Performance of MIMO Schemes with Channel Estimation Errors

In full-duplex orthogonal frequency-division multiplexing systems with IQ imbalances, a frequency-domain least-squares (FD-LS) channel estimator is proposed to estimate both source-to-destination (intended) and destination-to-destination (self-interference) channels. Subsequently, an optimal closed-form pilot matrix is derived to minimize the sum of mean square errors (sum-MSE) of the proposed FD-LS channel estimator. Then, an improved FD-LS estimator is presented and proved to further improve the performance of the FD-LS by exploiting the time-domain property of the channel. In the presence of channel estimation error, an optimal low-complexity maximum likelihood (ML) detector is developed by using eigenvalue and singular value decompositions and whitening the residual self-interference plus noise. Simulation results show that given the proposed FD-LS estimator, the optimal pilot matrix performs much better than those nonsingular pilot matrices with larger conditional numbers (CN). To be specific, the former achieves about 10-dB signal-to-noise ratio (SNR) gain over the latter with CN = 10, the improved FD-LS channel estimator provides about 6-dB SNR gain over the FD-LS estimator at a fixed bit error rate (BER), and the proposed whitening-filter ML detector performs at least 0.6 dB better than the conventional ML detector at a given BER of $10^{-3}$ in the medium-and high-SNR regions.

A log-max generalized bit log-likelihood ratio (GLLR) was derived in an earlier work of Wang <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> for soft decision decoding of quadrature amplitude modulation that takes into account channel estimation error. The results in the above paper show that the GLLR metric outperforms the conventional LLR metric that does not account for channel estimation error. In trying to reproduce the results of the above paper, our simulations indicate that their results were obtained without proper scaling of the transmit constellation. Conversely, through simulations, we demonstrate that by properly scaling the constellation to have unity average energy, the GLLR metric does not result in a noticeable advantage in the bit error rate over the conventional LLR metric for practically meaningful values of the channel estimation error.

Visible light communication (VLC) has emerged as a green, low-cost, and secure supplement for existing radio frequency (RF) based systems. Although promising, the performance of VLC based systems is limited by several impairments, which degrade the achievable bit error-rate (BER) performance, viz. variations in channel-gain due to user-mobility, and channel-estimation error. Hence, in this letter, the bit error rate (BER) of maximal ratio combining is quantified over a multiple-input multiple-output (MIMO) VLC system, while considering the aforementioned impairments. Next, using the derived expressions, exact and asymptotic combiners based on the minimum bit error-rate (MBER) criterion are formulated for MIMO VLC systems impaired by user-mobility, and channel-estimation error. The accuracy of the contributed expressions for BER, and the performance of the proposed MBER combiner (MBERC) are corroborated by simulations performed over realistic MIMO VLC channels. Additionally, it is found that the proposed MBERC delivers improved BER performance in presence of channel-estimation error and user-mobility, which makes the proposed methodology viable.

Cooperation is an effective technique to increase the diversity in wireless relay networks and hence improve the Bit Error Rate (BER). In this paper, a scheme combining turbo coding and cooperative relay techniques, comprising one source, one destination and a single relay is proposed and studied. The aim of this study is to investigate the bit error rate (BER) performance in cooperative turbo coded systems equipped with an omni-directional antenna element at the transmission and the reception in the presence of channel estimation errors. Herein, the Amplify-and-Forward (AF) cooperation protocol is adopted at the relay level. Furthermore, a single hop scenario is considered, and the imperfect channel state information (CSI) is assumed to be present at the source-destination link. Two turbo codes, are generated at the source using the same polynomial, with overall rates of 1/2 and 1/3, respectively, the 1/2-rated one being generated from the latter using puncturing. Before iterative decoding, the destination performs a maximum ratio combing (MRC) of the signals emanating from the source and the relay transmitters. According to the authors 'knowledge, the investigation of the effect of channel estimation errors on the performance of such systems has not yet been reported.

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 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.

In this paper, we examine the effect of channel estimation error on the error and outage probabilities of a multi-relay system with amplify-and-forward relaying over frequency-flat Rician fading channel. We consider orthogonal relaying and study both conventional cooperative systems (i.e., all relays participate in the relaying phase) and opportunistic cooperative systems (i.e., only the best relay participates in the relaying phase). Based on the derivation of effective signal-to-ratio (SNR) at the receiver taking into account channel estimation error, we obtain closed-form expressions for error and outage probabilities in high SNR regime. Such closed form solutions are highly desirable because they allow for rapid and efficient evaluation of system performance. Computer simulations are used to validate our analytical results.

Recently, Cao and Beaulieu presented an insightful analysis on the bit-error performance of 16-quadrature amplitude modulation (QAM) scheme on Rayleigh fading channels with maximal ratio combining diversity and channel estimation errors. Unfortunately, although exact, the results presented in that paper are based on a complicated parabolic cylinder function, and a two-dimensional numerical integration has to be performed to evaluate the average probability of bit error. In this letter, we present a surprisingly simple expression for the average probability of error in a well-known closed form. We point out that the error rates for any N-ary square/rectangular QAM constellation with Gray mapping can also be expressed in this form. Furthermore, we show that the presented results can also be modified, in a simple fashion, for a generalized selection combining scheme in the presence of channel estimation errors.

The paper presents expressions for the received signals for rate 1, 1/2 and 3/4 space-time block codes in the presence of channel estimation errors and over mutually correlated flat frequency Rayleigh fading channels. It is shown analytically and through simulations how these codes suffer performance degradation as a consequence of the loss of orthogonality of the code produced by channel estimation errors. Quantitative results are provided which allow the space-time block codes performance to be evaluated and compared as a function of the channel estimation error power.

We consider Multiple-input multiple-output (MIMO) wiretap channel with one transmitter, one receiver, one cooperative jammer, and one eavesdropper, where each node equips with multiple antennas. Eigenbeam-space division multiplexing (E-SDM) and cooperative jamming are known as the techniques improving secrecy rate. E-SDM enables the transmitter and the legitimate receiver to communicate with each other in parallel using channel state information (CSI) known to them to maximize the legitimate receiver's mutual information. On the other hand, cooperative jamming is to jam only the eavesdropper to degrade eavesdropper's mutual information. However, co-channel interference and residual interference from the cooperative jammer are caused by channel estimation error, which degrades legitimate receiver's mutual information. How these interference influence on the secrecy rate has not been clarified. In this paper, we derive lower and upper bounds on secrecy rate using legitimate receiver's mutual information in the presence of channel estimation error and eavesdropper's mutual information who uses minimum mean square error (MMSE) receiver. We analyze the effect of co-channel interference and residual interference from the cooperative jammer on the secrecy rate.

Lower bounds are computed on the throughput of packet-switched space-time coded systems with delay constraints. The delay constraints are accounted for by defining a delay-limited throughput as the instantaneous throughput of each packet that can be maintained with a certain probability. The analysis assumes quasi-static and independent fading across packets, packet retransmissions until success, and negligible overhead for acknowledgment packets and guard times. Upper bounds on the outage probabilities of orthogonal space-time block codes (OSTBC) and spatial multiplexing with horizontal encoding (SM-HE) are computed in the presence of channel estimation errors to obtain lower bounds on the delay-limited throughput. The target physical-layer data rate is selected at each signal-to-noise ratio (SNR) to maximize the lower bounds on the throughput. The results indicate that higher throughput is achieved using OSTBC at low SNR and SM-HE at high SNR. Furthermore, the loss of throughput due to channel estimation errors is quantified.

In the fifth generation (5G) and beyond 5G (B5G) mobile communication, non-orthogonal multiple access (NOMA) has attracted great attention due to higher spectral efficiency and massive connectivity. We investigate the impacts of the channel estimation errors on the bit-error rate (BER) of NOMA, especially with the single-user decoding (SUD) receiver, which does not perform successive interference cancellation (SIC), in contrast to the conventional SIC NOMA scheme. First, an analytical expression of the BER for SUD NOMA with channel estimation errors is derived. Then, it is demonstrated that the BER performance degrades severely up to the power allocation less than about 20%. Additionally, we show that for the fixed power allocation of 10% in such power allocation range, the signal-to-noise (SNR) loss owing to channel estimation errors is about 5 dB. As a consequence, the channel estimation error should be considered for the design of the SUD NOMA scheme

The optimum detection of binary antipodal signals in additive white Gaussian noise (AWGN) channels with Gaussian channel estimation error has been studied in prior work. In this paper, we present the optimum detector based on the maximum- likelihood criterion for binary orthogonal signals in the presence of Gaussian distributed channel estimation error and AWGN. It is shown that the optimum detector is a linear combination of the optimum coherent and optimum noncoherent detectors. We derive the exact closed-form expression of the average bit error probability of the proposed optimum detector in Rayleigh fading channels with AWGN. It is found that if the variance of channel estimation error for a given average SNR is greater than a threshold, then orthogonal signalling outperforms antipodal modulation, and the analytical expression of this threshold is derived.

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 &amp; Sons, Ltd.

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.