Michael Joham

Linear transmit processing in MIMO communications systems

We examine and compare the different types of linear transmit processing for multiple input, multiple output systems, where we assume that the receive filter is independent of the transmit filter contrary to the joint optimization of transmit and receive filters. We can identify three filter types similar to receive processing: the transmit matched filter, the transmit zero-forcing filter, and the transmit Wiener filter. We show that the transmit filters are based on similar optimizations as the respective receive filters with an additional constraint for the transmit power. Moreover, the transmit Wiener filter has similar convergence properties as the receive Wiener filter, i.e., it converges to the matched filter and the zero-forcing filter for low and high signal-to-noise ratio, respectively. We give closed-form solutions for all transmit filters and present the fundamental result that their mean-square errors are equal to the errors of the respective receive filters, if the information symbols and the additive noise are uncorrelated. However, our simulations reveal that the bit-error ratio results of the transmit filters differ from the results for the respective receive filters.

Efficient Tomlinson-Harashima precoding for spatial multiplexing on flat MIMO channel

Nonlinear minimum mean square error Tomlinson-Harashima precoding considered in this paper is an attractive solution for a scenario where a transmitter serves spatially separated receivers and no cooperation among them is possible. Unfortunately, the large performance gain against linear precoding comes along with significantly higher complexity than linear filters in the case of a large number of receivers. We show that superior performance of the nonlinear minimum mean square error Tomlinson-Harashima precoding can be obtained with complexity equivalent to linear precoding. Our proposed algorithm reduces the complexity by a factor of N/sub R/ which is the number of receivers.

Cholesky Factorization With Symmetric Permutation Applied to Detecting and Precoding Spatially Multiplexed Data Streams

We study computationally efficient spatial multiplexing transmission techniques aiming at high spectral efficiency. Two nonlinear transmission schemes based on the minimum mean-squared error criterion are considered in this paper: a detection scheme also known as V-BLAST and a precoding scheme called Tomlinson-Harashima precoding. The nonlinear techniques are known to be more powerful than simple linear filters, however, a large complexity overhead results. Initial proposals for the nonlinear schemes require the complexity proportional to N4 if the number of data streams is denoted by N. We propose to apply Cholesky factorization with symmetric permutation for finding a very simple and efficient algorithm that reduces the complexity by a factor of N. We conclude that the large performance advantage of the nonlinear detection and precoding schemes against their simple linear alternatives can be obtained without complexity overhead

Minimum Mean Square Error Vector Precoding

We derive the minimum mean square error (MMSE) solution to vector precoding for frequency flat multiuser scenarios with a centralized multi-antenna transmitter. The receivers employ a modulo operation, giving the transmitter the additional degree of freedom to choose a perturbation vector. Similar to existing vector precoding techniques, the optimum perturbation vector is found with a closest point search in a lattice. The proposed MMSE vector precoder does not, however, search for the perturbation vector resulting in the lowest transmit energy, as proposed in all previous contributions on vector precoding, but finds an optimum compromise between noise enhancement and residual interference. We present simulation results showing that the proposed technique outperforms existing vector precoders, as well as the MMSE Tomlinson-Harashima precoder

Minimum mean square error vector precoding

We derive the minimum mean square error (MMSE) solution to vector precoding for frequency flat multiuser scenarios with a centralised multi-antenna transmitter. The receivers employ a modulo operation, giving the transmitter the additional degree of freedom to choose a perturbation vector. Similar to existing vector precoding techniques, the optimum perturbation vector is found with a closest point search in a lattice. The proposed MMSE vector precoder does not, however, search for the perturbation vector resulting in the lowest unscaled transmit power, as proposed in all previous contributions on vector precoding, but finds an optimum compromise between noise enhancement and residual interference. We present simulation results showing that the proposed technique outperforms existing vector precoders, as well as the MMSE Tomlinson-Harashima precoder, and compare the turbo-coded performance to the capacity of the broadcast channel. Copyright

Robust transmit zero-forcing filters

We present linear and nonlinear robust transmit zero-forcing filters for the downlink of multiuser multiple-input single-output (MU-MISO) time-division-duplex (TDD) systems which are robust with respect to errors in the channel state information (CSI) arising from channel estimation and time lags in mobile communications. Based on a set of estimated CSI of previous uplink slots, we apply a conditional mean to the cost function underlying the respective filter for the current downlink slot resulting in channel prediction for the CSI and robust filter structures. Thus, the respective transmit filters are less sensitive to imperfect channel knowledge and show dramatic performance improvements compared to their nonrobust counterparts. Our approach can be interpreted as a joint optimization of channel prediction and preequalization. Additionally, we point out the relation of the presented approach to another robust technique named stochastic programming and show the analogy to a regularization approach

A Complete Description of the QoS Feasibility Region in the Vector Broadcast Channel

We characterize the complete quality-of-service (QoS) feasibility region and present a simple feasibility test for given QoS requirements in the Gaussian vector broadcast channel. While most contributions in the literature recast the QoS constraints into requirements for the signal-to-interference-and-noise ratios (SINRs), we convert them into upper bounds for the minimum mean square errors (MMSEs) instead and test feasibility in the MMSE domain. Our main contribution is a complete description of the feasible MMSE region. Its closure is shown to be a polytope and we find the complete set of its bounding half-spaces noniteratively after a finite number of steps. The polytope can easily be converted into any other QoS domain like SINR or rate. However, the simple geometry of the MMSE domain is lost in other domains. Once the bounding half-spaces are determined, any target MMSE tuple can quickly be checked for feasibility by verifying its membership to the interior of the polytope. For nondegenerate channels, the only relevant bounding half-space is essentially the lower bound on the sum mean square error. No further computations are necessary contrary to existing feasibility checks which iteratively solve eigenproblems in an alternating optimization framework for every single QoS requirement to test. For two particular user/antenna configurations, we find a noniterative closed form solution for the optimum power allocation of the signal-to-interference ratio (SIR) balancing.

A General Rate Duality of the MIMO Multiple Access Channel and the MIMO Broadcast Channel

We present a general rate duality between the multiple access channel (MAC) and the broadcast channel (BC) which is applicable to systems with and without nonlinear interference cancellation. Different to the state-of-the-art rate duality with interference subtraction from Vishwanath et al., the proposed duality is filter-based instead of covariance-based and exploits the arising unitary degree of freedom to decorrelate every point- to-point link. Therefore, it allows for noncooperative stream-wise decoding which reduces complexity and latency. Moreover, the conversion from one domain to the other does not exhibit any dependencies during its computation making it accessible to a parallel implementation instead of a serial one. We additionally derive a rate duality for systems with multi-antenna terminals when linear filtering without interference (pre-)subtraction is applied and the different streams of a single user are not treated as self-interference. Both dualities are based on a framework already applied to a mean-square-error duality between the MAC and the BC. Thanks to this novel rate duality, any rate-based optimization with linear filtering in the BC can now be handled in the dual MAC where the arising expressions lead to more efficient algorithmic solutions than in the BC due to the alignment of the channel and precoder indices.

Efficient Weighted Sum Rate Maximization With Linear Precoding

Achieving the boundary of the capacity region in the multiple-input multiple-output (MIMO) broadcast channel requires the use of dirty paper coding (DPC). As practical nearly optimum implementations of DPC are computationally complex, purely linear approaches are often used instead. However, in this case, the problem of maximizing a weighted sum rate constitutes a nonconvex and, in most cases, also a combinatorial optimization problem. In this paper, we present two heuristic nearly optimum algorithms with reduced computational complexity. For this purpose, a lower bound for the weighted sum rate under linear zero-forcing constraints is used. Based on this bound, both greedy algorithms successively allocate data streams to users. In each step, the user is determined that is given an additional data stream such that the increase in weighted sum rate becomes maximum. Thereby, the data stream allocations and filters obtained in the previous steps are kept fixed and only the filter corresponding to the additional data stream is optimized. The first algorithm determines the receive and transmit filters directly in the downlink. The other algorithm operates in the dual uplink, from which the downlink transmit and receive filters can be obtained via the general rate duality leading to nonzero-forcing in the downlink. Simulation results reveal marginal performance losses compared to more complex algorithms.

Design of Single-Group Multicasting-Beamformers

For the single-group multicast scenario, where K users are served with the same data by a base station equipped with N antennas, we present two beamforming algorithms which outperform state-of-the-art multicast filters and feature a drastically reduced complexity at the same time. For the power minimization problem, where QoS constraints need to be satisfied, we introduce a successive beamforming filter computation approach aiming at satisfying at least one additional SNR constraint per orthogonal filter update. As long as the number of users K is smaller than the number N of transmit antennas, this procedure delivers excellent results. Our second approach is an iterative update algorithm for the max-min problem subject to a limitation of the transmit power. Given a low-complexity initialization beamformer, we search within the local vicinity of this filter vector for a filter-update preserving the transmit power and achieving a larger minimum SNR. To this end, we improve the weakest users SNR during each iteration and keep on applying this procedure as long as the updates increase the smallest SNR. Otherwise, we adapt the step-size and continue investigating the local vicinity. It turns out that this novel approach is superior to existing state-of-the-art multicast beamformers for an arbitrary number of users.