary signaling. We prove that the diversity order is given by the product of the rank of the transmit and receive correlation matrix. Moreover, we quantify the loss in coding gain due to the spatial correlation. Simulation results demonstrate that our analysis provides accuracy.