arXiv subjects

Martin Haardt

Publications and source records attributed to Martin Haardt.

44 records · Page 3Linked to original sources

arXiv2015

R-dimensional ESPRIT-type algorithms for strictly second-order non-circular sources and their performance analysis

High-resolution parameter estimation algorithms designed to exploit the prior knowledge about incident signals from strictly second-order (SO) non-circular (NC) sources allow for a lower estimation error and can resolve twice as many sources. In this paper, we derive the R-D NC Standard ESPRIT and the R-D NC Unitary ESPRIT algorithms that provide a significantly better performance compared to their original versions for arbitrary source signals. They are applicable to shift-invariant R-D antenna arrays and do not require a centrosymmetric array structure. Moreover, we present a first-order asymptotic performance analysis of the proposed algorithms, which is based on the error in the signal subspace estimate arising from the noise perturbation. The derived expressions for the resulting parameter estimation error are explicit in the noise realizations and asymptotic in the effective signal-to-noise ratio (SNR), i.e., the results become exact for either high SNRs or a large sample size. We also provide mean squared error (MSE) expressions, where only the assumptions of a zero mean and finite SO moments of the noise are required, but no assumptions about its statistics are necessary. As a main result, we analytically prove that the asymptotic performance of both R-D NC ESPRIT-type algorithms is identical in the high effective SNR regime. Finally, a case study shows that no improvement from strictly non-circular sources can be achieved in the special case of a single source.

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arXiv2013

Low-Complexity Lattice Reduction-Aided Channel Inversion Methods for Large-Dimensional Multi-User MIMO Systems

Low-complexity precoding {algorithms} are proposed in this work to reduce the computational complexity and improve the performance of regularized block diagonalization (RBD) {based} precoding {schemes} for large multi-user {MIMO} (MU-MIMO) systems. The proposed algorithms are based on a channel inversion technique, QR decompositions{,} and lattice reductions to decouple the MU-MIMO channel into equivalent SU-MIMO channels. Simulation results show that the proposed precoding algorithms can achieve almost the same sum-rate performance as RBD precoding, substantial bit error rate (BER) performance gains{,} and a simplified receiver structure, while requiring a lower complexity.

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arXiv2013

Frequency-Domain Group-based Shrinkage Estimators for UWB Systems

In this work, we propose low-complexity adaptive biased estimation algorithms, called group-based shrinkage estimators (GSEs), for parameter estimation and interference suppression scenarios with mechanisms to automatically adjust the shrinkage factors. The proposed estimation algorithms divide the target parameter vector into a number of groups and adaptively calculate one shrinkage factor for each group. GSE schemes improve the performance of the conventional least squares (LS) estimator in terms of the mean-squared error (MSE), while requiring a very modest increase in complexity. An MSE analysis is presented which indicates the lower bounds of the GSE schemes with different group sizes. We prove that our proposed schemes outperform the biased estimation with only one shrinkage factor and the best performance of GSE can be obtained with the maximum number of groups. Then, we consider an application of the proposed algorithms to single-carrier frequency-domain equalization (SC-FDE) of direct-sequence ultra-wideband (DS-UWB) systems, in which the structured channel estimation (SCE) algorithm and the frequency domain receiver employ the GSE. The simulation results show that the proposed algorithms significantly outperform the conventional unbiased estimator in the analyzed scenarios.

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arXiv2013

Sum-Rate Maximization with Minimum Power Consumption for MIMO DF Two-Way Relaying: Part I - Relay Optimization

The problem of power allocation is studied for a multiple-input multiple-output (MIMO) decode-and-forward (DF) two-way relaying system consisting of two source nodes and one relay. It is shown that achieving maximum sum-rate in such a system does not necessarily demand the consumption of all available power at the relay. Instead, the maximum sum-rate can be achieved through efficient power allocation with minimum power consumption. Deriving such power allocation, however, is nontrivial due to the fact that it generally leads to a nonconvex problem. In Part I of this two-part paper, a sum-rate maximizing power allocation with minimum power consumption is found for MIMO DF two-way relaying, in which the relay optimizes its own power allocation strategy given the power allocation strategies of the source nodes. An algorithm is proposed for efficiently finding the optimal power allocation of the relay based on the proposed idea of relative water-levels. The considered scenario features low complexity due to the fact that the relay optimizes its power allocation without coordinating the source nodes. As a trade-off for the low complexity, it is shown that there can be waste of power at the source nodes because of no coordination between the relay and the source nodes. Simulation results demonstrate the performance of the proposed algorithm and the effect of asymmetry on the considered system.

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arXiv2013

Blind Adaptive Constrained Constant-Modulus Reduced-Rank Interference Suppression Algorithms Based on Interpolation, Switched Decimation and Filtering

This work proposes a blind adaptive reduced-rank scheme and constrained constant-modulus (CCM) adaptive algorithms for interference suppression in wireless communications systems. The proposed scheme and algorithms are based on a two-stage processing framework that consists of a transformation matrix that performs dimensionality reduction followed by a reduced-rank estimator. The complex structure of the transformation matrix of existing methods motivates the development of a blind adaptive reduced-rank constrained (BARC) scheme along with a low-complexity reduced-rank decomposition. The proposed BARC scheme and a reduced-rank decomposition based on the concept of joint interpolation, switched decimation and reduced-rank estimation subject to a set of constraints are then detailed. The proposed set of constraints ensures that the multi-path components of the channel are combined prior to dimensionality reduction. In order to cost-effectively design the BARC scheme, we develop low-complexity decimation techniques, stochastic gradient and recursive least squares reduced-rank estimation algorithms. A model-order selection algorithm for adjusting the length of the estimators is devised along with techniques for determining the required number of switching branches to attain a predefined performance. An analysis of the convergence properties and issues of the proposed optimization and algorithms is carried out, and the key features of the optimization problem are discussed. We consider the application of the proposed algorithms to interference suppression in DS-CDMA systems. The results show that the proposed algorithms outperform the best known reduced-rank schemes, while requiring lower complexity.

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arXiv2012

Sum-Rate Maximization with Minimum Power Consumption for MIMO DF Two-Way Relaying: Part II - Network Optimization

In Part II of this two-part paper, a sum-rate-maximizing power allocation with minimum power consumption is found for multiple-input multiple-output (MIMO) decode-and-forward (DF) two-way relaying (TWR) in a network optimization scenario. In this scenario, the relay and the source nodes jointly optimize their power allocation strategies to achieve network optimality. Unlike the relay optimization scenario considered in part I which features low complexity but does not achieve network optimality, the network-level optimal power allocation can be achieved in the network optimization scenario at the cost of higher complexity. The network optimization problem is considered in two cases each with several subcases. It is shown that the considered problem, which is originally nonconvex, can be transferred into different convex problems for all but two subcases. For the remaining two subcases, one for each case, it is proved that the optimal strategies for the source nodes and the relay must satisfy certain properties. Based on these properties, an algorithm is proposed for finding the optimal solution. The effect of asymmetry in the number of antennas, power limits, and channel statistics is also considered. Such asymmetry is shown to have a negative effect on both the achievable sum-rate and the power allocation efficiency in MIMO DF TWR. Simulation results demonstrate the performance of the proposed algorithm and the effect of asymmetry in the system.

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arXiv2012

A framework for the analytical performance assessment of matrix and tensor-based ESPRIT-type algorithms

In this paper we present a generic framework for the asymptotic performance analysis of subspace-based parameter estimation schemes. It is based on earlier results on an explicit first-order expansion of the estimation error in the signal subspace obtained via an SVD of the noisy observation matrix. We extend these results in a number of aspects. Firstly, we derive an explicit first-order expansion of the Higher- Order SVD (HOSVD)-based subspace estimate. Secondly, we show how to obtain explicit first-order expansions of the estimation error of ESPRIT-type algorithms and provide the expressions for matrix-based and tensor-based Standard ESPRIT and Unitary ESPRIT. Thirdly, we derive closed-form expressions for the mean square error (MSE) and show that they only depend on the second-order moments of the noise. Hence, we only need the noise to be zero mean and possess finite second order moments. Fourthly, we investigate the effect of using Structured Least Squares (SLS) to solve the overdetermined shift invariance equations in ESPRIT and provide an explicit first-order expansion as well as a closed-form MSE expression. Finally, we simplify the MSE for the special case of a single source and compute the asymptotic efficiency of the investigated ESPRIT-type algorithms in compact closed-form expressions which only depend on the array size and the effective SNR. Our results are more general than existing results on the performance analysis of ESPRIT-type algorithms since (a) we do not need any assumptions about the noise except for the mean to be zero and the second-order moments to be finite (in contrast to earlier results that require Gaussianity or second-order circular symmetry); (b) our results are asymptotic in the effective SNR, i.e., we do not require the number of samples to be large; (c) we present a framework that incorporates various ESPRIT-type algorithms in one unified manner.

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arXiv2012

Sum-Rate Maximization in Two-Way AF MIMO Relaying: Polynomial Time Solutions to a Class of DC Programming Problems

Sum-rate maximization in two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying belongs to the class of difference-of-convex functions (DC) programming problems. DC programming problems occur as well in other signal processing applications and are typically solved using different modifications of the branch-and-bound method. This method, however, does not have any polynomial time complexity guarantees. In this paper, we show that a class of DC programming problems, to which the sum-rate maximization in two-way MIMO relaying belongs, can be solved very efficiently in polynomial time, and develop two algorithms. The objective function of the problem is represented as a product of quadratic ratios and parameterized so that its convex part (versus the concave part) contains only one (or two) optimization variables. One of the algorithms is called POlynomial-Time DC (POTDC) and is based on semi-definite programming (SDP) relaxation, linearization, and an iterative search over a single parameter. The other algorithm is called RAte-maximization via Generalized EigenvectorS (RAGES) and is based on the generalized eigenvectors method and an iterative search over two (or one, in its approximate version) optimization variables. We also derive an upper-bound for the optimal values of the corresponding optimization problem and show by simulations that this upper-bound can be achieved by both algorithms. The proposed methods for maximizing the sum-rate in the two-way AF MIMO relaying system are shown to be superior to other state-of-the-art algorithms.

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