Precoder Designs for MIMO Broadcast Channels with Imperfect CSI

[1] D. Tse and P. Viswanath, Fundamentals of Wireless Communication.Cambridge University Press, 2006. [2] H. Bolcskei, D. Gesbert, C. B. Papadias, and A.-J. van der Veen, Spacetime Wireless Systems: From Array Processing to MIMO Communications.Cambridge University Press, 2006. [3] Q. H. Spencer, C. B. Peel, A. L. Swindlehurst, and M. Haardt, “An introduction to the multiuser MIMO downlink,” IEEE Commun. Mag.,vol. 42, pp. 60–67, Oct. 2004. [4] K. Kusume, M. Joham,W. Utschick, and G. Bauch, “Efficient tomlinsonharashima precoding for spatial multiplexing on flat MIMO channel,”in Proc. IEEE ICC’2005, May 2005, pp. 2021–2025. [5] R. Fischer, C. Windpassinger, A. Lampe, and J. Huber, “MIMO precoding for decentralized receivers,” in Proc. IEEE ISIT’2002, 2002, p.496. [6] M. Schubert and H. Boche, “Iterative multiuser uplink and downlink beamforming under SINR constraints,” IEEE Trans. Signal Process.,vol. 53, pp. 2324–2334, Jul. 2005. [7] ——, “Solution of multiuser downlink beamforming problem with individual SINR constraints,” IEEE Trans. Veh. Technol., vol. 53, pp.18–28, Jan. 2004. [8] A. Wiesel, Y. C. Eldar, and Shamai, “Linear precoder via conic optimization for fixed MIMO receivers,” IEEE Trans. Signal Process., vol. 52,pp. 161–176, Jan. 2006. [9] N. Jindal, “MIMO broadcast channels with finite rate feed-back,” in Proc. IEEE GLOBECOM’2005, Nov. 2005. [10] R. Hunger, F. Dietrich, M. Joham, and W. Utschick, “Robust transmit zero-forcing filters,” in Proc. ITG Workshop on Smart Antennas, Munich,Mar. 2004, pp. 130–137. [11] M. B. Shenouda and T. N. Davidson, “Linear matrix inequality formulations of robust QoS precoding for broadcast channels,” in Proc.CCECE’2007, Apr. 2007, pp. 324–328. [12] M. Payaro, A. Pascual-Iserte, and M. A. Lagunas, “Robust power allocation designs for multiuser and multiantenna downlink communication systems through convex optimization,” IEEE J. Sel. Areas Commun.,vol. 25, pp. 1392–1401, Sep. 2007. [13] M. Biguesh, S. Shahbazpanahi, and A. B. Gershman, “Robust downlink power control in wireless cellular systems,” EURASIP Jl. Wireless Commun. Networking, vol. 2, pp. 261–272, 2004. [14] B. Bandemer, M. Haardt, and S. Visuri, “Liner MMSE multi-user MIMO downlink precoding for users with multple antennas,” in Proc.PIMRC’06, Sep. 2006, pp. 1–5. [15] J. Zhang, Y. Wu, S. Zhou, and J. Wang, “Joint linear transmitter and receiver design for the downlink of multiuser MIMO systems,” IEEE Commun. Lett., vol. 9, pp. 991–993, Nov. 2005. [16] S. Shi, M. Schubert, and H. Boche, “Downlink MMSE transceiver optimization for multiuser MIMO systems: Duality and sum-mse minimization,”IEEE Trans. Signal Process., vol. 55, pp. 5436–5446, Nov.2007. [17] A. Mezghani, M. Joham, R. Hunger, and W. Utschick, “Transceiver design for multi-user MIMO systems,” in Proc. WSA 2006, Mar. 2006. [18] R. Doostnejad, T. J. Lim, and E. Sousa, “Joint precoding and beamforming design for the downlink in a multiuser MIMO system,” in Proc.WiMob’2005, Aug. 2005, pp. 153–159. [19] N. Vucic, H. Boche, and S. Shi, “Robust transceiver optimization in downlink multiuser MIMO systems with channel uncertainty,” in Proc.IEEE ICC’2008, Beijing, China, May 2008. [20] A. Ben-Tal and A. Nemirovsky, “Selected topics in robust optimization,”Math. Program., vol. 112, pp. 125–158, Feb. 2007. [21] D. Bertsimas and M. Sim, “Tractable approximations to robust conic optimization problems,” Math. Program., vol. 107, pp. 5–36, Jun. 2006. [22] P. Ubaidulla and A. Chockalingam, “Robust Transceiver Design for Multiuser MIMO Downlink,” in Proc. IEEE Globecom’2008, New Orleans, USA, Dec. 2008, to appear. [23] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press, 2004. [24] G. H. Golub and C. F. V. Loan, Matrix Computations. The John Hopkins University Press, 1996.

On the Successive Refinability of MIMO channels: DMT and codes

Diversity embedded space time codes are high rate codes that are designed such that they have a high diversity code embedded within them. A recent work by Diggavi and Tse characterizes the performance limits that can be achieved by diversity embedded space-time codes in terms of the achievable Diversity Multiplexing Tradeoff (DMT). In particular, they have shown that the trade off is successively refinable for rayleigh fading channels with one degree of freedom using superposition coding and Successive Interference Cancellation (SIC). However, for Multiple-Input Multiple-Output (MIMO) channels, the questions of successive refinability remains open. We consider MIMO Channels under superposition coding and SIC. We derive an upper bound on the successive refinement characteristics of the DMT. We then construct explicit space time codes that achieve the derived upper bound. These codes, constructed from cyclic division algebras, have minimal delay. Our results establish that when the channel has more than one degree of freedom, the DMT is not successive refinable using superposition coding and SIC. The channels considered in this work can have arbitrary fading statistics.

Antenna Selection Training in MIMO-OFDM/OFDMA Cellular Systems

Antenna selection allows multiple-antenna systems to achieve most of their promised diversity gain, while keeping the number of RF chains and, thus, cost/complexity low. In this paper we investigate antenna selection for fourth-generation OFDMA- based cellular communications systems, in particular, 3GPP LTE (long-term evolution) systems. We propose a training method for antenna selection that is especially suitable for OFDMA. By means of simulation, we evaluate the SNR-gain that can be achieved with our design. We find that the performance depends on the bandwidth assigned to each user, the scheduling method (round-robin or frequency-domain scheduling), and the Doppler spread. Furthermore, the signal-to-noise ratio of the training sequence plays a critical role. Typical SNR gains are around 2 dB, with larger values obtainable in certain circumstances.

Design of MMSE filterbank precoder and equalizer for MIMO frequency selective channels

In this paper, we consider the problem of designing minimum mean squared error (MMSE) filterbank precoder and equalizer for multiple input multiple output (MIMO) frequency selective channels. We derive the conditions to be satisfied by the optimal precoder-equalizer pair, and provide an iterative algorithm for solving them. The optimal design is very general, in that it is not constrained by channel dimensions, channel order, channel rank, or the input constellation. We also discuss some pertinent difierences between the filterbank approach and the space-time approach to the design of optimal precoder and equalizer. Simulation results demonstrate that the proposed design performs better than the space-time systems while supporting a higher data rate.

Achieving the D-MG and DMD Tradeoffs of MIMO fading channels

An overview of our recent results relating to the explicit construction of space-time block codes achieving the DMG tradeoff of the quasi-static fading channel is presented. The results include the explicit construction of D-MG optimal codes,generalization of perfect codes to any number of transmit antennas as well as optimal diversity-multiplexing-delay constructions for the MIMO ARQ Channel.

Relay Precoder Optimization in MIMO-Relay Networks With Imperfect CSI

In this paper, we consider robust joint designs of relay precoder and destination receive filters in a nonregenerative multiple-input multiple-output (MIMO) relay network. The network consists of multiple source-destination node pairs assisted by a MIMO-relay node. The channel state information (CSI) available at the relay node is assumed to be imperfect. We consider robust designs for two models of CSI error. The first model is a stochastic error (SE) model, where the probability distribution of the CSI error is Gaussian. This model is applicable when the imperfect CSI is mainly due to errors in channel estimation. For this model, we propose robust minimum sum mean square error (SMSE), MSE-balancing, and relay transmit power minimizing precoder designs. The next model for the CSI error is a norm-bounded error (NBE) model, where the CSI error can be specified by an uncertainty set. This model is applicable when the CSI error is dominated by quantization errors. In this case, we adopt a worst-case design approach. For this model, we propose a robust precoder design that minimizes total relay transmit power under constraints on MSEs at the destination nodes. We show that the proposed robust design problems can be reformulated as convex optimization problems that can be solved efficiently using interior-point methods. We demonstrate the robust performance of the proposed design through simulations.

A Low ML-Decoding Complexity, Full-Diversity, Full-Rate MIMO Precoder

Precoding for multiple-input multiple-output (MIMO) antenna systems is considered with perfect channel knowledge available at both the transmitter and the receiver. For two transmit antennas and QAM constellations, a real-valued precoder which is approximately optimal (with respect to the minimum Euclidean distance between points in the received signal space) among real-valued precoders based on the singular value decomposition (SVD) of the channel is proposed. The proposed precoder is obtainable easily for arbitrary QAM constellations, unlike the known complex-valued optimal precoder by Collin et al. for two transmit antennas which is in existence for 4-QAM alone and is extremely hard to obtain for larger QAM constellations. The proposed precoding scheme is extended to higher number of transmit antennas on the lines of the E - d(min) precoder for 4-QAM by Vrigneau et al. which is an extension of the complex-valued optimal precoder for 4-QAM. The proposed precoder's ML-decoding complexity as a function of the constellation size M is only O(root M)while that of the E - d(min) precoder is O(M root M)(M = 4). Compared to the recently proposed X- and Y-precoders, the error performance of the proposed precoder is significantly better while being only marginally worse than that of the E - d(min) precoder for 4-QAM. It is argued that the proposed precoder provides full-diversity for QAM constellations and this is supported by simulation plots of the word error probability for 2 x 2, 4 x 4 and 8 x 8 systems.

Interference Alignment Algorithms for the K User Constant MIMO Interference Channel

This paper considers the degrees of freedom (DOF) for a K user multiple-input multiple-output (MIMO) M x N interference channel using interference alignment (IA). A new performance metric for evaluating the efficacy of IA algorithms is proposed, which measures the extent to which the desired signal dimensionality is preserved after zero-forcing the interference at the receiver. Inspired by the metric, two algorithms are proposed for designing the linear precoders and receive filters for IA in the constant MIMO interference channel with a finite number of symbol extensions. The first algorithm uses an eigenbeamforming method to align sub-streams of the interference to reduce the dimensionality of the interference at all the receivers. The second algorithm is iterative, and is based on minimizing the interference leakage power while preserving the dimensionality of the desired signal space at the intended receivers. The improved performance of the algorithms is illustrated by comparing them with existing algorithms for IA using Monte Carlo simulations.

Degrees of freedom of relay aided MIMO X network with orthogonal components

We consider the one-way relay aided MIMO X fading Channel where there are two transmitters and two receivers along with a relay with M antennas at every node. Every transmitter wants to transmit messages to every other receiver. The relay broadcasts to the receivers along a noisy link which is independent of the transmitters channel. In literature, this is referred to as a relay with orthogonal components. We derive an upper bound on the degrees of freedom of such a network. Next we show that the upper bound is tight by proposing an achievability scheme based on signal space alignment for the same for M = 2 antennas at every node.

Low-Complexity Detection in Large-Dimension MIMO-ISI Channels Using Graphical Models

In this paper, we deal with low-complexity near-optimal detection/equalization in large-dimension multiple-input multiple-output inter-symbol interference (MIMO-ISI) channels using message passing on graphical models. A key contribution in the paper is the demonstration that near-optimal performance in MIMO-ISI channels with large dimensions can be achieved at low complexities through simple yet effective simplifications/approximations, although the graphical models that represent MIMO-ISI channels are fully/densely connected (loopy graphs). These include 1) use of Markov random field (MRF)-based graphical model with pairwise interaction, in conjunction with message damping, and 2) use of factor graph (FG)-based graphical model with Gaussian approximation of interference (GAI). The per-symbol complexities are O(K(2)n(t)(2)) and O(Kn(t)) for the MRF and the FG with GAI approaches, respectively, where K and n(t) denote the number of channel uses per frame, and number of transmit antennas, respectively. These low-complexities are quite attractive for large dimensions, i.e., for large Kn(t). From a performance perspective, these algorithms are even more interesting in large-dimensions since they achieve increasingly closer to optimum detection performance for increasing Kn(t). Also, we show that these message passing algorithms can be used in an iterative manner with local neighborhood search algorithms to improve the reliability/performance of M-QAM symbol detection.

Frequency domain turbo equalization for MIMO-CPSC systems with large delay spreads

In this paper, we consider low-complexity turbo equalization for multiple-input multiple-output (MIMO) cyclic prefixed single carrier (CPSC) systems in MIMO inter-symbol interference (ISI) channels characterized by large delay spreads. A low-complexity graph based equalization is carried out in the frequency domain. Because of the reduction in correlation among the noise samples that happens for large frame sizes and delay spreads in frequency domain processing, improved performance compared to time domain processing is shown to be achieved. This improved performance is attractive for equalization in severely delay spread ISI channels like ultrawideband channels and underwater acoustic channels.

Factor graph based joint detection/decoding for LDPC coded large-MIMO systems

In this paper, we employ message passing algorithms over graphical models to jointly detect and decode symbols transmitted over large multiple-input multiple-output (MIMO) channels with low density parity check (LDPC) coded bits. We adopt a factor graph based technique to integrate the detection and decoding operations. A Gaussian approximation of spatial interference is used for detection. This serves as a low complexity joint detection/decoding approach for large dimensional MIMO systems coded with LDPC codes of large block lengths. This joint processing achieves significantly better performance than the individual detection and decoding scheme.

DMT-optimal, Low ML-Complexity STBC-Schemes for Asymmetric MIMO Systems

For an n(t) transmit, nr receive antenna (n(t) x n(r)) MIMO system with quasi- static Rayleigh fading, it was shown by Elia et al. that space-time block code-schemes (STBC-schemes) which have the non-vanishing determinant (NVD) property and are based on minimal-delay STBCs (STBC block length equals n(t)) with a symbol rate of n(t) complex symbols per channel use (rate-n(t) STBC) are diversity-multiplexing gain tradeoff (DMT)-optimal for arbitrary values of n(r). Further, explicit linear STBC-schemes (LSTBC-schemes) with the NVD property were also constructed. However, for asymmetric MIMO systems (where n(r) < n(t)), with the exception of the Alamouti code-scheme for the 2 x 1 system and rate-1, diagonal STBC-schemes with NVD for an nt x 1 system, no known minimal-delay, rate-n(r) LSTBC-scheme has been shown to be DMT-optimal. In this paper, we first obtain an enhanced sufficient criterion for an STBC-scheme to be DMT optimal and using this result, we show that for certain asymmetric MIMO systems, many well-known LSTBC-schemes which have low ML-decoding complexity are DMT-optimal, a fact that was unknown hitherto.

Increasing System Capacity in Uplink Multiuser MIMO Using Sparsity Exploiting Receiver

In multiuser communication on the uplink, all subscribed users may not be active simultaneously. This leads to sparsity in the activity pattern in the users' transmissions, which can be exploited in the multiuser MIMO receiver at the base station (BS). Because of no transmissions from inactive users, joint detection at the BS has to consider an augmented signal set that includes zero. In this paper, we propose a receiver that exploits this inactivity-induced sparsity and considers the zero-augmented signal set. The proposed receiver is based on Markov Chain Monte Carlo techniques. Near-optimal performance and increased system capacity (in terms of number of users in the system) are demonstrated. For example, a multiuser MIMO system with N = 32 receive antennas at the BS and an user activity factor of 0.2 supports 51 uplink users meeting a QoS of 10(-3) coded bit error rate.