Impact Of Antenna Correlation Research Articles

Impact of antenna correlation on the physical layer security of cooperative relaying with OSTBC system

This study presents an analysis for evaluating the physical layer (PHY) security performance of a two-hop amplify-and-forward cooperative relaying system employing Alamouti orthogonal space–time block coding (OSTBC) in the presence of an eavesdropper, where the transmit antennas for OSTBC are assumed to be spatially correlated. It is also assumed that the authorised main channels as well as the non-authorised eavesdropper channels follow Rayleigh fading distribution. Closed-form mathematical expressions are derived for three performance metrics for evaluating the PHY security, namely the probability of non-zero secrecy capacity, the secrecy outage probability, and the average secrecy capacity. Using the extensive numerical results obtained from the derived mathematical expressions, the impact of antennas correlation on the PHY secrecy performance of the system is studied and evaluated under different parameters. It is also shown that the antennas correlation corresponding to the main channels has more impact than the antennas correlation corresponding to the eavesdropper channels.

Impact of Antenna Correlation on Full-Duplex Two-Way Massive MIMO Relaying Systems

This paper investigates the impact of antenna correlation on full duplex massive multiple-input multiple-output (MIMO) two-way relaying systems. To be general, all nodes in the system are equipped with multiple antennas and arbitrary antenna correlation is considered. Deterministic equivalent of the achievable sum-rate is first given, which enables the derivation of the asymptotic sum-rate when the number of relay antennas is large. The impact of antenna correlation on the asymptotic sum-rate is then thoroughly analyzed. The results reveal that with a large number of relay antennas, the asymptotic sum-rate is independent of the antenna correlation at the relay’s transmitter side, however it is Schur-concave with respect to the eigenvalue vectors of the involved antenna correlation matrices at both the users’ transceiver sides and the relay’s receiver side. In other words, the antenna correlations at both the users’ transceiver sides and the relay’s receiver side have detrimental effects on the sum-rate. Moreover, the antenna correlation at the users is more significant to the asymptotic sum-rate than that at the relay. The analysis is general and can be easily reduced to consider half-duplex and/or one-way massive MIMO relaying systems. Numerical results are finally provided to validate the analysis. It is also shown that a larger number of user antennas may not always lead to a higher sum-rate, and thus proper selection of the number of user antennas is necessary to maximize the sum-rate.

Power Scaling of Full-Duplex Two-Way Massive MIMO Relay Systems With Correlated Antennas and MRC/MRT Processing

In this paper, the performance of full-duplex (FD) two-way massive multiple-input multiple-output (MIMO) relay systems is analyzed. One popular linear relaying scheme, i.e., maximum ratio combining/maximum ratio transmission relaying, is particularly investigated. Different from prior analyses, multi-pair of MIMO users and antenna correlation at both the relay and the users are considered. Asymptotic sum-rate under a general case is first derived. Four special power scaling cases are then discussed and the corresponding asymptotic sum-rates are derived in simple forms with clear insights. The analytical results clearly quantify the impacts of self-loop interference, intra-group interference and antenna correlation, and discover the power scaling laws under various cases. It is found that the transmission powers at both the MIMO users and the relay can be scaled down inversely proportional to the number of antennas at the relay while maintaining a desirable sum-rate when the number of antennas at the relay grows large. The FD two-way massive MIMO relay system is finally compared with the half-duplex (HD) counterpart. It is revealed that under two special power scaling cases, the FD system can achieve double sum-rate when compared with the HD system. However, under the other two power scaling cases, self-loop interference and intra-group interference degrade the asymptotic sum-rate and the FD system may perform worse than the HD system. The maximum allowable self-loop interference for the FD system to outperform the HD system is given explicitly. In addition, the impact of antenna correlation at the users and the relay is analyzed. The results show that the antenna correlation at the users has complicate impact on the sum-rate, while the antenna correlation at the relay may not affect the sum-rate under certain power scaling cases.

Wireless Powered Dual-Hop Multi-Antenna Relaying Systems: Impact of CSI and Antenna Correlation

This paper investigates the impact of the channel state information (CSI) and antenna correlation at the multi-antenna relay on the performance of wireless powered dual-hop amplify-and-forward relaying systems. Depending on the available CSI at the relay, two different scenarios are considered, namely, instantaneous CSI and statistical CSI where the relay has access only to the antenna correlation matrix. Adopting the power-splitting architecture, we present a detailed performance study for both cases. Closed-form analytical expressions are derived for the outage probability and ergodic capacity. In addition, simple high signal-to-noise ratio (SNR) outage approximations are obtained. Our results show that, antenna correlation itself does not affect the achievable diversity order, the availability of CSI at the relay determines the achievable diversity order. Full diversity order can be achieved with instantaneous CSI, while only a diversity order of one can be achieved with statistical CSI. In addition, the transmit antenna correlation and receive antenna correlation exhibit different impacts on the ergodic capacity. Moreover, the impact of antenna correlation on the ergodic capacity also depends heavily on the available CSI and operating SNR.

On the Outage Probability of MIMO Full-Duplex Relaying: Impact of Antenna Correlation and Imperfect CSI

This paper analyzes the performance of multiple-input multiple-output (MIMO) full-duplex (FD) relaying systems, where the source and destination nodes are equipped with single antenna and communicate via a dual-hop amplify-and-forward (AF) relay with multiple receive and transmit antennas. The system performance due to practical wireless transmission impairments of spatial fading correlation and imperfect channel state information (CSI) is investigated. At the relay, the loopback self-interference (LI) is mitigated by using the receive zero-forcing (ZF) precoding scheme, then steering the signal to the destination by using a maximum and ratio transmission (MRT) technique. To this end, new exact closed-form expressions for the outage probability are derived, where the case of arbitrary, exponential, and no correlations are considered. Meanwhile, for better system performance insights, simpler outage probability lower bound expressions are also included, through which the achievable diversity order of the receive ZF/MRT scheme is shown to be $\text{min}(N_{R}-1, N_{T})$ , where $N_{R}$ and $N_{T}$ are the number of relay receive and transmit antennas, respectively. Numerical results sustained by Monte Carlo simulations show the exactness and tightness of the proposed closed-form exact and lower bound expressions, respectively. In addition, it is seen that the outage probability performance of FD relaying outperforms that of the conventional half-duplex (HD) relaying at low to medium signal-to-noise ratio (SNR). However, at high SNR, the performance of HD relaying outperforms that of the FD relaying. Furthermore, in the presence of channel estimation errors, an outage probability error floor is seen at high SNR. Therefore, for optimum outage performance, hybrid relaying modes that switches between HD and FD relaying modes is proposed.

Performance Analysis and Power Allocation for Underlay Cognitive MIMO Relaying Networks with Transmit Antenna Selection Under Antenna Correlation

In this paper, we examine transmit antenna selection with receiver maximal ratio combining (TAS/MRC), and selection combining (TAS/SC) in underlay multiple-input multiple-output cognitive relay networks with decode-and-forward relaying protocol, considering optimal and suboptimal cases. The considered secondary user (SU) network consists of a source, a relay and a destination each equipped with multiple correlated antennas. On the other hand, the primary network is composed of L primary users (PU) destinations, each of which is equipped with multiple correlated antennas. The SU transmission power is limited to the minimum between the maximum allowable power for transmission and the maximum interference power allowed by the PU network. In the analysis, all the channel coefficients between the PU and SU networks and between the SU nodes are assumed to follow independent and identically distributed (i.i.d.) Rayleigh fading distribution. Hence, new exact closed-form expressions are derived to study the outage performance of the considered CRN system. Moreover, for the high SNR values, simple asymptotic expressions for the outage probability are obtained to get more insights on the characterization of the achievable diversity orders and coding gains. The impact of antenna correlation on the system outage probability is investigated for special correlation cases. To enhance SU network performance, a power allocation optimization problem is formulated to minimize the SU asymptotic outage probability by optimally distributing the SU power budget between the SU source and SU relay under the constraints of total allowable SU transmission power and maximum allowable PU interference limit. The derived analytical formulas herein are supported by numerical and simulation results to clarify the main contributions. The results show that although the antenna correlation harms the system coding gain, the considered system can still achieve a full diversity order. Also, The results show that although the outage performance of optimal case outperforms the suboptimal case, the optimal case is more complicated compared to the suboptimal one. Moreover, the optimal power allocation solutions enhance the system outage performance compared to equal distribution model.

Impact of Antenna Correlation on the BER Performance of a Cognitive Radio Network with Alamouti STBC

This letter presents an average bit error-rate (BER) performance analysis for spectrum sharing in a cognitive radio network in which primary and secondary users employ Alamouti space-time block coding (STBC) under correlated antennas over Rayleigh fading channels. Closed-form expressions are derived for the cumulative density function (CDF) of the secondary user's signal-to-noise-ratio (SNR) under correlated antennas. Then, closed-form expressions are derived for the average BER of the system with coherent modulation schemes as well as with noncoherent modulation techniques. Using numerical evaluation results from the derived expressions, verified by Monte Carlo simulations, the impacts of antenna correlation on the average BER of the system in different cases are evaluated.

On the Impact of Antenna Correlation and CSI Errors on the Pilot-to-Data Power Ratio

In systems employing pilot-symbol aided channel estimation, the pilot-to-data power ratio is known to have a large impact on performance. Therefore, previous works proposed methods setting the pilot power such that either the weighted sum of the mean squared error (MSE) of the estimated data symbols is minimized or the overall spectral efficiency (SE) is maximized. However, previous works did not take into account the impact of correlated antennas and channel state information (CSI) errors on the optimal pilot power setting. In this paper, we consider the uplink of a multiuser multiple-input multiple-output (MU MIMO) system employing a receiver that minimizes the MSE of the received data symbols in the presence of CSI errors and derive closed-form expressions for the MSE and the achievable SE. These expressions take into account the impact of antenna correlation and CSI errors, and are a function of pilot power and the number of receive antennas. The analytical and numerical results can help set the pilot power, minimizing the MSE in multiple antenna systems.

Channel Estimation and Optimal Training Design for Correlated MIMO Two-Way Relay Systems in Colored Environment

In this paper, while considering the impact of antenna correlation and the interference from neighboring users, we analyze channel estimation and training sequence design for multi-input multi-output (MIMO) two-way relay (TWR) systems. To this end, we propose to decompose the bidirectional transmission links into two phases, i.e., the multiple access (MAC) phase and the broadcasting (BC) phase. By considering the Kronecker-structured channel model, we derive the optimal linear minimum mean-square-error (LMMSE) channel estimators. The corresponding training designs for the MAC and BC phases are then formulated and solved to improve channel estimation accuracy. For the general scenario of training sequence design for both phases, two iterative training design algorithms are proposed that are verified to produce training sequences that result in near optimal channel estimation performance. Furthermore, for specific practical scenarios, where the covariance matrices of the channel or disturbances are of particular structures, the optimal training sequence design guidelines are derived. In order to reduce training overhead, the minimum required training length for channel estimation in both the MAC and BC phases are also derived. Comprehensive simulations are carried out to demonstrate the effectiveness of the proposed training designs.

Impact of Antenna Correlation on Optimum Improved Energy Detector in Cognitive Radio

This paper investigates the detection performance of an improved energy detector for a secondary user with spatially correlated multiple antennas. In an improved energy detector, an arbitrary positive power operation p replaces the squaring operation in a conventional energy detector, and the optimum value of p that gives the best detection performance may be different from 2. Firstly, for a given value of p, we derive closed-form expressions for the probability of detection and the probability of false alarm when antennas at the secondary user are exponentially correlated. We then find the optimum value of p for two different detection criteria−maximizing the probability of detection for a target probability of false alarm, and minimizing the probability of false alarm for a target probability of detection. We show that the optimum p is strongly dependent on system parameters like number of antennas, antenna correlation coefficient among multiple antennas, and average received signal-to-noise ratio (SNR). From results, we infer that, in low SNR regime, the effect of antenna correlation is less pronounced on the optimum p. Finally, we find the optimum values of p and threshold jointly that minimize the total error rate. key words: cognitive radio; correlation, improved energy detector, multiple antennas, total error rate

Impact of antenna correlation on the performance of partial relay selection

Abstract Antenna correlation is generally viewed as an obstacle to realize the desired performance of a wireless system. In this article, we investigate the performance of partial relay selection in the presence of antenna correlation. We consider both channel state information (csi)-assisted and fixed gain amplify-and-forward (AF) relay schemes. The source and the destination are equipped with multiple antennas communicating via the best first hop signal-to-noise ratio (SNR) relay. We derived the closed form expression for outage probability, average symbol error rate (SER) for both schemes. Further, an exact expression is derived for the ergodic capacity in the csi-assisted relay case and an approximated expression is considered for the fixed gain case. Moreover, we provide simple asymptotic results and show that the diversity order of the system remains unchanged with the effect of antenna correlation for both types of relay schemes.

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.

On the impact of antenna correlation in multi-user MIMO systems with rate constraints

This letter is concerned with multi-user multiple-input multiple-output (MIMO) systems with rate constraints. We show that antenna correlation at mobile units (MUs) is actually beneficial from the capacity point of view. This finding is useful in practice as minimizing the physical size of MUs is highly desirable, but it may result in antenna correlation.

Beneficial impact of antenna correlation at mobile units in MIMO MACs with covariance feedback

The impact of antenna correlation at mobile units (MUs) on the sum capacity of multiple-input multiple-output (MIMO) multiple access channels (MACs) with covariance feedback is investigated. In contrast to the common impression that correlation among antennas is detrimental, it is shown that antenna correlation at MUs is potentially beneficial for such channels.

Impact of Antenna Correlation on the Capacity of Multiantenna Channels

This paper applies random matrix theory to obtain analytical characterizations of the capacity of correlated multiantenna channels. The analysis is not restricted to the popular separable correlation model, but rather it embraces a more general representation that subsumes most of the channel models that have been treated in the literature. For arbitrary signal-to-noise ratios (SNR), the characterization is conducted in the regime of large numbers of antennas. For the low- and high-SNR regions, in turn, we uncover compact capacity expansions that are valid for arbitrary numbers of antennas and that shed insight on how antenna correlation impacts the tradeoffs among power, bandwidth, and rate.

Space–Time Turbo Trellis Codes for Two, Three, and Four Transmit Antennas

New space-time turbo trellis codes (ST turbo TCs) with 4-phase-shift keying (PSK) and 8-PSK for two, three, and four transmit antennas in slow and fast fading channels are proposed in this paper. The component codes of the space-time turbo schemes are constructed by choosing the feedforward coefficients to maximize the minimum squared Euclidean distance and the feedback coefficients to minimize the iterative decoding threshold. The performance of the proposed ST turbo TCs with various memory orders, transmit antennas, and interleaver structures is evaluated by simulation. It is shown that the new codes achieve better performance than previously designed codes. The impact of antenna correlation and imperfect channel estimation on the code performance is also discussed.