Channel Hardening Research Articles

Selection Based List Detection With Approximate Matrix Inversion for Large-Scale MIMO Systems

Large-scale multiple-input multiple-output (LS-MIMO) technology constitutes a foundation for next generation wireless communication systems. Detection techniques are a key issue for practical applications of LS-MIMO. Selection-based list detection is an attractive approach for LS-MIMO systems because of its massively parallelizable nature. In this paper, we propose an improved selection-based list detection algorithm that exploits the channel hardening phenomenon, making it suitable for LS-MIMO. We start by introducing a low latency approximate inversion technique for large dimensional complex matrices, which can be used not only in selection-based list detection but also in many other LS-MIMO detection algorithms. The proposed matrix inversion technique is integrated into linear as well as selection-based list detection algorithms for lower latency and deeper parallelism. Then our analysis of the impact of channel hardening on selection-based list detection motivates the use of an improved ordering scheme for the successive interference cancellation sub-detector. Finally, we compare our improved selection-based list detector with other two state-of-art low complexity LS-MIMO detection algorithms, namely, multistage likelihood ascent search (LAS) and message passing detection (MPD). Computer simulations show that the proposed selection-based list detector performs better than multistage LAS and has just a small fraction of dB performance loss compared with MPD. Because of its good performance and parallelizable nature, the proposed algorithm offers an attractive alternative for detection in practical LS-MIMO systems.

Benefits of Beamforming Training Scheme in Distributed Large-Scale MIMO Systems

The downlink training yields rather modest performance gains due to the high degree of channel hardening effect in co-located large-scale multi-input multi-output (MIMO) systems. However, in distributed large-scale MIMO systems, the potential benefits of the downlink training become larger, since there is a high probability that each user is very close to only a part of remote antenna units and is effectively served by them which results in less channel hardening effect. In this paper, we study the benefits of the beamforming training (BT) scheme (users estimate the channel state information by using the received training symbols, which are processed by linear beamforming in advance) in distributed large-scale MIMO systems. We derive accurate and tractable closed-form analytical expressions for the spectral efficiency (SE) of the BT scheme in distributed large-scale MIMO systems with maximum ratio transmission and zero-forcing (ZF) beamforming. Based on these expressions, we analyze the benefits of the BT scheme and investigate how the number of transmit antennas and the length of coherence interval affect the SE of the BT scheme in the co-located and distributed large-scale MIMO systems. The analytical results show that the BT scheme is more suitable for distributed large-scale MIMO systems with ZF beamforming, and a less number of transmit antennas and longer coherence interval can improve the performance gain of BT scheme.

Wireless Power Transfer-Based Multi-Pair Two-Way Relaying With Massive Antennas

In this paper, we study a multi-pair two-way relay network consisting of two groups of user equipments (UEs), who want to exchange information through a common relay equipped with massive antennas. In the multiple access phase, the UEs transmit information to the relay using the energy harvested in the last time block, and the relay decodes information using zero-forcing (ZF) or maximal ratio combining (MRC) technique. In the broadcasting phase, the relay performs simultaneous wireless information and power transfer (SWIPT), and each UE receives energy and information using the power-splitting scheme. Due to the channel hardening effect of the large-scale antenna array, the harvested energy of each UE in each time block is asymptotically constant. Based on the derived achievable rates of UEs, a multi-objective optimization problem (MOOP) is formulated to maximize the achievable rates of all the pairs. Through solving the MOOP, the power-splitting ratios of UEs can be determined in closed-form for the ZF-based relaying. For the MRC-based relaying, a two-stage iterative Pareto improvement algorithm is proposed to achieve the Pareto optimality. Simulation results are presented to validate our theoretical analysis and verify the efficiency of our proposed algorithm in improving the system rate.

Large-Scale Multiantenna Multisine Wireless Power Transfer

Wireless Power Transfer (WPT) is expected to be a technology reshaping the landscape of low-power applications such as the Internet of Things, Radio Frequency identification (RFID) networks, etc. Although there has been some progress towards multi-antenna multi-sine WPT design, the large-scale design of WPT, reminiscent of massive MIMO in communications, remains an open challenge. In this paper, we derive efficient multiuser algorithms based on a generalizable optimization framework, in order to design transmit sinewaves that maximize the weighted-sum/minimum rectenna output DC voltage. The study highlights the significant effect of the nonlinearity introduced by the rectification process on the design of waveforms in multiuser systems. Interestingly, in the single-user case, the optimal spatial domain beamforming, obtained prior to the frequency domain power allocation optimization, turns out to be Maximum Ratio Transmission (MRT). In contrast, in the general weighted sum criterion maximization problem, the spatial domain beamforming optimization and the frequency domain power allocation optimization are coupled. Assuming channel hardening, low-complexity algorithms are proposed based on asymptotic analysis, to maximize the two criteria. The structure of the asymptotically optimal spatial domain precoder can be found prior to the optimization. The performance of the proposed algorithms is evaluated. Numerical results confirm the inefficiency of the linear model-based design for the single and multi-user scenarios. It is also shown that as nonlinear model-based designs, the proposed algorithms can benefit from an increasing number of sinewaves.

3D MIMO Outdoor-to-Indoor Propagation Channel Measurement

The 3-D multiple-input multiple-output (3-D MIMO) systems have received great interest recently because of the spatial diversity advantage and capability for full-dimensional beamforming, making them promising candidates for practical realization of massive MIMO. In this paper, we present a low-cost test equipment (channel sounder) and post-processing algorithms suitable for investigating the 3-D MIMO channels as well as the results from a measurement campaign for obtaining elevation and azimuth characteristics in an outdoor-to-indoor (O2I) environment. Due to limitations in available antenna switches, our channel sounder consists of a hybrid switched/virtual cylindrical array with effectively 480 antenna elements at the base station. The virtual setup increased the overall MIMO measurement duration, thereby introducing phase drift errors in the measurements. Using reference antenna measurements, we estimate and correct for the phase errors during post-processing. We provide the elevation and azimuth angular spreads for the measurements done in an urban macro-cellular and urban micro-cellular environments, and study their dependence on the user equipment (UE) height. Based on the measurements done with UE placed on different floors, we study the feasibility of separating users in the elevation domain. The measured channel impulse responses are also used to study the channel hardening aspects of the massive MIMO and the optimality of the maximum ratio combining receiver.

No Downlink Pilots Are Needed in TDD Massive MIMO

We consider the Massive Multiple-Input Multiple-Output downlink with maximum-ratio and zero-forcing processing and time-division duplex operation. To decode, the users must know their instantaneous effective channel gain. Conventionally, it is assumed that by virtue of channel hardening, this instantaneous gain is close to its average and hence that users can rely on knowledge of that average (also known as statistical channel information). However, in some propagation environments, such as keyhole channels, channel hardening does not hold. We propose a blind algorithm to estimate the effective channel gain at each user, that does not require any downlink pilots. We derive a capacity lower bound of each user for our proposed scheme, applicable to any propagation channel. Compared with the case of no downlink pilots (relying on channel hardening), and compared with training-based estimation using downlink pilots, our blind algorithm performs significantly better. The difference is especially pronounced in environments that do not offer channel hardening.

Design and Performance Analysis of Noncoherent Detection Systems With Massive Receiver Arrays

Harvesting the gain of a large number of antennas in a mmWave band has mainly been relying on the costly operation of channel state information (CSI) acquisition and cumbersome phase shifters. Recent works have started to investigate the possibility to use receivers based on energy detection (ED), where a single data stream is decoded based on the channel and noise energy. The asymptotic features of the massive receiver array lead to a system where the impact of the noise becomes predictable due to a noise hardening effect. This in effect extends the communication range compared to the receiver with a small number of antennas, as the latter is limited by the unpredictability of the additive noise. When the channel has a large number of spatial degrees of freedom, the system becomes robust to imperfect channel knowledge due to channel hardening. We propose two detection methods based on the instantaneous and average channel energy, respectively. Meanwhile, we design the detection thresholds based on the asymptotic properties of the received energy. Differently from existing works, we analyze the scaling law behavior of the symbol-error-rate (SER). When the instantaneous channel energy is known, the performance of ED approaches that of the coherent detection in high SNR scenarios. When the receiver relies on the average channel energy, our performance analysis is based on the exact SER, rather than an approximation. It is shown that the logarithm of SER decreases linearly as a function of the number of antennas. Additionally, a saturation appears at high SNR for PAM constellations of order larger than two, due to the uncertainty on the channel energy. Simulation results show that ED, with a much lower complexity, achieves promising performance both in Rayleigh fading channels and in sparse channels.

Analysis of Massive MIMO-Enabled Downlink Wireless Backhauling for Full-Duplex Small Cells

Using tools from stochastic geometry, we develop a framework to model the downlink rate coverage probability of a user in a given small cell network (SCN) with massive MIMO-enabled wireless backhauls. The considered SCN is composed of a mixture of small cells that are configured in either in-band or out-of-band backhaul modes with a certain probability. The performance of the user in the considered hierarchical network is limited by several sources of interference such as the backhaul interference, small cell base station (SBS)-to-SBS interference and the SI. Moreover, due to the channel hardening effect in massive MIMO, the backhaul links experience long term channel effects only, whereas the access links experience both the long term and short term channel effects. Consequently, the developed framework is flexible to characterize different sources of interference while capturing the heterogeneity of the access and backhaul channels. In specific scenarios, the framework enables deriving closed-form coverage probability expressions. Under perfect backhaul coverage, the simplified expressions are utilized to optimize the proportion of in-band and out-of-band small cells in the SCN in closed-form. Finally, few remedial solutions are proposed that can potentially mitigate the backhaul interference and in turn improve the performance of in-band FD wireless backhauling. Numerical results investigate the scenarios in which in-band wireless backhauling is useful and demonstrate that maintaining a correct proportion of in-band and out-of-band FD small cells is crucial in wireless backhauled SCNs.

WiFlix: Adaptive Video Streaming in Massive MU-MIMO Wireless Networks

We consider the problem of simultaneous on-demand streaming of stored video to multiple users in a multicell wireless network where multiple unicast streaming sessions are run in parallel and share the same frequency band. Each streaming session is formed by the sequential transmission of video “chunks,” such that each chunk arrives into the corresponding user playback buffer within its playback deadline. We formulate the problem as a network utility maximization (NUM) where the objective is to fairly maximize users’ video streaming quality of experience (QoE) and then derive an iterative control policy using Lyapunov optimization, which solves the NUM problem up to any level of accuracy and yields an online protocol with control actions at every iteration decomposing into two layers interconnected by the users’ request queues : 1) a video streaming adaptation layer reminiscent of dynamic adaptive streaming over HTTP (DASH), implemented at each user node; and 2) a transmission scheduling layer where a max-weight scheduler is implemented at each base station. The proposed chunk request scheme is a pull strategy where every user opportunistically requests video chunks from the neighboring base stations and dynamically adapts the quality of its requests based on the current size of the request queue. For the transmission scheduling component, we first describe the general max-weight scheduler and then particularize it to a wireless network where the base stations have multiuser multiple-input multiple-output (MU-MIMO) beamforming capabilities. We exploit the channel hardening effect of large-dimensional MIMO channels (massive MIMO) and devise a low complexity user selection scheme to solve the underlying combinatorial problem of selecting user subsets for downlink beamforming, which can be easily implemented and run independently at each base station. Furthermore, through simulations, we show that deploying MU-MIMO significantly improves video streaming performance and also that the proposed cross-layer approach is able to serve users more fairly than a baseline scheme representative of current systems running independently designed protocol layers.

User Association and Interference Management in Massive MIMO HetNets

Two key traits of 5G cellular networks are much higher base station (BS) densities—especially in the case of low-power BSs—and the use of massive MIMO at these BSs. This paper explores how massive MIMO can be used to jointly maximize the offloading gains and minimize the interference challenges arising from adding small cells. We consider two interference management approaches: joint transmission (JT) with local precoding, where users are served simultaneously by multiple BSs without requiring channel state information exchanges among cooperating BSs, and resource blanking, where some macro BS resources are left blank to reduce the interference in the small cell downlink. A key advantage offered by massive MIMO is channel hardening, which enables to predict instantaneous rates a priori . This allows us to develop a unified framework, where resource allocation is cast as a network utility maximization (NUM) problem, and to demonstrate large gains in cell-edge rates based on the NUM solution. We propose an efficient dual subgradient based algorithm, which converges towards the NUM solution. A scheduling scheme is also proposed to approach the NUM solution. Simulations illustrate more than 2x rate gain for 10th percentile users vs. an optimal association without interference management.

BER Performance Analysis and Comparison for Large Scale MIMO Receiver

Objective: Multiple Input Multiple Output (MIMO) low complexity CHEMP (Channel Hardening Exploiting Message Passing) receiver which utilizes the channel hardening in the large scale MIMO channel to reduce the complexity. Methods: The Channel Hardening refers that the off diagonal elements of HTH matrix become progressively weaker than the diagonal elements because of the channel gain matrix H size increases. It is used for detection and estimation. The proposed receiver uses Message Passing Detection (MPD) algorithm and the estimation HTH matrix. Findings: Hence, the proposed receiver gives better performance than the Minimum Mean Square Error (MMSE) and Subspace Marginalization with Interference Suppression (SUMIS) detectors since the MPD detection algorithm uses only the matrix multiplication and it does not need the matrix inversion. Improvements: The optimized Low Density Parity Check (LDPC) codes are used to provide the considerable improvement than LDPC cods.

Ergodic Capacity Analysis of Full-duplex Mimo Relay Channel using Tracy-Widom Distribution with Processing Delay

We explore a full-duplex technique in wireless communication particularly for relay networks. We consider the relay to operate in full-duplex, which occurs when transmission and reception are conducted in the same channel. We investigate potential benefits of full-duplex technique in relay networks, which uses multiple antennas for transmission and reception combined with the Amplify-Forward (AF) scenario. We study the effects of multiple antennas in terms of relay capacity. We derive an ergodic capacity expression using the Tracy-Widom distribution. Using Singular Value Decomposition (SVD) and perfect Channel State Information (CSI), we investigate these three scenarios: First, we consider the relay to have an antenna larger than that of both source and destination. Second, we consider both relay and destination to have an antenna larger than that of the source. Third, we consider both relay and source to have antenna larger than that of the destination. We show the results that the capacity of the relay with a fullduplex technique is almost twice the capacity of an half-duplex. We show that increasing the number of destination antennas is not help much when one of the source antennas is small. Moreover, the capacity decreases due to a channel hardening effect, when the number of destination antennas is larger than that of the source.

Channel Hardening-Exploiting Message Passing (CHEMP) Receiver in Large-Scale MIMO Systems

In this paper, we propose a multiple-input multiple-output (MIMO) receiver algorithm that exploits channel hardening that occurs in large MIMO channels. Channel hardening refers to the phenomenon where the off-diagonal terms of the H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sup> H matrix become increasingly weaker compared to the diagonal terms as the size of the channel gain matrix H increases. Specifically, we propose a message passing detection (MPD) algorithm which works with the real-valued matched filtered received vector (whose signal term becomes H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sup> Hx, where x is the transmitted vector), and uses a Gaussian approximation on the off-diagonal terms of the H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sup> H matrix. We also propose a simple estimation scheme which directly obtains an estimate of H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sup> H (instead of an estimate of H), which is used as an effective channel estimate in the MPD algorithm. We refer to this receiver as the channel hardening-exploiting message passing (CHEMP) receiver. The proposed CHEMP receiver achieves very good performance in large-scale MIMO systems (e.g., in systems with 16 to 128 uplink users and 128 base station antennas). For the considered large MIMO settings, the complexity of the proposed MPD algorithm is almost the same as or less than that of the minimum mean square error (MMSE) detection. This is because the MPD algorithm does not need a matrix inversion. It also achieves a significantly better performance compared to MMSE and other message passing detection algorithms using MMSE estimate of H. Further, we design optimized irregular low density parity check (LDPC) codes specific to the considered large MIMO channel and the CHEMP receiver through EXIT chart matching. The LDPC codes thus obtained achieve improved coded bit error rate performance compared to off-the-shelf irregular LDPC codes.

Phase compensation communication technique against time reversal for ultra‐wideband channels

Phase compensation (PC) prefiltering is experimentally investigated for multipath channels over the frequency band spanning 2–12 GHz, a topic which to the best of the authors knowledge has not been studied in the literature on ultra-wideband (UWB) communications. The authors emphasis is to assess the capabilities of PC compared to time reversal (TR) prefilters over indoor UWB channels regarding multipath suppression, channel hardening, noise sensitivity and high-speed data transmission. Experiments were carried out for PC and TR prefilters in both line-of-sight (LOS) and non-LOS (NLOS) environments. The multipath compression effectiveness is characterised by computing the root-mean-square delay spread and peak-to-average power ratio for actual measured channels and for the IEEE 802.15.4(a) UWB model. The authors study suggests PC outperforms TR considerably in mitigating the multipath channel dispersion. Bit-error-rate (BER) curves have been simulated for data rates in the range of 125–4000 Mbps based on the measured channel responses. The BER simulations suggest that while the TR performance is prohibitively saturated by its residual intersymbol interference for data rates of 500 Mbps and above (especially in NLOS), PC can be used for high-speed data transmissions as fast as 2 Gbps in both LOS and NLOS environments.

Spectral efficiency analysis of rate-adaptive user selection diversity in orthogonal space time block coding multiple-input multiple-output systems with antenna selection

In this study, the performance of user selection diversity for rate-adaptive multiuser multiple-input multiple-output (MIMO) systems employing orthogonal space time block coding (OSTBC) is analysed and evaluated. An antenna selection scheme is used to overcome the drawback of channel hardening effects in multiuser MIMO systems. Closed-form expressions for the average spectral efficiency and outage probability of the system are derived. Using numerical evaluations the considered schemes are compared in terms of outage probability and spectral efficiency. The effects of antenna correlation at the receiver ends on the performance of the system are analysed and evaluated, indicating that spatial correlation may be beneficial for the spectral efficiency of the multiuser OSTBC MIMO systems employing user selection.

Asymptotic Ergodic Capacity Analysis for MIMO Amplify-and-Forward Relay Networks

In this letter, we analyze asymptotic ergodic capacity of MIMO amplify-and-forward (AF) relaying systems which employ linear processing at the relay. By exploiting the asymptotic results for eigenvalue distributions, we derive the ergodic capacity in various asymptotic antenna regimes as a closed-form expression with arbitrary system parameters. The analyzed results demonstrate that increasing the number of source antennas causes the capacity shrink phenomenon which is analogous to the channel hardening effect in multi-user MIMO systems. Although we assume asymptotically large antennas to obtain the closed-form expressions, simulation results show that our derived expressions are surprisingly accurate even with the moderate number of antennas, and thus can serve for analyzing practical MIMO relay networks.

Experimental Investigation on Time Reversal Precoding for Space–Time Focusing in Wireless Communications

This paper presents the results of indoor wideband measurements investigating the space-time properties of wireless signal transmission with online time-reversal (TR) precoding. The measurements were conducted using a new TR wideband multiple-input-multiple-output (MIMO) channel sounder operating at 2.45 GHz with a bandwidth of 240 MHz. Both line-of-sight (LOS) and non-line-of-sight (NLOS) propagation conditions were investigated. Spatial focusing and temporal compression can clearly be seen with TR precoding, which may be useful for future wireless system applications. Channel hardening due to TR is also observed under both LOS and NLOS conditions.

Rate of Channel Hardening of Antenna Selection Diversity Schemes and Its Implication on Scheduling

For a multiple-antenna system, we find a simple and accurate expression for the asymptotic distribution of the antenna selection gain when the transmitter selects the transmit antenna with the strongest channel. We use this to estimate the underlying channel capacity distributions and obtain the approximate ergodic capacity. This estimate is compared with upper and lower bounds. This analysis demonstrates that unlike multiple-input/multiple-output (MIMO) systems, the channel for antenna selection systems hardens at a slower rate, and thus a significant multiuser scheduling gain can exist-Theta (1/logm) for channel selection as opposed to Theta (1/radicm) for MIMO, where m is the number of transmit antennas.

Multiple-Antenna Channel Hardening and Its Implications for Rate Feedback and Scheduling

Wireless data traffic is expected to grow over the next few years and the technologies that will provide data services are still being debated. One possibility is to use multiple antennas at base stations and terminals to get very high spectral efficiencies in rich scattering environments. Such multiple-input/multiple-output (MIMO) channels can then be used in conjunction with scheduling and rate-feedback algorithms to further increase channel throughput. This paper provides an analysis of the expected gains due to scheduling and bits needed for rate feedback. Our analysis requires an accurate approximation of the distribution of the MIMO channel mutual information. Because the exact distribution of the mutual information in a Rayleigh-fading environment is difficult to analyze, we prove a central limit theorem for MIMO channels with a large number of antennas. While the growth in average mutual information (capacity) of a MIMO channel with the number of antennas is well understood, it turns out that the variance of the mutual information can grow very slowly or even shrink as the number of antennas grows. We discuss implications of this "channel-hardening" result for data and voice services, scheduling, and rate feedback. We also briefly discuss the implications when shadow fading effects are included.