High Signal-to-noise Ratio Approximation Research Articles

Splitting Receiver With Joint Envelope and Coherent Detection

This letter proposes a new splitting receiver design with joint envelope detection (ED) and coherent detection (CD). To characterize its fundamental performance limit, we conduct high signal-to-noise ratio (SNR) analysis on the proposed ED-CD splitting receiver and obtain closed-form approximations of both the achievable mutual information and the optimal splitting ratio (i.e., a key design parameter of the receiver). Our numerical results show that these high SNR approximations are accurate over a wide range of moderate SNR values, signifying the usefulness of the obtained analytical results. We also provide insights on the conditions at which the proposed splitting receiver has significant performance advantages over the traditional receivers.

Channel Capacity of an Asymmetric Constellation in Rayleigh Fading With Noncoherent Energy Detection

The channel capacity of noncoherent reception of multi-level one-sided amplitude-shift keying (ASK), which is an asymmetric constellation, in Rayleigh fading with receive diversity and energy detection is considered. The asymmetries result in capacity achieving input probability distributions, that is, a priori probability distributions, that deviate from uniformity. An analytical expression for the mutual information in terms of a single integral is derived, and from it the set of equations, which can be solved to obtain the optimum or capacity achieving input probabilities, is obtained. High and low signal-to-noise ratio (SNR) approximations of the optimum input probabilities and the capacity are derived next. Furthermore, a logarithmic upper bound on the mutual information is obtained. Numerical results confirm that the uniform distribution of input probabilities is not capacity achieving. For example, with average SNR per symbol per branch of 6 dB, the relative deviation of the mutual information (with uniform input distribution) from the capacity is nearly 20% for 4-level ASK with one transmit diversity branch and two receive diversity branches. Furthermore, the derived high and low SNR approximations to the capacity are shown to be reasonably accurate.

Performance of Integrated Satellite-Terrestrial Relay Network With Relay Selection and Outdated CSI

Satellite communication plays an important role in future wireless network. In this article, we investigate the outage performance of the integrated satellite-terrestrial relay network (ISTRN) with relay selection based adaptive decode-and-forward (RSADF), where the relay selection is based on outdated channel state information (CSI), and the multiple-antenna relays conduct maximum-ratio receiving and transmitting for decoding and forwarding, respectively. Particularly, we first obtain a novel closed-form expression for the outage probability of the considered ISTRN with RSADF. Furthermore, to get further insights of the effect of key system parameters, e.g., the number of relays, the number of antennas, the CSI outdating level, and the channel fading characteristics, on the system performance, we conduct asymptotic analysis for three typical high average signal-to-noise-ratio (SNR) scenarios, i.e., 1) all satellite and terrestrial links are with high average SNR, 2) the satellite-to-relay link and the relay-to-user link are with high average SNR, and 3) only the relay-to-user link is with high average SNR. The derived high SNR approximations of outage probability explicitly reveal the impact of key system parameters in the form of diversity gain and coding gain. Finally, numerical simulations are presented to validate the analytical results.

Performance of SWIPT-Based Differential AF Relaying Over Nakagami- $m$ Fading Channels With Direct Link

This letter investigates the error rate performance of simultaneous wireless information and power transfer-based differential amplify-and-forward relaying in the presence of Nakagami- ${m}$ fading and a direct link. We provide a closed-form expression for the probability density function of the signal-to-noise ratio (SNR) of the two-hop (TH) link based on a high SNR approximation. Novel closed-form approximate average bit-error rate expressions are derived for both the single TH scenario and the scenario with a linear combiner for the TH link and a direct link. The impacts of different values of the fading parameter ${m}$ on error rate performance are also investigated. Analyses are verified through Monte Carlo simulations.

High SNR approximation for performance analysis of two-way multiple relay networks

Signal-to-Noise Ratio (SNR) is the key parameter in the performance evaluation of Two-Way, Amplify-and-Forward, Multiple-Relaying (TAF-MR) networks. This paper introduces new methods that use high SNR (HSNR) level approximations to analyze accurately the Bit Error Rate (BER), optimize the Relay Location (RL), and balance the energy efficiency (EE) and spectral efficiency (SE) of such networks. We consider a flat-fading channel and a strategy for selecting a relay with the highest SNR. Standardized BER expressions are obtained for a wide range of SNRs (low, high, and optimal) to yield more accurate predictions of the BER performance. Thus, by using HSNR, a unified analysis for calculating the Asymptotic BER (ABER) and the exact BER (EBER) performance is developed. The optimal SNR level is obtained by optimizing the power of network sources, which include the relay and user powers. Further, we propose a method for integrating the RL with the balancing of the EE and SE optimally to achieve the best EE improvement. The derived expressions for the methods are validated by simulation.

Transmission Optimized Generalized Spatial Modulation Over Correlated Fading Channels

Generalized spatial modulation (GSM) has shown its promising performance as an alternative to large-scale multiple-input multiple-output technology for future wireless communications. A novel transmission optimized GSM (TOGSM) is proposed based on minimizing the average bit error probability (ABEP) over spatial correlated fading environments. First, a union upper bound and a high signal-to-noise ratio (SNR) approximation of ABEP for traditional GSM with multi-stream transmission is derived when assuming maximum likelihood detection at the receiver side. In contrast, the new analytical result relaxes basic constraints on the channel model and the symbol modulation type in use when measuring the ABEP of SM. Then, TOGSM is presented through seeking the solution of an optimization problem for particular channel realizations, where the best combination of spatial modulation set and symbol modulation set can be obtained at a given spectral efficiency. Finally, the accuracy of the ABEP upper bound and its high SNR approximation is verified by Monte Carlo simulations. In addition, the performance advantages of TOGSM over the other schemes, such as fixed-GSM, V-BLAST and generalized space shift keying, are comparatively illustrated via some numerical examples.

Interference mitigation scheme by antenna selection in device-to-device communication underlaying cellular networks

In this paper, we investigate an interference mitigation scheme by antenna selection in device-to-device (D2D) communication underlaying downlink cellular networks. We first present the closed-form expression of the system achievable rate and its asymptotic behaviors at high signal-to-noise ratio (SNR) and the large antenna number scenarios. It is shown that the high SNR approximation increases with more antennas and higher ratio between the transmit SNR at the base station (BS) and the D2D transmitter. In addition, a tight approximation is derived for the rate and we reveal two thresholds for both the distance of the D2D link and the transmit SNR at the BS above which the underlaid D2D communication will degrade the system rate. We then particularize on the small cell setting where all users are closely located. In the small cell scenario, we show that the relationship between the distance of the D2D transmitting link and that of the D2D interfering link to the cellular user determines whether the D2D communication can enhance the systemachievable rate. Numerical results are provided to verify these results.

Analysis of the Alamouti STBC MIMO System With Spatial Division Multiplexing Over the Rayleigh Fading Channel

The Alamouti space-time block coding (STBC) multiple input multiple output (MIMO) system with spatial division multiplexing (SDM) is different from the pure SDM MIMO system in transmitting groups of Alamouti STBC symbols. Because of the Alamouti STBC, the zero-forcing with successive interference cancellation (ZF-SIC) detector for this MIMO system also detects one group of Alamouti STBC symbols in its one iteration. Previous analytical studies on this MIMO system were concentrated on the scenario of only four transmit antennas and did not take full advantage of the group-wise properties of the equivalent channel matrix due to Alamouti STBC. To deliver indepth analysis of this MIMO system with arbitrary number of transmit antennas, the ZF-SIC detection of the groups of Alamouti STBC symbols over the independent identically distributed Rayleigh fading channel is analyzed. Exact average block error probability of detecting all groups of Alamotui STBC symbols and its high signal-to-noise ratio (SNR) approximation are computed. Also, exact average group error probability of detecting each group of Alamotui STBC symbols and its high SNR approximation are computed. These analytical results are shown to agree with the simulation results.

Approximate Closed-Form Energy Efficient PA for MIMO Relaying Systems in the High SNR Regime

Energy efficient power coefficients at the relay are derived in a closed-form expression for the green multi-input-multi-output relaying system in the high signal-to-noise ratio (SNR) regime, where the objective is to maximize the energy efficiency (EE), which is defined by the ratio of the spectral efficiency (SE) to total power consumption, with a minimum SE requirement under practical power consumption models. In particular, we derive closed-form solutions using the high SNR approximation, which turn out to be different from the water-filling solution. Simulation results show that the proposed solution nearly achieves the optimal EE in all SNR regimes.

Cognitive opportunistic relaying systems with mobile nodes: average outage rates and outage durations

In the existing literature about cognitive radio opportunistic relaying (CR-OR) systems, the first-order statistics such as outage probability are investigated widely. However, for the second-order statistics, such as average outage duration (AOD) and average outage rate (AOR), there is not open works, still. To obtain a comprehensive cognition on the behaviour of mobile communication systems, this study focuses on the second-order statistical properties of CR-OR systems. There are two CR-OR schemes considered, in which the canonical amplify-and-forward (AF) and reactive decode-and-forward (RDF) are employed, respectively. Since the equivalent end-to-end signal-to-noise ratio (SNR) of AF CR-OR is complicated such that it is very difficult to obtain the closed-form solution to AOR of AF CR-OR schemes, the high SNR approximation in AF CR-OR schemes is employed. For the two schemes, first the closed-form solutions to AORs and AODs are obtained by using appropriate mathematical proof. Based on the derivations, the comparison analyses about AORs and AODs of the two schemes are provided. The comparison results show that, under high SNR approximation, the AF CR-OR scheme achieves the same AOR and AOD as RDF CR-OR. Finally, the impact of system parameters on AORs and AODs is provided.

Sum Rate Analysis of Two-Way MIMO AF Relay Networks with Zero-Forcing

The sum rate of multiple-input multiple-output (MIMO) amplify-and-forward (AF) two-way relay networks (TWRNs) with zero-forcing (ZF) transmission is analyzed. Namely, (1) ZF at the two sources for transmission and reception and (2) ZF at the relay for transmission and reception, are treated. Specifically, the exact sum rate expressions and corresponding high signal-to-noise ratio (SNR) approximations are derived for uncorrelated and min-semi-correlated (i.e., correlation exists only at the minimum antenna terminal) Rayleigh fading cases in closed-form. Moreover, the closed-form upper and lower bounds of the sum rate are derived for max-semi-correlated (i.e., correlation exists only at the maximum antenna terminal) and doubly-correlated Rayleigh fading cases. Notably, these sum rate bounds and high SNR approximations provide valuable insights into practical MIMO AF TWRN system-design and the maximum achievable spatial multiplexing gain. All the analyses are verified by using Monte-Carlo simulations.

Optimal-Switching Adaptive Modulation for Multiuser Relay Networks with Feedback Delays

The performance of optimal switching adaptive modulation for multiuser amplify-and-forward (AF) relay networks over Nakagami-m fading channel is studied. Moreover, we consider two types of communication: i) relay-assisted communication (RAC): the source transmits its message to best user via relay path, ii) selective communication (SC): the source decides whether to forward the source message to the best user via relay path or direct path by comparing the end-to-end instantaneous signal-to-noise ratio (SNR) at the best user, which is independent of modulation scheme. Specifically, multiuser diversity and adaptive discrete-rate five-mode M-ary quadrature amplitude modulation (M-QAM) with constant transmit power is employed with fixed and optimal switching thresholds. The optimization criterion for switching thresholds is the maximization of spectral efficiency subject to target bit-error-rate. In particular, the detrimental effect of feedback delays in multiuser opportunistic scheduling (which exploits multiuser diversity) and adaptive modulation is quantified. To this end, an exact and an upper bound of the end-to-end SNRs are obtained and used to derive the cumulative distribution function and probability density function for each case. Moreover, exact outage probabilities, and lower bounds for the outage probabilities and average bit error rates, and the average spectral efficiencies are derived in closed-form. Further, we also present the high SNR approximations for outage probabilities and BERs. We observe that, for a particular spectral efficiency, adaptive five-mode M-QAM with optimal switching outperforms fixed switching and provides approximately 2 dB and 2.5 dB gain in average SNR for RAC and SC, respectively. Monte-Carlo simulations are performed to validate the analytical results.

Performance Analysis of Macrodiversity MIMO Systems with MMSE and ZF Receivers in Flat Rayleigh Fading

Consider a multiuser system where an arbitrary number of users communicate with a distributed receive array over independent Rayleigh fading paths. The receive array performs minimum mean squared error (MMSE) or zero forcing (ZF) combining and perfect channel state information is assumed at the receiver. This scenario is well-known and exact analysis is possible when the receive antennas are located in a single array. However, when the antennas are distributed, the individual links all have different average signal to noise ratio (SNRs) and this is a much more challenging problem. In this paper, we provide approximate distributions for the output SNR of a ZF receiver and the output signal to interference plus noise ratio (SINR) of an MMSE receiver. In addition, simple high SNR approximations are provided for the symbol error rate (SER) of both receivers assuming M-PSK or M-QAM modulations. These high SNR results provide array gain and diversity gain information as well as a remarkably simple functional link between performance and the link powers.

Performance Analysis of Dual-User Macrodiversity MIMO Systems with Linear Receivers in Flat Rayleigh Fading

The performance of linear receivers in the presence of co-channel interference in Rayleigh channels is a fundamental problem in wireless communications. Performance evaluation for these systems is well-known for receive arrays where the antennas are close enough to experience equal average SNRs from a source. In contrast, almost no analytical results are available for macrodiversity systems where both the sources and receive antennas are widely separated. Here, receive antennas experience unequal average SNRs from a source and a single receive antenna receives a different average SNR from each source. Although this is an extremely difficult problem, progress is possible for the two-user scenario. In this paper, we derive closed form results for the probability density function (pdf) and cumulative distribution function (cdf) of the output signal to interference plus noise ratio (SINR) and signal to noise ratio (SNR) of minimum mean squared error (MMSE) and zero forcing (ZF) receivers in independent Rayleigh channels with arbitrary numbers of receive antennas. The results are verified by Monte Carlo simulations and high SNR approximations are also derived. The results enable further system analysis such as the evaluation of outage probability, bit error rate (BER) and capacity.

Regularized Transceiver Designs for Multi-User MIMO Interference Channels

For multi-user interference channels (IC), an altruistic approach based on the zero-forcing (ZF) criterion shows the near-optimal performance at high signal-to-noise ratio (SNR), whereas its performance at low SNR becomes poor compared to a simple egoistic algorithm (selfish beamforming). Thus, balancing between the egoism and the altruism has been an important issue to achieve good sum-rate performance at overall SNR regime. In this paper, we propose a new approach for enhancing the performance by regularizing the ZF based transceivers. To this end, we start with investigating efficient ZF transceivers for 2-user and 3-user ICs. First, coordinated spatial multiplexing (CSM) is proposed for 2-user IC. For the 3-user case, it is shown that the enhanced interference alignment (E-IA) introduced in our previous work is the optimal ZF transceivers in terms of the sum-rate performance. Next, to improve the performance of the CSM and E-IA schemes at low SNR, we propose a non-iterative regularization method under the high SNR approximation. The distributed implementation of the proposed regularization method is also presented where each node is able to compute its own precoding or decoding matrix using local channel state information. From simulations, it is observed that the proposed regularized design outperforms the conventional schemes in overall SNR regime. Also, we confirm that our distributed approach provides a substantial performance gain over the conventional distributed scheme with reduced computational complexity.

Optimum antenna configuration in MIMO systems: a differential evolution based approach

AbstractIn this paper, we address the problem of determining the optimum antenna configuration for a multi‐input multi‐output (MIMO) system at any given signal‐to‐noise ratio (SNR). We used two‐level differential evolution (DE) algorithm that finds both an appropriate expression among a set of candidate expressions within the list of the optimization software used, and the parameter values (coefficients) belonging to the selected expression. The results of the proposed expression are compared with the results of high SNR approximation, asymptotic approach and optimum antenna number ratios. It is shown that the numerical outcomes produced by the new expression exhibit very good agreement with the optimum antenna number ratios, and this agreement is almost independent of the specific value of SNR. Copyright © 2010 John Wiley & Sons, Ltd.

Tight performance bounds for two-way opportunistic amplify-and-forward wireless relaying networks with TDBC protocols

Abstract Based on amplify-and-forward network coding (AFNC) protocol, the outage probability and ergodic capacity of two-way network coding opportunistic relaying (TWOR-AFNC) systems are investigated as well as the corresponding closed-form solutions. For the TWOR-AFNC systems, it is investigated under two scenarios, namely, the TWOR-AFNC systems without direct link (TWOR-AFNC-Nodir) and the TWOR-AFNC systems with direct link (TWOR-AFNC-Dir). First, we investigate TWOR-AFNC-Nodir systems by employing the approximate analysis in high SNR, and obtain closed-form solutions to the cumulative distribution function (CDF) and the probability density function (PDF) of the instantaneous end-to-end signal-to-noise ratio (SNR) with very simple expressions. The derived simple expressions are given by defining an equivalent variable ω eq-k (θ), 2 ≤ θ ≤ 3. When θ = 2, the derived results are the tight lower bounds to CDF and PDF. The sequent simulation demonstrates that the derived tight lower bounds are also very effective over the entire SNR region though which the results are derived in high SNR approximation. Then, with the derived tight closed-form lower bound solutions (θ = 2) in TWOR-AFNC-Nodir systems, we investigate TWOR-AFNC-Dir systems as well as the overall comparison of the outage probability and the ergodic capacity between the two system models. The comparison analysis performed over path loss model basis shows that, in urban environment, due to utilizing the direct link the TWOR-AFNC-Dir outperform considerably the TWOR-AF-Nodir systems. However, when the value of path loss exponent is relatively large, the achievable gain is very small and the direct link can be omitted. In this case, the TWOR-AFNC-Dir model can be displaced by TWOR-AFNC-Nodir model having lower implementation complexity.

Amplify-and-Forward Relaying with Optimal and Suboptimal Transmit Antenna Selection

Antenna selection schemes offer a good complexity versus performance tradeoff for amplify-and-forward (AF) relay network implementation. In this paper, we consider a dual-hop channel state information assisted AF relay network with a direct source-destination link and investigate the performance of two antenna selection schemes (one optimal and another suboptimal). We derive analytical expressions for the systems' rate outage probabilities and the average bit error rate (BER) that match perfectly with simulation based results in the medium to high signal-to-noise ratio (SNR) regimes. We also investigate the channel capacity of the two schemes by deriving tight upper bounds. In order to gain further insights, simple high SNR approximations for the outage probability and the average BER have also been developed. Our theoretical analysis shows that the performance gap between the optimal and suboptimal schemes largely diminishes in the high SNR regime by increasing the number of antennas at the source. Since the suboptimal scheme has a near optimal performance as well as low signaling overhead compared to the optimal scheme, it seems to be a promising solution for implementing future cellular networks expecting to support relay based communications.

Impact of Antenna Correlation on a New Dual-Hop MIMO AF Relaying Model

A novel system model is proposed for the dual-hop multiple-input multiple-output amplify-andforward relay networks, and the impact of antenna correlation on the performance is studied. For a semiarbitrary correlated source-relay channel and an arbitrary correlated relay-destination channel, the complementary cumulative distribution function (CCDF) and the moment-generating function (MGF) approximations of the end-to-end signal-to-noise ratio (SNR) are derived. The outage probability, the average symbol error rate (SER), and the ergodic capacity approximations are also derived. Two special cases are treated explicitly: (1) dual-antenna relay and multiple-antenna destination and (2) uncorrelated antennas at the relay and correlated antennas at the destination. For the first case, the CCDF, the MGF and the average SER of an upper bound of the end-to-end SNR are derived in closed-form. For the second case, the CCDF, the MGF, the average SER, and the moments of SNR are derived in closed-form; as well, the high SNR approximations for the outage probability and the average SER are derived, and the diversity gain and coding gain are developed. Extensive numerical results and Monte Carlo simulation results are presented to verify the analytical results and to quantify the detrimental impact of antenna correlations on the system performance.

Analysis of area under the ROC curve of energy detection

A simple figure of merit to describe the performance of an energy detector is desirable. The area under the receiver operating characteristic (ROC) curve, denoted (AUC), is such a measure, which varies between 1/2 and 1. If the detector's performance is no better than flipping a coin, then the AUC is 1/2 , and it increases to one as the detector performance improves. However, in the wireless literature, the AUC measure has gone unnoticed. In this paper, to address this gap, we comprehensively analyze the AUC of an energy detector with no-diversity reception and with several popular diversity schemes. The channel model is assumed to be Nakagami-m fading. First, the average AUC is derived for the case of no-diversity reception. Second, the average AUC is derived for diversity reception cases including maximal ratio combining (MRC), square-law combining (SLC) and selection combining (SC). Further, for Rayleigh fading channels, the impacts of channel estimation errors and fading correlations are analyzed. High SNR (signal-to-noise ratio) approximations and the detection diversity gain are also derived. The analytical results are verified by numerical computations and by Monte-Carlo simulations.