Performance Analysis of Multiuser Diversity on OSTBC MIMO Systems with Antenna Selection in the Presence of Feedback Delay CSI

Abstract

In this paper, we studied a comprehensive analytical symbol error probability (SEP) performance analysis of downlink multiuser diversity (MUD) on orthogonal space–time block code (OSTBC) system with transmit antenna selection (TAS) in the presence of imperfect channel state information (CSI) due to feedback delay over Rayleigh fading channels. The novel analytical approach is suitable for MUD with TAS/OSTBC systems in which effective receiver signal-to-noise ratio (SNR) is described as highest order statistic of Chi square distribution. Based on this framework, the closed-form SEP expressions are evaluated for the MUD exploiting TAS/OSTBC with normalized SNR based scheduling in heterogeneous wireless networks. Further, we derive approximate SEP; upper bound and lower bound SEP at high SNR under delayed feedback CSI. Thereafter the impact of feedback delay and antenna structures with significance on the consideration of MUD on the performance of the system has been analyzed.

Appendix

Inserting (16) and (25) into (18)

$$\begin{aligned} P_{M} \left( s \right) & = \sum\limits_{z = 1}^{2} {a_{z} } \sum\limits_{i = 1}^{{max\left( {M/4,1} \right)}} {\sum\limits_{k = 1}^{K} {\sum\limits_{s = 0}^{K - 1} {\sum\limits_{r = 0}^{{s\left( {N_{r} N_{t} - 1} \right)}} {\sum\limits_{l = 0}^{r} {\frac{{\left( { - 1} \right)^{s} a_{s,r} }}{{\left( {s + 1 - s\rho_{k}^{2} } \right)^{{N_{r} N_{t} + r + l}} }}\left( {\begin{array}{*{20}c} {K - 1} \\ s \\ \end{array} } \right)} } } } } \\ & \quad \times \frac{{\left( { - 1} \right)^{l} r!}}{l!}\frac{{\left( { - r} \right)_{l} }}{{\varGamma \left( {N_{r} N_{t} + l} \right)}} \left( {\begin{array}{*{20}c} {r + N_{r} N_{t} - 1} \\ r \\ \end{array} } \right)\frac{{\rho_{k}^{2l} \left( {\sigma_{k}^{2} } \right)^{r - l} }}{{max\left( {log_{2} M,2} \right)}}\frac{1}{{\left( {\lambda^{\left( k \right)} } \right)^{{N_{r} N_{t} + l}} }} \\ & \quad \times \mathop \int \limits_{0}^{\infty } e^{{ - \left( {\frac{{\left( {s + 1} \right)\gamma }}{{\lambda^{\left( k \right)} \left( {s + 1 - s\rho_{k}^{2} } \right)}}} \right)}} e^{{\left( { - \eta_{v} b_{z} \gamma } \right)}} \gamma^{{N_{r} N_{t} + l - 1}} d\gamma \\ \end{aligned}$$

(37)

Utilizing the identity [11] $\mathop \int \limits_{0}^{\infty } x^{v - 1} e^{ - \mu x} dx = \frac{1}{{\mu^{v} }}\varGamma \left( v \right)$, we can achieve approximate closed-form expression of average SEP of MUD-MIMO with TAS/MRC using MPSK in (26).