Optimal differential detection and performance analysis of orthogonal space-time block codes over semi-identical MIMO fading channels

Abstract

This paper considers the optimal detector and its error performance of differential orthogonal space-time block codes over independent and semi-identically distributed, block Rayleigh fading channels. This semi-identically distributed case refers to the situation where the channel gains associated with a common receive antenna are identically distributed, but the ones associated with a common transmit antenna are not. We first derive the optimal symbol-by-symbol differential detector, and show that the conventional differential detector is suboptimal. We then derive an exact bit error probability expression for both BPSK and QPSK constellations based on the optimal detector. The result is applicable for any number of transmit and receive antennas, and assumes arbitrary block fading rates. Simple and insightful upper bounds are also obtained. especially common when the antenna spacing is relatively large (compared with the carrier wavelength) to ensure low correlation. The performance analysis of diversity reception in SIMO channels using various kinds of modulation schemes over non-identically distributed branches has been studied in, for example, (10) and (11). In this paper, we consider the error probability analysis of differential OSTBC over independent, semi-identically distrib- uted (i.s.i.d) and block-correlated Rayleigh fading channels. This i.s.i.d case refers to the situation where the channel path gains associated with a common receive antenna are identically distributed, but the ones associated with a common transmit antenna are not. Such situation would most likely occur in the uplink of a cellular system, where the antennas on the base station are mounted relatively far apart from one another, whereas the antennas on a mobile handset are inside a small antenna panel. We first propose an optimal symbol-by- symbol differential detector, and show that the conventional differential detector is suboptimal in the i.s.i.d case. We then derive an exact bit error probability (BEP) expression for the optimal detector. This result is applicable for any number of receive antennas and transmit antennas where OSTBCs exist. It also assumes arbitrary block fading rates. This BEP expression involves only a single integral over finite limits, and hence can be numerically computed easily. Moreover, simple and insightful upper bounds are also obtained. II. CHANNEL MODEL Let H(k) denote the M × N channel gain matrix in an M -transmit and N -receive antenna system during the k-th block, with each block consisting of L symbol intervals. The (m, n)-th entry hm,n(k) is the path gain from the m-th transmit antenna to the n-th receive antenna. The paths are all indepen- dent, and each sequence {hm,n(k)}k is modeled as samples of a complex, zero-mean, Gaussian random process having