MIMO Multiple Access Channel Research Articles

Differential Coding for MAC Based Two-User MIMO Communication Systems

In this paper, we explain how to implement differential modulation in multiple access channel (MAC) based uplink two-user multiple-input multiple-output (MIMO) communication system. It is assumed that the users cannot exchange their information and transmit data over uplink MAC channels simultaneously in the same frequency band and without any orthogonal signatures (no CDMA). We derive two types of differential decoders for two-user MIMO MAC system namely 1) Partial differential decoder, 2) Heuristic based differential decoders. The partial differential decoder is able to avoid the knowledge of the channel gains of one user at the receiver for joint decoding of the data of both users. Whereas, the heuristic differential decoders are obtained heuristically and work without any channel knowledge of both users. For the heuristic differential decoder to work properly, the data of one user must be rotated before transmission. An upper bound of the pairwise error probability (PEP) is derived for the proposed scheme. The upper bound of the PEP is minimized for obtaining an optimized value of the rotation angle.

Linear Precoding for MIMO Multiple Access Channels with Finite Discrete Inputs

In this paper, we study linear precoding for multiple-input multiple-output (MIMO) multiple access channels (MAC) with finite discrete inputs. We derive the constellation-constrained capacity region for the MIMO MAC with an arbitrary number of users and find that the boundary can be achieved by solving the problem of weighted sum rate maximization with constellation and individual power constraints. Due to the non-concavity of the objective function, we obtain a set of necessary conditions for the optimization problem through Karush-Kuhn-Tucker analysis. To find the optimal precoding matrices for all users, we propose an iterative algorithm utilizing alternating optimization strategy. In particular, each iteration of the algorithm involves the gradient descent update with backtracking line search. Numerical results show that when inputs are digital modulated signals and the signal-to-noise ratio is in the medium range, our proposed algorithm offers considerably higher sum rate than non-precoding and the traditional method which maximizes Gaussian-input sum capacity. Furthermore, a low-density parity-check coded system with iterative detection and decoding for MAC is presented to evaluate the bit error rate (BER) performance of precoders. BER results also indicate that the system with the proposed linear precoder achieves significant gains over the non-precoding system and the precoder designed for Gaussian inputs.

On Maximum Eigenmode Beamforming and Multi-User Gain

This paper is concerned with the advantages of multi-user concurrent transmission in multiple-input multiple-output (MIMO) systems with rate constraints. We first study a maximum eigenmode beamforming (MEB) strategy for fading multiple access channels (MACs). This strategy allows each user to transmit only in its maximum eigenmode direction and applies a suboptimal matched-filter receiver with successive interference cancellation at the base station (BS). We derive a closed-form expression for the average minimum transmitted sum power required by MEB. Based on this, we show that: a) the MEB strategy is asymptotically optimal when the number of simultaneous users is sufficiently large; b) multi-user concurrent transmission has a power advantage, referred to as multi-user gain, over orthogonal transmission approaches such as time-division multiple-access; c) the number of antennas at the BS has a far stronger impact on the system performance than that at each user side. These properties are verified by simulation. Both numerical analyses and simulation results show that a major part of multi-user gain can be achieved in practical environments even with a quite small number of simultaneous users. We also study the MEB strategy for MIMO broadcast channels (BCs). The dirty paper coding (DPC) technique is necessary in this case. It is analytically shown that most observations made for MIMO MACs are extendable to MIMO BCs.

Game-Theoretic Opportunistic Spectrum Sharing Strategy Selection for Cognitive MIMO Multiple Access Channels

This paper studies opportunistic spectrum sharing strategy (i.e., quantized precoding strategy) selection for cognitive multiple-input multiple-output multiple access channels with limited feedback under interference power constraint and maximum transmission stream number constraint. We put forward a game-theoretic framework to model the precoding strategy selection behaviors of the secondary users under the specified constraints. First, we prove the formulated discrete game is a potential game which possesses at least one feasible pure strategy Nash equilibrium. The feasibility and optimality of the Nash equilibrium are also analyzed. Then we prove that the solution to the sum rate maximization problem constitutes a feasible pure strategy Nash equilibrium of our formulated game. Furthermore, we design two algorithms. The iterative precoding strategy selection algorithm based on the best response rule is designed to attain a feasible Nash equilibrium. The modified algorithm is designed to improve the sum rate performance. Simulation results show that our designed algorithms can achieve optimal or near optimal sum rate performance with low complexity.

A Deterministic Equivalent for the Analysis of Correlated MIMO Multiple Access Channels

In this article, novel deterministic equivalents for the Stieltjes transform and the Shannon transform of a class of large dimensional random matrices are provided. These results are used to characterize the ergodic rate region of multiple antenna multiple access channels, when each point-to-point propagation channel is modelled according to the Kronecker model. Specifically, an approximation of all rates achieved within the ergodic rate region is derived and an approximation of the linear precoders that achieve the boundary of the rate region as well as an iterative water-filling algorithm to obtain these precoders are provided. An original feature of this work is that the proposed deterministic equivalents are proved valid even for strong correlation patterns at both communication sides. The above results are validated by Monte Carlo simulations.

On the Performance of the Two-Cell Cooperative Single User (CSU) MIMO System with Hybrid Feedback

Achievable rates of two different transmission schemes of the two-cell cooperative single user (CSU) multi-input multi-output (MIMO) system with hybrid feedback is studied, in which one cell has the channel state information (CSI) from a mobile station (MS) and the other has channel covariance information (CCI) from it. Disjoint encoding over two base stations (BSs) is shown to achieve the capacity of the CSU-MIMO with hybrid feedback. Rather than finding an optimal transmission scheme, a suboptimal one is proposed such that the transmit directions of the BSs with CSI and CCI are eigen directions of the instantaneous channel correlation matrix and transmit covariance matrix respectively. The optimum power allocation for these transmit directions is derived as an iterative power allocation (IPA) similar to that of the MIMO multiple access channel (MAC) with CCI only. We also propose a simple disjoint power allocation (DPA). The simulation results show that the proposed transmit directions and IPA for the CSU-MIMO with hybrid feedback outperforms the MIMO-MAC with CCI only, while the DPA achieves almost the same performance as the IPA, only when the SNR is low.

Optimality of Beamforming for MIMO Multiple Access Channels Via Virtual Representation

In this correspondence, we consider the optimality of beamforming for achieving the ergodic capacity of multiple-input multiple-output (MIMO) multiple access channel (MAC) via virtual representation (VR) model. We assume that the receiver knows the channel state information (CSI) perfectly but that the transmitter knows only partial CSI, i.e., the channel statistics. For the single-user case, we prove that the capacity-achieving beamforming angle (c.b.a.) is unique, and there exists a signal-to-noise ratio (SNR) threshold below which beamforming is optimal and above which beamforming is strictly suboptimal. For the multi-user case, we show that the c.b.a is not unique and we obtain explicit conditions that determine the beamforming angles for a special class of correlated MAC-VR models. Under mild conditions, we show that a large class of power allocation schemes can achieve the sum-capacity within a constant as the number of users in the system becomes large. The beamforming scheme, in particular, is shown to be asymptotically capacity-achieving only for certain MAC-VR models.

Game Theoretic Multimode Precoding Strategy Selection for MIMO Multiple Access Channels

This paper is concerned with decentralized selection of multimode precoding strategy for multiple-input multiple-output (MIMO) multiple access channels. We formulate it as a discrete noncooperative game. This game is shown to possess at least one pure strategy Nash equilibrium (NE) and the optimal strategy profile which maximizes the sum rate constitutes a pure strategy NE. Then we propose a decentralized algorithm based on learning automata to achieve the NE. A repeated mechanism is introduced to improve the sum rate performance and a mechanism for adapting step size is designed to control the convergence speed. Simulation results show that the proposed algorithm, which only requires limited feedback, can achieve near optimal or optimal sum rate performance.

Capacity Bounds and Low Complexity Transceiver Design for Double-Scattering MIMO Multiple Access Channels

We investigate the sum capacity and present low complexity transceiver designs for the multiple-input multiple-output (MIMO) multiple access channel (MAC) under a general class of fading, known as <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">double-scattering</i> . We assume that the receiver has perfect channel state information (CSI), while each transmitter only has access to its own statistical CSI. We show that the optimum transmit directions for each user coincide with the eigenvectors of the user's own transmit spatial correlation matrix. We also derive new closed-form upper bounds on the sum capacity of the MIMO MAC under double-scattering, which are subsequently employed to obtain low complexity power allocation policies which are easy to compute, and require each user to know only their own channel statistics. Then, we establish beamforming optimality conditions for all users. Finally, we consider the case as the number of users becomes large, in which case we demonstrate that beamforming is asymptotically optimal.

Duality of MIMO multiple access channel and broadcast channel with amplify-and-forward relays

In this work, we consider a two-hop multiuser amplify-and-forward relay network with multi-antenna nodes. The results are three-fold. First, for any relay amplification matrix D in the multiple-access channel (MAC), we show that duality holds when ¿D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</sup> is employed in the broadcast channel (BC), and vice versa, where re is obtained from switching the total source and relay power constraints. Second, under a total network power constraint, we show that MAC-BC duality holds when D and D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</sup> are the relaying matrices in the MAC and BC respectively. Third, for any D in the MAC and cD <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</sup> in the BC where c is any positive real scalar, MAC-BC duality under total network power constraint holds only for the above two cases.

Multiuser detection of alamouti signals

In a MIMO multiple-access channel where users employ Space-Time Block Codes (STBC), interference cancellation can be used to suppress co-channel interference and recover the desired signal of each user at the receiver. Leveraging the special properties of Alamouti matrices, we first show that spatial multiplexing of Alamouti signals retains the space-time diversity gain of Alamouti signaling using our proposed low-complexity Alamouti BLAST-MMSE (A-BLAST) Algorithm. Next, in contrast to traditional transmit diversity that focuses on STBC construction at the transmitter, this paper looks at transmit diversity from the perspective of the receiver. In other words, the receiver gets to choose the STBCiquests, which are favourable to the channel assuming a fixed BLAST receive algorithm. In a multiuserMAC setting, we first present a systematic methodology to exploit different decomposition structure in Alamouti matrices, each with different tradeoff between performance and decoding complexity using possibly different MIMO receive algorithms. We then demonstrate that the notion of angles (the inner product of two quaternionic vectors) between multiuser channels determines the performance of MIMO receive algorithms. As an application of the general theory, we transform the decoding problem for several types of Quasi-Orthogonal STBC (QOSTBC) into multiuser detection of virtual Alamouti users. Building upon our A-BLAST Algorithm, we propose new algorithms for decoding single-user and multiuser QOSTBC. In particular, we show that bit error probability is a function of the quaternionic angle between virtual users (for a single user) or multiple users. This angle varies with the type of QOSTBC and leads to a new form of adaptive modulation called code diversity, where feedback instructs the transmitter how to choose from a plurality of codes.

Power allocation games for mimo multiple access channels with coordination

A game theoretic approach is used to derive the optimal decentralized power allocation (PA) in fast fading multiple access channels where the transmitters and receiver are equipped with multiple antennas. The players (the mobile terminals) are free to choose their PA in order to maximize their individual transmission rates (in particular they can ignore some specified centralized policies). A simple coordination mechanism between users is introduced. The nature and influence of this mechanism is studied in detail. The coordination signal indicates to the users the order in which the receiver applies successive interference cancellation and the frequency at which this order is used. Two different games are investigated: the users can either adapt their temporal PA to their decoding rank at the receiver or optimize their spatial PA between their transmit antennas. For both games a thorough analysis of the existence, uniqueness and sum-rate efficiency of the network Nash equilibrium is conducted. Analytical and simulation results are provided to assess the gap between the decentralized network performance and its equivalent virtual multiple input multiple output system, which is shown to be zero in some cases and relatively small in general.

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.

Optimal Successive Group Decoders for MIMO Multiple-Access Channels

We consider a slow-fading narrowband multiple-input multiple-output (MIMO) multiple-access channel (MAC) in which multiple users, each equipped with multiple transmit antennas, communicate to a receiver equipped with multiple receive antennas. The users are unaware of the channel state information (CSI) whereas the receiver has perfect CSI and employs a successive group decoder (SGD). We obtain achievable outage probabilities for the case where an outage must be declared simultaneously for all users (common outage) as well as the case where outages can be declared individually for each user (individual outage). We then derive the optimum successive group decoder (OSGD) that simultaneously minimizes the common outage probability and the individual outage probability of each user, over all SGDs of permissible decoding complexity. For each channel realization, the OSGD is also shown to maximize the error exponent of the decodable set of users. An adaptive SGD is derived which not only retains the outage optimality of the OSGD but also minimizes the expected decoding complexity. Asymptotically tight (in the limit of high signal-to-noise ratio (SNR)) affine approximations are then obtained for the weighted sum common and individual outage capacities and the symmetric outage capacity yielded by the OSGD. Limiting expressions for the relevant capacities as the number of users and the number of receive antennas approach infinity are also obtained and it is shown that the OSGD yields symmetric capacity gains commensurate with the decoding complexity allowed. Simulation results with practical low-density parity-check (LDPC) outer codes show that the OSGD offers significantly improved performance at low decoding complexity.

On the Capacity and Design of Limited Feedback Multiuser MIMO Uplinks

The theory of multiple-input-multiple-output (MIMO) technology has been well developed to increase fading channel capacity over single-input-single-output (SISO) systems. This capacity gain can often be leveraged by utilizing channel state information at the transmitter and the receiver. Users make use of this channel state information for transmit signal adaptation. In this correspondence, we derive the capacity region for the MIMO multiple access channel (MIMO MAC) when partial channel state information is available at the transmitters, where we assume a synchronous MIMO multiuser uplink. The partial channel state information feedback has a cardinality constraint and is fed back from the basestation to the users using a limited rate feedback channel. Using this feedback information, we propose a finite codebook design method to maximize the sum rate. In this correspondence, the codebook is a set of transmit signal covariance matrices. We also derive the capacity region and codebook design methods in the case that the covariance matrix is rank one (i.e., beam- forming). This is motivated by the fact that beamforming is optimal in certain conditions. The simulation results show that when the number of feedback bits increases, the capacity also increases. Even with a small number of feedback bits, the performance of the proposed system is close to an optimal solution with the full feedback.

On the achievable sum-rate of correlated mimo multiple access channel with imperfect channel estimation

We study upper and lower bounds on the achievable sum-rate of a correlated MIMO MAC with channel estimation error at the receiver when the correlation information is available to the users' transmitters, and prove that, for Gaussian input signals with arbitrary input covariance matrices, the gap between these bounds does not exceed a limiting value at any input transmit power. We further prove that in systems with uniform input power utilization over the transmit antennas, the gap between the mutual information bounds increases monotonically as the input power of each user increases. Furthermore, we show that in the absence of correlation, the gap between the mutual information bounds is maximum for beamforming and minimum for uniform input power allocation over the transmit antennas. We further prove that utilizing the input power of each user towards the directions of the eigenvectors of its transmit correlation matrix maximizes the mutual information lower bound. Moreover, we derive the transmit directions that maximize the mutual information lower and upper bounds in an uncorrelated MIMO MAC with delayed feedback from the receiver to the transmitters, and characterize the power allocation of this system in terms of its beamforming range. Numerical simulations are conducted to corroborate our theoretical results.

Guaranteed Performance Region in Fading Orthogonal Space-Time Coded Broadcast Channels

Recently, the capacity region of the MIMO broadcast channel (BC) was completely characterized and duality between MIMO multiple access channel (MAC) and MIMO BC with perfect channel state information (CSI) at transmitter and receiver was established. In this work, we propose a MIMO BC approach in which only information about the channel norm is available at the base and hence no joint beamforming and dirty paper precoding (DPC) can be applied. However, a certain set of individual performances in terms of MSE or zero-outage rates can be guaranteed at any time by applying an orthogonal space-time block code (OSTBC). The guaranteed MSE region without superposition coding is characterized in closed form and the impact of diversity, fading statistics, and number of transmit antennas and receive antennas is analyzed. Finally, six CSI and precoding scenarios with different levels of CSI and precoding are compared numerically in terms of their guaranteed MSE region. Depending on the long-term SNR, superposition coding as well as successive interference cancellation (SIC) with norm feedback performs better than linear precoding with perfect CSI.

Optimal operating point for MIMO multiple access channel with bursty traffic

Multiple antennas at the transmitters and receivers in a multiple access channel (MAC) can provide simultaneous diversity, spatial multiplexing, and space-division multiple access gains. The fundamental tradeoff in the asymptotically large SNR regime is shown by Tse et al. (2004). On the other hand, MAC scheduling can provide a statistical-multiplexing gain to improve the delay performance as shown by Bertsimas et al. (1998) and Stolyar and Ramanan (2001). In this paper, we formulate and analytically derive bounds on the optimal operating point for MIMO-MAC channel for bursty sources with delay constraints. Our system model brings together the four types of gains: diversity, spatial multiplexing, space-division multiple-access, and statistical-multiplexing gains. Our objective is to minimize the end-to-end performance as defined by the delay bound violation probability as well as the channel decoding error probability. We And the optimal diversity gain and rate region in which the system should operate. As an example, we illustrate our technique and the optimal operating point for the case of a compound Poisson source. In addition, we note an interesting interplay between the intensity of the traffic and resource pooling with regard to both multiple-access and statistical-multiplexing gains.

The Cost of Uncorrelation and Noncooperation in MIMO Channels

We investigate the capacity loss for using uncorrelated Gaussian input over a multiple-input multiple-output (MIMO) linear additive-noise channel. We upper-bound the capacity loss by a universal constant C* which is independent of the channel matrix and the noise distribution. For a single-user MIMO channel with nt inputs and nr outputs C* = min [ 1/2, nr/nt log2 (1+nt/nr) ] bit per input dimension (or 2C* bit per transmit antenna per second per hertz), under both total and per-input power constraints. If we restrict attention to (colored) Gaussian noise, then the capacity loss is upper-bounded by a smaller constant CG = nr/2nr log2 (nt/nr) for nr ges nt/e, and CG = 0.265 otherwise, and this bound is tight for certain cases of channel matrix and noise covariance. We also derive similar bounds for the sum-capacity loss in multiuser MIMO channels. This includes in particular uncorrelated Gaussian transmission in a MIMO multiple-access channel (MAC), and flat Gaussian dirty-paper coding (DPC) in a MIMO broadcast channel. In the context of wireless communication, our results imply that the benefit of beamforming and spatial water-filling over simple isotropic transmission is limited. Moreover, the excess capacity of a point-to-point MIMO channel over the same MIMO channel in a multiuser configuration is bounded by a universal constant.

Optimization of Training and Scheduling in the Non-Coherent SIMO Multiple Access Channel

Channel state information (CSI) is important for achieving large rates in MIMO channels. However, in time-varying MIMO channels, there is a tradeoff between the time/energy spent acquiring channel state information (CSI) and the time/energy remaining for data transmission. This tradeoff is accentuated in the MIMO multiple access channel (MAC), since the number of channel vectors to be estimated increases with the number of users. Furthermore, the problem of acquiring CSI is tightly coupled with the problem of exploiting CSI through multiuser scheduling. This paper considers a block-fading MAC with coherence time <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> , n uncoordinated users-each with one transmit antenna and the same average power constraint, and a base station with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> receive antennas and no a priori CSI. For this scenario, a training-based communication scheme is proposed and the training and multiuser-scheduling aspects of the scheme are jointly optimized. In the high-SNR regime, the sum capacity of the non-coherent SIMO MAC is characterized and used to establish the SNR-scaling-law optimality of the proposed scheme. In the low-SNR regime, the sum-rate of the proposed scheme is found to decay linearly with vanishing SNR when flash signaling is incorporated. Furthermore, this linear decay is shown to be order-optimal through comparison to the low-SNR sum capacity of the non-coherent SIMO MAC. A by product of these SNR-asymptotic analyses is the observation that non-trivial scheduling (i.e., scheduling a strict subset of trained users) is advantageous at low SNR, but not at high SNR. The sum-rate and per-user throughput are also explored in the large- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> and large- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> regimes. Non-coherent capacity, training, multiple access channel, multiuser scheduling, opportunistic scheduling.