Statistical Properties of Amplify and Forward Relay Links with Channel Estimation Errors

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.

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 Under erroneous channel estimation and outdated feedback cases, statistical expressions and several performance metrics related to the post‐processing signal‐to‐noise ratio (SNR) are derived for four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.

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.

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.

In this paper, we investigate the performance of an amplify-and-forward (AF) cooperative diversity system with multiple relays in the presence of channel estimation errors. We consider both conventional relaying (in which all relay nodes participate in the relaying phase) and opportunistic relaying (in which only a single relay is allowed to participate). We derive closed-form expressions for error probability, outage probability, and ergodic channel capacity. The derivations are confirmed through Monte Carlo simulations. We further deploy the derived expressions to obtain optimal power allocation rules for performance improvements.

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.

In this paper, we investigate the outage performance of decode-and-forward (DF) based opportunistic cooperative communications with channel estimation errors at the receivers under Rayleigh fading channels, in which the effect of the direct link has been explicitly evaluated. To be specific, the exact expression of outage probability has been derived for arbitrary values of signal-to-noise ratio (SNR) when pilot power is fixed. Through asymptotic analysis, the closed-form expressions of outage probability in the high SNR region and the diversity order are obtained. The analysis shows that the channel estimation errors due to limited pilot power impose a significant impact on the outage performance, leading to the diversity order be 0 even when the direct link is available. Although deploying more relays can mitigate the estimation errors effectively, the performance limit caused by the estimation errors becomes more obvious as SNR grows. For specific pilot power configuration and relay deployment, the outage probability remains unchanged even if data power approaches to infinity. Furthermore, simulation results are presented to verify our analysis.

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.

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.

This paper investigates the outage performance of an unmanned aerial vehicle (UAV) relaying system with decode-and-forward (DF) protocol, where multiple sources access the destination via UAV. By assuming that the destination is corrupted by multiple co-channel interferers, we first obtain the end-to-end signal-to-noise ratio (SNR) expression. Then, based on the SNR expression, we derive the closed-form expression of the outage probability (OP) for the UAV relaying system, where both of the uplink and downlink channels undergo Nakagami-m fading while the interference channels experience Rayleigh fading. Finally, numerical results are given to demonstrate the effectiveness of the performance analysis, and reveal the impacts of UAV antenna numbers and co-channel interferer on the system performance.

In this paper, multiple access channels are considered in which user data rates increase with the signal-to-noise ratio (SNR). To account for channel estimation errors, a finite- SNR diversity-multiplexing tradeoff framework is formulated. The multiplexing gain is defined for each user as the ratio of the user's data rate to the capacity of an additive white Gaussian noise (AWGN) channel. For a set of user multiplexing gains, a finite-SNR diversity gain is defined by the slope of the common outage probability as a function of SNR for quasi-static fading. These definitions have been used in previous work to characterize a finite-SNR diversity-multiplexing tradeoff in multiple access channels and point-to-point multiantenna channels. Inner and outer bounds on the feasible rate region of a multiple access channel with channel estimation errors are used to obtain estimates of the common outage probability. The outage probability is then used to estimate the diversity gain as a function of user multiplexing gains and SNR. It is shown that a finite-SNR formulation is essential to characterizing the impact of channel estimation errors on the diversity-multiplexing tradeoff.

In this paper, spatial modulation (SM) is used in a cooperative decode-and-forward (DF) cognitive radio system in order to enhance the overall spectral efficiency. In particular, a multi- antenna secondary transmitter communicates with a single antenna secondary receiver with the help of DF secondary relays in the presence of multiple primary users (PUs). To study the secondary system performance, we derive a closed-form expression for the average pairwise error probability (PEP) over Rayleigh fading channels assuming limited feedback from the PUs. A tight upper bounded average bit error rate is obtained using the PEP expression. Moreover, simple approximate expressions are obtained to get insights on the system diversity and estimation errors effects. Numerical results, which match simulations, show the effectiveness of SM in improving the overall secondary performance in the presence of channel estimation errors.

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.

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.

In this study, the authors examine the effect of a channel-estimation error on the error and outage probabilities of a multi-relay system with amplify-and-forward relaying over a frequency-flat Rician fading channel. The authors 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 an effective signal-to-noise ratio (SNR) at the destination node taking into account channel-estimation error, the authors obtain closed-form expressions for error and outage probabilities in a 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 the authors' analytical results.