Abstract-In this paper we consider optimal multiuser downlink beamforming in the presence of a massive number of arbitrary quadratic shaping constraints. We combine beamforming with full-rate high dimensional real-valued orthogonal space time block coding (OSTBC) to increase the number of beamforming weight vectors and associated degrees of freedom in the beamformer design. The original multi-constraint beamforming problem is converted into a convex optimization problem using semidefinite relaxation (SDR) which can be solved efficiently. In contrast to conventional (rank-one) beamforming approaches in which an optimal beamforming solution can be obtained only when the SDR solution (after rank reduction) exhibits the rank-one property, in our approach optimality is guaranteed when a rank of eight is not exceeded. We show that our approach can incorporate up to 79 additional shaping constraints for which an optimal beamforming solution is guaranteed as compared to a maximum of two additional constraints that bound the conventional rank-one downlink beamforming designs. Simulation results demonstrate the flexibility of our proposed beamformer design.Index Terms-Downlink beamforming, shaping constraints, semidefinite relaxation (SDR), orthogonal space time block coding (OSTBC). I. INTRODUCTIONWith the massive growth of the number of wireless communication users and the increasing demands for high-rate services, the spectral resource is becoming more and more scarce. Research on spectrally efficient transmission schemes for current and next generation cellular networks that are capable of mitigating effects of multiuser and co-channel interference is attracting considerable interest [1]. As a spectrally efficient multi-antenna technique [2], downlink beamforming has been extensively studied in the past few years [3]- [8]. With the aid of channel state information (CSI) at the transmitter, downlink beamforming is employed at the base station of cellular networks to serve multiple co-channel users simultaneously using spatially selective transmission.As a pioneering work in downlink beamforming, the authors in [3] consider the problem of minimizing the total transmitted power subject to quality of service (QoS) constraints in the form of minimum signal to interference plus noise ratio (SINR) requirements at each user. A particular form of uplink-downlink duality theory is established in [3] and under this framework the downlink beamforming problem is solved

This paper addresses adaptive beamforming in multi-group multicasting networks where groups of users subscribe to independent services that are simultaneously served by the base station. Beamformers are designed to maximize the minimum signal-to-interference-plus-noise ratio (SINR) of the users in all groups subject to a total transmit power constraint. By combining multi-group multicast beamforming with Alamouti space-time block coding, the degrees of freedom in the beamformer design is doubled resulting in drastically improved beamforming performance. In our paper we extend recent approaches in [1] and [2] for rank-two beamforming, originally devised for single-group multicasting networks that are free of multiuser interference, to multi-group multicasting networks, where multiuser interference represents a major challenge. Simulation results demonstrate that the proposed approach significantly outperforms the existing approaches.

Abstract-We study the invertibility of M -variate Laurent polynomial N × P matrices. Such matrices represent multidimensional systems in various settings such as filter banks, multiple-input multiple-output systems, and multirate systems. Given an N × P Laurent polynomial matrix H (z1, ..., zM ) of degree at most k, we want to find a P × N Laurent polynomial left inverse matrix G(z) of H (z) such that G(z)H (z) = I. We provide computable conditions to test the invertibility and propose algorithms to find a particular inverse.The main result of this paper is to prove that H (z) is generically invertible when N − P ≥ M ; whereas when N − P < M , then H (z) is generically noninvertible. As a result, we propose an algorithm to find a particular inverse of a Laurent polynomial matrix that is faster than current algorithms known to us.

This paper investigates a new beamforming approach for interference exploitation, which has recently attracted interest as an alternative to conventional interferenceavoidance beamforming for the downlink of multiple-input multiple-output systems. Contrary to existing interference exploitation approaches that focus on signal-to-noise ratio performance, we adopt an approach based on the detection region of the signal constellation. Focusing on quality of service, we then formulate the optimization for minimizing the error probability (EP) for the worst user, subject to power constraints. We do this by employing the knowledge of channel state information at the transmitter, along with all downlink users' data that are readily available at the base station during downlink transmission. In this context, we also show that the detection-region-based beamforming and the worst user EP downlink beamforming are equivalent problems. Finally, we further propose a sum EPs approach and provide an analytic bound of average symbol error rate performance. Our simulations verify that the proposed techniques provide significantly improved performance over conventional downlink beamforming techniques.

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