The downlink (DL) communication of single channel codewords is supported by providing a multiple-input multiple-output (MIMO) transmitter and receiver. The transmitter includes NT transmit antennas for transmitting spatial streams to a receiver having NR receive antennas, a precoder and a space- time or space-frequency matrix construction unit in communication with the precoder and the transmit antennas. The space-time or space-frequency matrix construction unit constructs a matrix that defines a threaded algebraic space- time (TAST) codeword based on a number of virtual antennas, NV, and the number of transmit antennas, NT. The transmitter operates in an open loop mode when no feedback information from the receiver is available, a semi-open loop mode when channel rank information is available, and a closed loop mode when channel state information (CSI) is available. The receiver is configured to provide feedback to the transmitter on a per received spatial stream basis.

MIMO transmitter and receiver for supporting downlink communication of single channel codewords

It is known that next generation mobile communications systems will most likely employ multi-cell signal processing - often referred to as network MIMO - in order to improve spectral efficiency and fairness. Many publications exist that predict strong achievable rate improvements, but usually neglecting various practical issues connected to network MIMO. In this paper, we analyse the impact of a constrained backhaul infrastructure and imperfect channel knowledge on uplink network MIMO from an information theoretical point of view. Especially the latter aspect leads to the fact that the channel conditions for which network MIMO is reasonably beneficial are strongly constrained. We observe different base station cooperation schemes in scenarios of maximal 3 base stations and 3 terminals, provide simulation results, and discuss the practicability of the discussed schemes and the implications of our results.

On Uplink Network MIMO under a Constrained Backhaul and Imperfect Channel Knowledge

Given symmetric matrices B,D?? n×n and a symmetric positive definite matrix W?? n×n , maximizing the sum of the Rayleigh quotient x ? D x and the generalized Rayleigh quotient $\frac{\mathbf{x}^{\top}B \mathbf{x}}{\vphantom{\mathrm{I}^{\mathrm{I}}}\mathbf{x}^{\top}W\mathbf{x}}$ on the unit sphere not only is of mathematical interest in its own right, but also finds applications in practice. In this paper, we first present a real world application arising from the sparse Fisher discriminant analysis. To tackle this problem, our first effort is to characterize the local and global maxima by investigating the optimality conditions. Our results reveal that finding the global solution is closely related with a special extreme nonlinear eigenvalue problem, and in the special case D=μW (μ>0), the set of the global solutions is essentially an eigenspace corresponding to the largest eigenvalue of a specially-defined matrix. The characterization of the global solution not only sheds some lights on the maximization problem, but motives a starting point strategy to obtain the global maximizer for any monotonically convergent iteration. Our second part then realizes the Riemannian trust-region method of Absil, Baker and Gallivan (Found. Comput. Math. 7:303---330, 2007) into a practical algorithm to solve this problem, which enjoys the nice convergence properties: global convergence and local superlinear convergence. Preliminary numerical tests are carried out and empirical evaluation of its performance is reported.

http://www.optimization-online.org/DB_FILE/2012/03/3388.pdf

On optimizing the sum of the Rayleigh quotient and the generalized Rayleigh quotient on the unit sphere

We are concerned with the maximization of $\frac{{tr(V^ \top AV)}}
{{tr(V^ \top BV)}} + tr(V^ \top AV)
$
 over the Stiefel manifold $\{ V \in \mathbb{R}^{m \times \ell } |V^ \top V = I_\ell \} (\ell < m)$
 , where B is a given symmetric and positive definite matrix, A and C are symmetric matrices, and tr(·) is the trace of a square matrix. This is a subspace version of the maximization problem studied in Zhang (2013), which arises from real-world applications in, for example, the downlink of a multi-user MIMO system and the sparse Fisher discriminant analysis in pattern recognition. We establish necessary conditions for both the local and global maximizers and connect the problem with a nonlinear extreme eigenvalue problem. The necessary condition for the global maximizers offers deep insights into the problem, on the one hand, and, on the other hand, naturally leads to a self-consistent-field (SCF) iteration to be presented and analyzed in detail in Part II of this paper.

Maximization of the sum of the trace ratio on the Stiefel manifold, I: Theory

The necessary condition established in Part I of this paper for the global maximizers of the maximization problem $\mathop {\max }\limits_V \left\{ {\frac{{tr(V^ \top AV)}}
{{tr(V^ \top BV)}} + tr(V^ \top CV)} \right\}
$
 over the Stiefel manifold $\{ V \in \mathbb{R}^{m \times \ell } |V^ \top V = I_\ell \} (\ell < m)$
 , naturally leads to a self-consistent-field (SCF) iteration for computing a maximizer. In this part, we analyze the global and local convergence of the SCF iteration, and show that the necessary condition for the global maximizers is fulfilled at any convergent point of the sequences of approximations generated by the SCF iteration. This is one of the advantages of the SCF iteration over optimization-based methods. Preliminary numerical tests are reported and show that the SCF iteration is very efficient by comparing with some manifold-based optimization methods.

Maximization of the sum of the trace ratio on the Stiefel manifold, II: Computation

In the downlink of a broadcast fading channel, the base station can capitalize on multiuser diversity through channel aware scheduling. In MIMO systems, the design of the scheduler has to take into account the processing performed at the transmitter and the receivers. In this work, we consider channel aware scheduling for orthogonal linear precoding at the base station that guarantees interference free reception for each scheduled users. The problem is set in a novel mathematical framework and a scheduling algorithm is proposed that is shown by simulation to guarantee superior performance as compared to know techniques. Moreover, fairness constraints inspired by the proportional fair criterion are introduced in the scheduling process in order to guarantee the desired long term fairness properties.

/pdf/channel-aware-scheduling-for-broadcast-mimo-systems-with-18uj9bvmp1.pdf

Channel aware scheduling for broadcast MIMO systems with orthogonal linear precoding and fairness constraints

The capacity of a multiple input multiple output (MIMO) broadcast system with orthogonal space division multiple access (OSDMA) is studied under the assumptions of noisy and/or delayed channel state information (CSI) available at the transmitter. The impact of channel estimation errors and outdated CSI is evaluated both analytically and through Monte Carlo simulations for varying system parameters (i.e., channel decorrelation, number of users, number of antennas). It is found that channel variability is the predominant cause of performance degradation in a realistic setting, where feedback of CSI from the receivers to the transmitter takes a finite amount of time, thus suggesting to limit the use of OSDMA to channels varying slowly enough.

Effects of imperfect channel state information on the capacity of broadcast OSDMA-MIMO systems

In the downlink of a multi-user MIMO system, the base station can multiplex signals intended to different users on the same spectral resource. Joint optimization of channel assignment (scheduling) and beamforming in such a scenario is an open problem. Assuming zero-focing linear beamforming at the base station, this paper addresses this task by investigating a novel greedy solution that approximately maximizes the sum-rate. Performance of the proposed method is studied through numerical simulation and compared with known solutions based on combinatorial search.

Towards a joint optimization of scheduling and beamforning for MIMO downlink

In the downlink of a multi-user MIMO system over a fading channel, the base station can assign the available spatial streams to different users by capitalizing on multiuser diversity or enforcing fairness constraints. Assuming linear precoding (beamforming) at the base station, the problem amounts to the joint design of precoding matrices and channel aware scheduling, according to the cross-layer paradigm. In this paper we formulate the joint optimization of scheduling and linear precoding within a physical layer-oriented framework, where the performance metric is the transmission rate. Moreover, we constraint the precoding scheme to ensure interference-free reception of spatial streams (orthogonal space division multiple access, OSDMA). Fairness constraints are either inspired by the max-min or the proportional fair criterion. Performance of different schemes is evaluated by numerical simulations allowing to assess the tradeoffs between sum-rate (multi-user diversity) and fairness

/pdf/fair-scheduling-and-orthogonal-linear-precoding-decoding-in-3q86hrtyx2.pdf

Fair scheduling and orthogonal linear precoding/decoding in broadcast MIMO systems

Fair scheduling and orthogonal linear precoding/decoding in broadcast MIMO systems (Invited Paper)

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