Delay-Limited Throughput of Space-Time Codes with Channel Estimation Errors

The main objective of this paper is to provide an extensive and complete examination on the effect of practical impairments such as channel estimation errors (CEEs) and feedback delay (FD) on the performance of diversity schemes over Nakagami‐mfading channels. Under erroneous channel estimation and outdated feedback cases, statistical expressions and several performance metrics related to the post‐processing signal‐to‐noise ratio (SNR) are derived for four different diversity schemes: transmit antenna selection (TAS)/orthogonal space–time block coding, TAS/maximal‐ratio transmission (MRT), MRT/receive antenna selection (RAS), and joint transmit and RAS. Exact analytical expressions for outage probability and average error rates ofM‐ary modulations are derived in order to provide insightful perspectives on the capacity and error performance of diversity schemes that experience both CEE and FD. The asymptotic diversity order of the investigated diversity schemes are derived via a high‐SNR approximation approach. In order to assess the real‐world performance of the investigated diversity schemes and to observe their robustness or sensitivities in practical imperfections, various configurations are considered together with several performance comparisons. Also, Monte Carlo simulations are performed in order to validate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.

It is well known that the performance of the wireless communication systems can be enhanced by using multiple transmit and receive antennas, which is generally referred to as the MIMO technique, and has been incorporated into the IEEE 802.11n standard, i.e. one of the Wi-Fi systems. The MIMO technique has also been adopted by the 3GPP Long Term Evolution (LTE) and the 3GPP2 Ultra Mobile Broadband (UMB) standards. The space-time coding is a promising way to realize the gain in the wireless communications system using MIMO. The space time block code, and the orthogonal space time block code in particular have been proposed in research and implemented in practical wireless communication systems due to their low computational complexity in maximum likelihood decoding implementation. However, the code rates of the orthogonal space time block codes are usually lower than $3/4$ when the number of transmit antennas is greater than two, which limit their throughput. To increase the code rate and the throughput of the orthogonal space time block code for more than two transmit antennas, a family of new space-time block codes (STBC) for 3 and 4 transmit antennas in a MIMO wireless communication system have been proposed in this Ph.D. research. These new codes are orthogonal and achieve full diversity, full rate using Triple QPSK'' modulation, which is proposed in this research. We investigated the performance of these STBCs when the channel state information (CSI) is perfectly known at the receiver. The CSI is not known to the transmitter in all of the studies in this dissertation. An analytical bound of the probability of bit error is developed and the Monte Carlo simulation is used when investigating these new STBC codes. In practical wireless communication system, the CSI is generally not available at the receiver and it is usually estimated by the receiver through the pilot signals or training signals known to the receiver. No matter what channel estimation method is used, the estimate of CSI will not match the CSI exactly and is noisy. The performance of these new STBCs using theTriple QPSK'' modulation when the estimate of the CSI is employed to detect the symbol is investigated in this dissertation. An upper bound of the bit error probability is developed when the noisy CSI is used to detect the symbols. The performance of the new STBCs using the Triple QPSK'' modulation is also evaluated using Monte Carlo simulation. When the CSI is not available to either the receiver or the transmitter, the differential encoding and decoding algorithm is applied to these new STBCs, which use theTriple QPSK'' modulation. The results showed that these orthogonal STBCs achieve full diversity full rate using ""Triple-QPSK"" modulation with differential detection. This provides a means of achieving space diversity and multiplexing gain without the CSI. A new differential encoding and decoding algorithm is proposed and analyzed for STBCs with 3 transmit antennas, whose transmission matrix is not square matrix, as part of this Ph.D. research. The STBCs using this algorithm achieve full diversity the MIMO system can possibly provide.

Pair-wise error probability (PEP) is analyzed in the presence of channel estimation error (CEE) for orthogonal frequency division multiplexing (OFDM) in a quasi-static Rayleigh fading channel. Subcarriers in OFDM are grouped in an equi-spaced manner with the number of subcarriers in a group equal to the number of channel taps. One group is dedicated for training and the rest are for data transmission. A linear minimum mean square error (LMMSE) based channel estimation for coherent detection is considered in this paper. This enables the signal dependent CEE to be uncorrelated to the data. Since ML decoding employed with perfect CSI becomes suboptimal in the presence of CEE, an optimal ML decoding is derived. It is observed from our training-based PEP expression that the CEE does not reduce the diversity order but contributes to a loss of coding gain. Moreover, a code design criterion is established. To reduce the loss of coding gain, an optimal training scheme is developed, based on the PEP expression. Loss of performance due to an imperfect channel estimate is quantified in terms of bounds on bit error probability (BEP) for high SNR. Our analytical findings are corroborated by simulation examples.

This paper studies the statistical properties of the signal-to-noise ratio (SNR) of the relay link in a cooperative wireless communication system with fixed gain relay in presence of channel estimation error. The SNR expression is derived and three different analytic approaches with different approximate assumptions are used to obtain the probability distribution function of the SNR and outage probability of the relay link. The first approach is the most accurate one in many cases, however it does not have a closed-form expression. The other two approaches result in closed-form expressions for the outage probability. Therefore, the third approach has been used to find a sub-optimum power allocation scheme for the source and the relay. The numerical results compare the accuracy of the analytic approaches and simulation results for different positions of the relay between the source and the destination. It is shown that the second approach has the most accurate closed-form expression and the third one leads to the simplest closed-form result suitable for power optimization purposes.

In this paper, we propose the analytical approach for amplify-and-forward (AF) relay cooperative transmission in the presence of channel estimation error (CEE) generated by pilot symbol assisted-channel estimation (PSA-CE) schemes over quasi-static Rayleigh fading channels. Average symbol error rate (SER) is expressed as the well-known closed-form by using moment generating function (MGF) of the received signal-to-noise ratio (SNR), which quantifies the SNR penalty arising from CEE. Moreover, the effect of CEE on SER performance is verified based on the number of pilot symbols and the accuracy of the derived average SER expression of M-ary phase shift keying (MPSK) is confirmed by comparison with simulation results.

The impact of the distance spectrum and interleaver structure on the bit error probability of turbo codes is considered. A new turbo code design method for Gaussian channels is presented. The proposed method combines a search for good component codes with interleaver design. The optimal distance spectrum is used as the design criterion to construct good turbo component codes at low signal-to-noise ratios (SNRs). In addition, an interleaver design method is proposed. This design improves the code performance at high SNR. Search for good component codes at low SNR is combined with a code matched interleaver design. This results in new turbo codes with a superior error performance relative to the best known codes at both low and high SNR. The performance is verified by both analysis and simulation.

In this paper, the problem of blind channel estimation under orthogonal space-time block coded (OSTBC) transmissions is solved by minimizing some distance measure between the theoretical and estimated correlation matrices of the observations. Specifically, the minimization of the Euclidean distance and the Kullback-Leibler divergence leads, respectively, to the Euclidean correlation matching (ECM) and Kullback correlation matching (KCM) criteria. The proposed techniques exploit the knowledge of the source correlation matrix to unambiguously recover the multiple-input multiple-output (MIMO) channel. Furthermore, due to the orthogonality properties of OSTBCs, both the ECM and KCM criteria result in closed form solutions. In particular, the channel estimate is given by the principal eigenvector of a matrix, which is obtained from the estimated correlation matrix of the observations modified by the code matrices and a set of weights. In the ECM case, the weights are fixed and equal to the eigenvalues of the source correlation matrix, whereas the KCM weights depend on both the signal-to-noise ratio (SNR) and the source eigenvalues. Additionally, we show that the proposed approaches are equivalent in the low SNR regime, whereas in the high SNR regime the KCM criterion is asymptotically equivalent to the relaxed blind maximum-likelihood (ML) decoder. Finally, the performance of the proposed criteria is illustrated by means of some numerical examples.

This paper compares the performance of a MIMO system applying a Mismatched Maximum Likelihood Detector (MMLD) with that applying a Generalized Likelihood Ratio Detector (GLRD) in the presence of channel estimation errors. Two sources of error are considered: errors due to noise and errors due to time variations induced by Doppler effects. The MMLD relies on the available channel estimate whereas the GLRD combines the channel estimate with a block of received data and uses a joint channel-symbol estimation approach to solve for the transmitted symbols. The GLRD is shown to outperform the MMLD whenever errors in channel estimation are incurred and the performance gap depends on the amount of error. Furthermore, the GLRD provides a unified receiver structure which can also be applied to differentially encoded MIMO systems and to situation where no channel estimate is available as in blind MIMO. The improved performance of the GLRD comes with increased computational complexity. This problem is addressed through search efficient algorithms based on the branch-estimate-bound optimization framework. We analyze the performance of the GLRD and provide a tight upper bound on the BER of the system at high SNR. Simulation results are shown for a 2 × 2 MIMO system.

A simple model for analysing channel estimation errors in space-time coding and modulation was constructed, and the Cramer-Rao bound expression for channel estimation errors was derived. It was also proved that the Cramer-Rao bound derived in the paper was a general and tight bound, as compared with the one given in the reported results of channel estimation errors. Moreover, the influence of channel estimation errors on the bit-error performance of space-time block coding and modulation was simulated by the Monte Carlo method showing that the losses of the performance caused by the channel estimation errors within the above Cramer-Rao bound are the minima in the losses of bit-error performance caused by all the channel estimation errors. This conclusion accorded with the analytical result in theory.

In this paper, we investigate the optimum detection of MIMO signals in the presence of channel estimation errors. A maximum likelihood (ML)-based detection algorithm is proposed for optimal MIMO signal detection based on the modified ML criterion which takes into account channel estimation errors. Moreover, we evaluate for both the uncoded and coded case, the bit-error-rate (BER) performance of the hard decoded MIMO systems. The new algorithm, taking into account channel estimation errors, achieves improvement in terms of BER gain over the conventional MIMO detector algorithm ignoring channel estimation errors. Moreover, the optimal designed constellations taking channel estimation errors into account, show an increase in the capacity over conventional schemes.

This study deals with the performance analysis of time division broadcast (TDBC) protocol with channel estimation errors. The tight lower bounds for individual and system outage probabilities are first presented in closed-form. It is shown that the presence of channel estimation error causes outage probability to maintain a fixed level even when a noiseless channel is adopted. Simulation results validate the accuracy of our analytical results. Furthermore, comparison of signal-to-noise ratio (SNR) gap ratio shows that TDBC protocol is less sensitive to the effect of channel estimate error than analog network coding (ANC) protocol.

We consider antenna selection in massive multi-input multi-output (MIMO) systems. Most prior works ideally assume perfect channel estimation at the receiver side. In this paper, we present an antenna selection scheme based on a genetic algorithm for massive MIMO systems in the presence of channel estimation error (CEE). Numerical results suggest that the proposed algorithm outperforms traditional antenna selection algorithms in terms of channel capacity, especially for low signal-to-noise ratio (SNR) scenarios.

This paper presents the performance analysis of decode-and-forward (DF) relaying system in presence of both channel estimation error (CEE) and radio frequency impairments (RFI). First, the end-to-end signal-to-noise-plus-distortion-and-error ratio (SNDER) expression is derived, followed by an exact closed-form outage probability (OP) expression for Nakagami-m fading channel. As a special case, the OP analysis for Rayleigh fading channel is also provided. From the derived expressions, the relation amongst CEE and RFI is analyzed. For a complete study, the high SNR analysis of the derived equations is also carried out. The analytical results have been verified using the Monte Carlo simulations. Finally, intriguing results are presented with the help of plots shown in the numerical analysis.

Outdoor channels can be modelled as as a sum of array response vectors of varying gain at different Angles of Departure (AoDs) from different point sources. Based on this characteristics, we derive a hybrid of Beam-Forming (BF) and Space-Time Block Coding (STBC), where the space-time code is transmitted over the beams generated by array response vectors. This is for the practical case where the transmit array may have adequate information on the departure angles of the dominant paths between transmitter and receiver. In the case where the transmitter has knowledge on the associated complex path gains, a power loading scheme is designed when. We compute analytically the Signal-to-Noise Ratio (SNR) of the proposed hybrid for the specific case of a two-path channel model and using the orthogonal Alamouti code, and compare the result to the SNR of optimal Linear Precoding (LP) and the theoretically possible SNR of Orthogonal STBC (OSTBC). Simulation results show that the performance of the BF/STBC hybrid with and without power loading can be very close to LP-under certain conditions-or even better in the practical case where there are phase estimation errors in the path gain estimates employed at the transmitter.© (2005) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

We study the optimal power allocation scheme for i.i.d. block-fading channels with a strict transmission delay constraint. In particular, we consider the maximization of the total throughput within a finite interval under a short-term average power constraint. When all the channel gains are known a priori, we demonstrate the mapping between the delay-constrained channel and the corresponding parallel channel for which both the single-user and multi-user channel results are well-known. The maximization problem becomes more complicated when only causal channel side information (CSI) is available. We show that under this assumption, constant power transmission is optimal in the limit of high signal-to-noise ratio (SNR). We also examine the optimal power policy and show that a simple linear power control scheme has near optimal performance. We next consider a two-user broadcast channel with a stringent delay constraint and causal feedback. We solve the optimal power control problem for this channel via dynamic programming. We discuss the solutions in the limit of both low and high SNR. Numerical results show the optimal scheme is approximately piecewise linear for general SNRs.