finite-SNR Diversity-multiplexing Tradeoff Research Articles

Finite SNR Diversity-Multiplexing Trade-Off in Hybrid ABCom/RCom-Assisted NOMA Networks

Finite SNR Diversity-Multiplexing Trade-Off in Hybrid ABCom/RCom-Assisted NOMA Networks

Outage Probability and Finite-SNR DMT Analysis for IRS-Aided MIMO Systems: How Large IRSs Need to be?

Intelligent reflecting surfaces (IRSs) are promising enablers for high-capacity wireless communication systems by constructing favorable channels between the transmitter and receiver. However, general, accurate, and tractable outage probability analysis for IRS-aided multiple-input-multiple-output (MIMO) systems is not available in the literature. In this paper, we first characterize the distribution of the mutual information (MI) for IRS-aided MIMO systems by capitalizing on large random matrix theory (RMT). Based on this result, a closed-form approximation for the outage probability is derived and a gradient-based algorithm is proposed to minimize the outage probability with statistical channel state information (CSI). We also investigate the diversity-multiplexing tradeoff (DMT) with finite signal-to-noise ratio (SNR). Based on these theoretical results, we further study the impact of the IRS size on system performance. In the high SNR regime, we provide closed-form expressions for the ergodic mutual information (EMI) and outage probability as a function of the IRS size, which analytically reveal that the benefit of increasing the IRS size saturates quickly. Simulation results validate the accuracy of the theoretical analysis and confirm the increasing cost to improve system performance by deploying larger IRSs. For example, for an IRS-aided MIMO system with 20 antennas at both the transmitter and receiver, we need to double the size of the IRS to increase the throughput from 90% to 95% of its maximum value.

Combining Non-orthogonal Transmission with Network-Coded Cooperation: Performance Analysis Over Nakagami-m Fading Channels

This paper investigates efficient transmission design in a class of multi-user cooperation networks, in which multiple information sources intend to distribute their messages to a sufficient proportion of ambient destinations with the assistance of multiple relays. We apply a relaying scheme that combines non-orthogonal transmission with network coding techniques to balance channel consumption and inter-user interference. The sources and relays are divided into clusters, terminals within each of which are allowed to non-orthogonally access the same channel. A class of finite-field network codes are adopted in the relays. We provide the methods to derive the system transmission error probability and diversity-multiplexing tradeoff (DMT), over Nakagami- $m$ fading channels. Through error probability and finite-SNR DMT analysis for certain clustering strategies, and infinite-SNR DMT analysis for general situations, we show that the considered relaying scheme can notably improve system performance over the conventional approach that demands only orthogonal transmission in network-coded cooperation networks.

Wireless Energy Harvesting-Based Relaying: A Finite-SNR Diversity-Multiplexing Tradeoff Perspective

This paper presents an analytical framework to derive the closed-form expressions for diversity-multiplexing tradeoff (DMT) for wireless energy harvesting (WEH) based amplify-and-forward (AF) and decode-and-forward (DF) protocols in finite signal-to-noise (SNR) regime. The results of this investigation suggest that both AF and DF offer similar performance except for few nuances. At low multiplexing gains, DF offers marginally better performance in the low SNR regime, whereas AF performs better in the high SNR scenarios. However, in the higher multiplexing gain regime, though subtle, DF uniformly dominates AF across all SNRs. Furthermore, an analytical study is presented to evaluate the effect of the fraction of time devoted to WEH (time-sharing parameter, $\epsilon $ ) on the finite SNR DMT (f-DMT). In addition, the impact of relay position on the outage performance is also presented. A distinguishing feature of the proposed work is the characterization of WEH-based f-DMT which reveals the complete interplay between the operating SNR and the time-sharing parameter ( $\epsilon $ ), which is of fundamental importance to system designers. Finally, Monte-Carlo simulations are provided to confirm the veracity of analytical solutions.

Performance analysis of non-coherent MIMO MRC scheme with training using finite-SNR diversity and multiplexing tradeoff

The inherent tradeoff between the twin benefits offered by multiple antenna systems, namely, the diversity gain and the multiplexing gain is captured as the diversity multiplexing tradeoff (DMT). The DMT at asymptotically high signal-to-noise ratio (SNR) is optimistic, whereas at finite SNR, it is practical. In this paper, point-to-point multiple input multiple output (MIMO) systems are considered under the assumption of coherent and non-coherent communication implying, respectively, whether perfect channel state information is available at the receiver (CSIR) or not. The literature mainly addresses non-coherent communication with training at asymptotically high SNR, whereas the finite-SNR analysis is more relevant in practice. We address the performance analysis of a MIMO maximal ratio combining scheme by deriving closed-form expressions of the DMT at finite SNR under non-coherent communication with training. At a fixed multiplexing gain and finite SNR, a reduction in the diversity gain is observed when coherent communication is replaced by non-coherent communication with training. We also show that for a high multiplexing gain, the reduction in diversity gain is much more pronounced as compared to that at a low multiplexing gain. A training-based channel estimation scheme discussed in the literature is used in two modes of power allocation, namely, the capacity optimal power allocation and equal power allocation (EPA). In both modes, at a fixed average SNR and with equal duration of training, we observe that the power allocation mode does not make a significant impact on the finite-SNR DMT of the MIMO scheme. We also observe that in the EPA mode, the diversity gain reduces with increase in training duration.

Adaptive Cooperation for Bidirectional Communication in Cognitive Radio Networks

In the interweave cognitive networks, the interference from the primary user degrades the performance of the cognitive user transmissions. In this paper, we propose an adaptive cooperation scheme in the interweave cognitive networks to improve the performance of the cognitive user transmissions. In the proposed scheme for the bidirectional communication of two end-source cognitive users, the bidirectional communication is completed through the non-relay direct transmission, the one-way relaying cooperation transmission, and the two-way relaying cooperation transmission depending on the limited feedback from the end-sources. For the performance analysis of the proposed scheme, we derive the outage probability and the finite-SNR diversity multiplexing tradeoff (f-DMT) in a closed form, considering the imperfect spectrum sensing, the interference from the primary user, and the power allocation between the relay and the end-sources. The results show that compared with the direct transmissions (DT), the pure one-way relaying transmissions (POWRT), and the pure two-way relaying transmissions (PTWRT), the proposed scheme has better outage performance. In terms of the f-DMT, the proposed scheme outperforms the full cooperation transmissions of the POWRT and PTWRT.

Finite-SNR Diversity-Multiplexing Tradeoff for Network Coded Cooperative OFDMA Systems

Network-coded cooperation (NCC) is an effective method to improve the throughput efficiency in cooperative wireless networks. The combined use of orthogonal frequency division multiplexing (OFDM) with NCC has been further studied in the literature to exploit the multipath diversity gains. In this paper, we consider orthogonal frequency division multiple access (OFDMA), an extension of OFDM to a multiuser system where subsets of carriers are assigned to different users. We first derive a closed-form expression for the outage probability of NCC-OFDMA over Rician fading channels and then present the asymptotical and finite-SNR DMT expressions. Our results provide insight into the performance mechanisms under practical SNR regime of NCC-OFDMA systems and demonstrate that NCC-OFDMA is able to fully exploit both frequency and spatial diversity. We also show that the derived finite-SNR DMT converges to an asymptotical one as expected. Furthermore, special cases for our derived analytical expressions are presented, to show that the derived expression is a generalized case of the related the state of the art results. Simulation results are further presented to verify our theoretical analyses.

Finite-SNR Diversity–Multiplexing Tradeoff With Accurate Performance Analysis for Fully Correlated Rayleigh MIMO Channels

Zheng and Tse were the first to discover the fundamental diversity–multiplexing tradeoff (DMT) that occurs in multiple-input multiple-output (MIMO) systems. Their research was limited to infinite signal-to-noise ratio (SNR) situations. Later, research was also conducted on finite-SNR situations; however, this research had significant problems with coarse approximation. In this paper, we propose more accurate approximations of the finite-SNR DMT and the outage probability for Rayleigh fading MIMO channels to solve these problems. The proposed formulas provide more general solutions that are applicable not only to uncorrelated and semicorrelated channels but also to fully correlated channels, which have not been considered in the literature. Utilizing the proposed finite-SNR DMT, we further investigate the influence of the deviation of the finite-SNR DMT on system performance. We also derived an accurate SNR offset quantity, which provides a link for transformation of finite-SNR DMT to actual outage probability. Finally, we present computer simulation results for illustration and comparison to confirm the validity of our research work.

Lower Bound for Finite-SNR DMT With Position Estimation Errors in MIMO Channels

The finite signal-to-noise ratio (SNR) situation for the diversity-multiplexing tradeoff (DMT) of multiple-input-multiple-output (MIMO) systems has become a fundamental research topic in wireless communications. In this letter, the impact of position estimation errors of the receiver on the finite-SNR DMT of the MIMO system is investigated. Formulas of the biased Cramer–Rao bound and the mean-square error lower bound of the biased finite-SNR DMT are proposed when the DMT value is influenced by the position estimation error of the receiver induced by a biased position estimator. Furthermore, based on the developed formulas, the case of the DMT over the Rayleigh fading channel and the position estimation errors raised by a radar is analyzed.

Finite SNR diversity-multiplexing tradeoff with spatial correlation and mutual coupling effects for Rayleigh MIMO channels

In the literature, the finite signal-to-noise ratio (SNR) situation for the fundamental diversity-multiplexing tradeoff (DMT) of multiple-input–multiple-output systems (MIMO systems) has been attached great importance. However, only lower bounds or coarse approximations of the outage probability have been proposed to develop coarse bounds of the finite-SNR DMT in the literature, and their approximation errors are still non-negligible. In order to solve the aforementioned weaknesses, we first propose an accurate finite-SNR outage probability for Rayleigh MIMO fading channels and then use it to derive the corresponding finite-SNR DMT. The proposed finite-SNR DMT can be used as an accurate guideline at finite SNR for rate-adaptive MIMO applications. In addition, the impact of antenna mutual coupling (along with antenna spatial correlation) on the finite-SNR outage probability and consequently its impact on the finite-SNR DMT are analyzed. Our results reveal that the spatial correlation of antenna arrays cannot provide gains to the outage performance and the finite-SNR DMT. In contrast, when the antenna spacing of antenna arrays is appropriately specified, the mutual coupling of antenna arrays is in favor of the outage performance and the finite-SNR DMT. Finally, we present computer simulation results for illustration and comparison to confirm the validity of our research work.

Finite‐signal‐to‐noise ratio diversity‐multiplexing‐delay tradeoff in half‐duplex hybrid automatic repeat request relay channels

In this paper, we consider a delay-limited hybrid automatic repeat request (HARQ) protocol that makes use of incremental redundancy over the three-node decode-and-forward (DF) relay fading channel where one source cooperates with a relay to transmit information to the desti nation. We provide an estimate of the diversity-multiplexing tradeoff (DMT) at finite signal to noise ratio (SNR) based on t ight bounds on outage probabilities for two channel models. The results for the long term quasi-static channel highlight the distributed diversity, ie. the cooperative sp ace diversity, and the HARQ coding gain, achieved by soft combining the successive transmitted punctured codewords via incremental redundancy. On the other hand, the results for the short term quasi-static channel illustrate the diversity gains obtained thanks to cooperative space diversity and time diversity, along with the HARQ coding gain. Using the DMT formulation, we show that equal power partitioning between the source and the relay nodes provides close to optimal performance. Furthermore, thanks to the extension of the finite-SNR DMT to the finite-SNR diversity-multiplexing-delay tradeoff, we show that, unl ike the asymptotic SNR analysis, the ARQ delay, defined as the number of retransmissions rounds, impacts the performance of the HARQ relay protocol for high effective multiplexing gain.

Finite-SNR Diversity-Multiplexing Tradeoff for Three-Phase ANC with Channel Estimation Errors

In this letter, we analyze the diversity-multiplexing tradeoff (DMT) performance of a two-way relay system that employs three-phase (3P) analog network coding (ANC) in the presence of channel estimation errors under Nakagami-m fading. By deriving an overall system outage probability expression, we compute the DMT for the considered scheme at finite signal-to-noise ratios (SNRs). We further derive an asymptotic and limiting behavior of the DMT, from which the effect of imperfect estimation on the system achievable performance is highlighted. Numerical and simulation results corroborate our theoretical findings and provide a comparison of the tradeoffs for the 3P ANC over its two-phase (2P) counterpart.

Finite-SNR Diversity-Multiplexing Tradeoff for Rayleigh MIMO Channels

In this paper, exact diversity-multiplexing tradeoff (DMT) at finite signal to noise ratio (SNR) for multiple-input multiple-output (MIMO) systems with dual antennas at the transmitter (2 x N_r) and/or at the receiver (N_tx 2) is derived over Rayleigh fading channels. We derive the outage probability of the mutual information between transmitted and received signals versus SNR. It is shown that at realistic SNRs, achievable diversity gains are significantly lower than asymptotic values. While space-time codes (STCs) for MIMO systems are conventionally designed to achieve the asymptotic DMT frontier, this finite-SNR DMT could provide a new insight to design STCs for practical MIMO systems optimized at operational SNRs.

Outage Exponent: A Unified Performance Metric for Parallel Fading Channels

The parallel fading channel, which consists of finite number of subchannels, is very important, because it can be used to formulate many practical communication systems. The outage probability, on the other hand, is widely used to analyze the relationship among the communication efficiency, reliability, SNR, and channel fading. To the best of our knowledge, the previous works only studied the asymptotic outage performance of the parallel fading channel which are only valid for a large number of subchannels or high SNRs. In this paper, a unified performance metric, which we shall refer to as the outage exponent, will be proposed. Our approach is mainly based on the large deviations theory and the Meijer's G-function. It is shown that the proposed outage exponent is not only an accurate estimation of the outage probability for any number of subchannels, any SNR, and any target transmission rate, but also provides an easy way to compute the outage capacity, finite-SNR diversity-multiplexing tradeoff, and SNR gain. The asymptotic performance metrics, such as the delay-limited capacity, ergodic capacity, and diversity-multiplexing tradeoff can be directly obtained by letting the number of subchannels or SNR tends to infinity. Similar to Gallager's error exponent, a reliable function for parallel fading channels, which illustrates a fundamental relationship between the transmission reliability and efficiency, can also be defined from the outage exponent. Therefore, the proposed outage exponent provides a complete and comprehensive performance measure for parallel fading channels.

Diversity–Multiplexing Tradeoff and Outage Performance for 2×2 Dual-Polarized Uncorrelated Rice MIMO Channels

In this paper, diversity-multiplexing tradeoff (DMT) curve for 2×2 Dual-Polarized uncorrelated Rice MIMO channels is studied. Exact expressions for statistic information of mutual information exponent are derived. Impacts of channel parameters such as signal to noise ratio (SNR), k-factor and cross polarization discrimination (XPD) on mutual information exponent are analyzed. Compared to conventional single-polarized (SP) Rice MIMO systems, a qualitatively different behavior is observed for DP Rice systems. The work in this paper, allows identifying quantitatively for which channels (k-factor) and SNR levels the use of dual polarization becomes beneficial. Gamma or lognormal distribution are used to describe mutual information component, and a theoretical formulation for finite-SNR DMT curve in 2×2 DP uncorrelated Rice channels is presented for the first time, which is valid in low and medium SNRs when multiplexing gain is larger than 0.75.

On the Finite-SNR DMT of Two-Way AF Relaying with Imperfect CSI

A general framework of finite-SNR diversity-multiplexing tradeoff (DMT) is formulated to evaluate the impact of imperfect channel estimation in two-way amplify-and-forward (AF) relaying systems over Nakagami-m fading channels. Imperfect self-interference cancellation and signal detection are performed at both sources due to channel estimation errors. The overall outage probability (OOP) is obtained and then the finite-SNR DMT is derived in the presence of channel estimation errors. Furthermore, the asymptotic and limiting behavior expressions of the finite-SNR DMT are also evaluated adequately. Numerical results verify the theoretical analysis and show that at realistic SNR and channel estimation quality, the DMT is significantly lower than the asymptotic result.

Finite-SNR Diversity-Multiplexing Trade-Off of Dual Hop Multiple-Relay Channels

This paper investigates the finite signal-to-noise ratio (SNR) diversity-multiplexing trade-off (DMT) of point-to-point wireless channels assisted by multiple relays. Results are derived for both amplify-and-forward (AF) and decode-and-forward (DF) relaying protocols. For the AF protocol, we derive accurate approximations for the system outage probability when the relays are clustered between the source and destination. For the case where all the relays are clustered near the destination, an exact closed-form expression for the system outage probability is obtained. For the DF protocol, under general multiple relaying configurations, we derive an exact closed-form expression for the system outage probability. The outage results for AF and DF are used subsequently to yield expressions for the finite-SNR DMT. We also extract the conventional asymptotic DMTs as special cases of the finite-SNR results, and demonstrate that the asymptotic DMTs can significantly overestimate the level of diversity that is achievable for practical error rates and SNRs.

Two Birds with One Stone: Exploiting Direct Links for Multiuser Two-Way Relaying Systems

This Letter proposes a mechanism to combine multiuser diversity (MUD) and incremental relaying in a multiuser two-way relaying system, where one end-source exchanges messages with one out of N available end-sources by using a half-duplex amplify-and-forward (AF) relay. Outage analysis for the proposed scheme is carried out and, compared with the time division broadcast (TDBC) protocol, reveals that it not only realizes full diversity order (N+1) but also achieves improved expected spectral efficiency. Also, it is indicated that the expected spectral efficiency of the proposed scheme approaches that of the analog network coding (ANC) protocol in high signal-to-noise ratio (SNR) regime. Furthermore, the finite-SNR diversity-multiplexing tradeoff (DMT) is examined, from which the superiority of the proposed scheme to TDBC is confirmed as well. Other insightful comparisons in terms of the outage performance are presented that show the practical usefulness of our multiuser two-way relaying framework.

Outage Probability and Optimum Power Allocation for Analog Network Coding

We study the analog network coding (ANC), which is a well-known amplify-and-forward (AF)-based bidirectional protocol, for a bidirectional network consisting of two different sources and a relay. In this protocol, the two sources exchange information with the help of the relay during two time slots in a half-duplex mode. For this system, we first derive a tight lower bound of outage probability, which is very close to the exact outage probability in the whole signal-to-noise ratio (SNR) range irrespective of the values of channel variances. Using the tight lower bound, we obtain finite-SNR diversity-multiplexing tradeoff of the ANC protocol. Furthermore, we propose an optimum power allocation scheme, which simultaneously minimizes the outage probability and maximizes the total mutual information of the ANC protocol.

Finite-SNR Diversity-Multiplexing Tradeoff via Asymptotic Analysis of Large MIMO Systems

Diversity-multiplexing tradeoff (DMT) was characterized asymptotically (SNR- > infinity) for i.i.d. Rayleigh fading channel by Zheng and Tse . The SNR-asymptotic DMT overestimates the finite-SNR one . This paper outlines a number of additional limitations and difficulties of the DMT framework and discusses their implications. Using the recent results on the size-asymptotic (in the number of antennas) outage capacity distribution, the finite-SNR, size-asymptotic DMT is derived for a broad class of fading distributions. The SNR range over which the finite-SNR DMT is accurately approximated by the SNR-asymptotic one is characterized. The multiplexing gain definition is shown to affect critically this range and thus should be carefully selected, so that the SNR-asymptotic DMT is an accurate approximation at realistic SNR values and thus has operational significance to be used as a design criterion. The finite-SNR diversity gain is shown to decrease with correlation and power imbalance in a broad class of fading channels, and such an effect is described in a compact, closed form. Complete characterization of the outage probability (or outage capacity) requires not only the finite-SNR DMT, but also the SNR offset, which is introduced and investigated as well. This offset, which is not accounted for in the DMT framework, is shown to have a significant impact on the outage probability for a broad class of fading channels, especially when the multiplexing gain is small. The analytical results and conclusions are validated via extensive Monte Carlo simulations. Overall, the size-asymptotic DMT represents a valuable alternative to the SNR-asymptotic one.