Impact of Channel Estimation Error on Time Division Broadcast Protocol in Bidirectional Relaying Systems

SUMMARYThis paper investigates two‐way relaying with direct link transmission. We propose to combine incremental relaying (IR) with the time division broadcast protocol (TDBC) to form a new scheme, termed TDBC‐IR, to increase the spectral efficiency of TDBC. Assuming half‐duplex decode‐and‐forward relaying, the performance of three protocols, that is, TDBC, TDBC‐IR, and physical‐layer network coding (PNC), are studied and compared, in terms of outage probability, expected rate (ER), and diversity‐multiplexing tradeoff. First, we reveal that the outage probability performance of TDBC‐IR is the same as that of TDBC and better than that of PNC. Second, we compare the ER and diversity‐multiplexing tradeoff performance of the three protocols based on the derived outage probability. The numerical results reveal that (1) the ER of TDBC‐IR is greater than that of TDBC and PNC in the whole signal‐to‐noise ratio (SNR) region, that is TDBC‐IR has improved spectral efficiency performance; (2) the ER performance of TDBC is better than PNC in the low SNR region but worse in the high SNR region; (3) the maximum achievable diversity order of TDBC‐IR and TDBC are both two whereas that of PNC is one; (4) the maximum achievable multiplexing gain of TDBC‐IR is one, which is better than TDBC (its maximum achievable is 2/3) and achieves the maximum of PNC (its maximum achievable is one). Copyright © 2012 John Wiley & Sons, Ltd.

This paper considers a multiuser two-way relay system with time division broadcast (TDBC) protocol, where multiple end-sources compete to exchange information with another end-source through the help of a single half-duplex amplify-and-forward (AF) relay. We derive a tight closed-form lower bound for the system outage probability over Nakagami-m fading channels with integer fading parameters. An asymptotic expression for the outage probability in high signal-to-noise ratio (SNR) regime is also obtained. Numerical results corroborate the theoretical analysis.

We study and compare the performance of three very typical bidirectional communication protocols based on the decode-and-forward relaying: time-division broadcast (TDBC), physical-layer network coding (PNC), and opportunistic source selection (OSS). We first derive the exact closed-form outage probabilities for the PNC and OSS protocols and an exact but one-integral form outage probability for the TDBC protocol. To gain more insight, we also derive closed-form asymptotic outage probability expressions for all protocols, with which we obtain further analytical results on the asymptotic optimal power allocation, the asymptotic optimal relay location, and the performance gain of the OSS protocol over the TDBC protocol in the high signal-to-noise ratio (SNR) regime. Finally, we study the diversity-multiplexing tradeoff (DMT) for each protocol both in the finite and infinite SNR regimes.

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.

A channel estimation based opportunistic scheduling scheme in wireless bidirectional networks

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.

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.

Analog network coding (ANC) and time division broadcasting (TDBC)are two major protocols used in bidirectional cooperative networks with half-duplex terminals. Most previous work on those two protocols was based on the assumption that there was no direct channel between the two sources. In this paper, we remove this limitation and investigate both protocols in a general bidirectional cooperative network with a direct channel between the two sources. Lower bounds on the outage probabilities of the two protocols are derived first. These lower bounds are very close to the exact outage probabilities in the whole signal-to-noise ratio (SNR) range irrespective of the values of channel variances. Based on the lower bounds, the finite-SNR diversity-multiplexing tradeoffs (DMTs) of the ANC and TDBC protocols are obtained. These tradeoffs establish a framework which enables us to make a comprehensive comparison between both protocols.

In this paper, switch-and-stay combining (SSC) is considered in two-way relay systems with amplify-and-forward (AF) relays, among which one is activated to assist the information exchange between two sources. We assume that the two-way relay system operates in the analog network coding (ANC) protocol where the communication can only be achieved through the active relay without the direct link. The outage probability and the average bit error rate (BER) for Rayleigh fading channels are studied. In particular, we derive closed-form lower bounds for the outage probability and the average BER, which is tight for different fading conditions. Moreover, we present asymptotic analysis for both the outage probability and the average BER at high signal-to-noise ratio (SNR) region. It is shown that SSC can achieve the full diversity order in two-way relay systems with proper switching thresholds. Numerical and simulation results are also provided to verify the theoretical study.

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.

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.

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 channel estimation errors is investigated in two-way relay networks (TWRNs) with two different channel state information (CSI) estimation schemes, namely separate and cascaded. In the former scheme, the relay node is chosen in accordance with the CSI of the individual channels between the source nodes and the relay node. By contrast, in the latter scheme, relay node selection is performed in accordance with the CSI of the cascaded channel between the two source nodes. For both estimation schemes, the effect of the CSI estimation error on the outage probability is examined by means of the Cramer–Rao lower bound. Moreover, in contrast to previous studies, the source nodes in the TWRN are assumed to have different estimation errors. The numerical results confirm the validity of the derived expressions and show that the presence of different estimation errors at the two source nodes has a significant effect on the performance of the TWRN.

This paper examines the impact of channel estimation errors on the distribution of the signal-to-interference ratio (SIR) at the output of the optimum combiner for space diversity reception in the uplink of wireless systems with multiple interferers. We generalize the results of prior work obtained for Rayleigh fading channels to a Rician/Rayleigh fading environment where the desired user is subject to Rician fading while the interferers experience Rayleigh fading. Using multivariate statistical analysis, an exact closed-form expression is derived for the probability density function (PDF) of the output SIR. The PDF expression is a useful tool to derive the analytical expressions of some other important measures of performance such as the outage probability and the average bit error probability. The theoretical result is verified by Monte Carlo simulations

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.