Analysis and Efficient Evaluation of the BER of OSTBCs With Imperfect Channel Estimation in Arbitrarily Correlated Fading Channels

Abstract

Abstract-An analysis of the exact bit error rate (BER) performance of orthogonal space-time block codes (OSTBCs) with maximum-likelihood detection in the presence of channel estimation errors is presented. The possibly correlated coefficients of the multiple-input multiple-output (MIMO) propagation channel are assumed to be affected by flat block fading and the transmitted symbols belong to a pulse amplitude modulation or quadrature amplitude modulation signal constellation. For both square and nonsquare OSTBCs, we derive approximate and exact BER expressions, irrespective of the distribution of the fading. It is also shown how the exact expressions can be efficiently and accurately evaluated using numerical integration techniques. Their application to the arbitrarily correlated Nakagamifading channel is presented and an efficient importance sampling technique is derived. As the high diversity order resulting from the application of OSTBCs gives rise to small BER values, the numerical evaluation of the presented BER expressions is much faster than straightforward Monte Carlo simulations. BER results have shown the impact of both imperfect channel estimation and antenna correlation on the performance of MIMO OSTBC systems. It is also shown that under highly correlated conditions, antenna correlation is the major source of BER degradation.

A simple importance sampling technique for orthogonal space-time block codes on Nakagami fading channels

“…However, the biased distribution from (7) is impractical, as it depends on the unknown bit error rate P b that is to be estimated by simulation. Nevertheless, (7) indicates that an efficient biased distribution should be proportional to an approximation of…”

“…where Q(·) is the Gaussian Q-function, β = 2λ in the case of binary phase-shift keying (BPSK), β = 3λ M−1 in the case of M-quadrature amplitude modulation (QAM) transmission with Gray mapping, and the parameter λ depends on the specific OSTBC [7]. A further approximation involves replacing Q(x) by the Chernoff upper bound (1/2) exp(−x 2 /2) [8].…”

“…Furthermore, we illustrate how the presented technique enables to derive a practical biased channel distribution for the case of OSTBCs transmitted over a spatially correlated Nakagami-m fading channel. Although perfect channel knowledge (PCK) is assumed for the derivation of the biased distribution, this distribution allows accurate BER estimation in a wide range of scenarios, such as pilot-based [7] or blind channel estimation, and in the presence of residual frequency offset, IQ imbalance, and phase noise. Moreover, the technique can easily be extended to the case of multicarrier communication on dispersive MIMO channels, using for instance OSTBCs or orthogonal space-frequency block codes.…”

Efficient BER simulation of orthogonal space-time block codes in Nakagami-m fading

“…To the best of our knowledge, such practical biased distribution for simulation over non-Rayleigh fading channels is not yet available from the literature. Although perfect channel knowledge (PCK) is assumed for the derivation of the biased distribution, it allows accurate BER estimation in a wide range of scenarios, such as pilot-based [7] or blind channel estimation, and in the presence of residual frequency offset, IQ imbalance, and phase noise. In addition, the technique also applies to single-input multiple-output (SIMO) systems with maximal-ratio combining (MRC) and can easily be extended to the case of multicarrier communication on dispersive MIMO channels, using for instance OSTBCs or orthogonal space-frequency block codes.…”

Moment generating function‐based pairwise error probability analysis of concatenated low density parity check codes with Alamouti coded multiple input multiple output‐orthogonal frequency division multiplexing systems

“…These papers neither considered any concatenation scheme nor the presence of OFDM for BER performance improvement. Papers [17][18][19][20] derive exact BER expressions for OSTBC codes in generalised Rayleigh and Rician fading channels in MIMO correlation channels, but no concatenation with channel coding techniques and OFDM is considered. In [21], the moment generating function (MGF) approach is used to analyse the PEP performance bounds for various channel coding techniques like convolutional codes, trellis codes etc.…”