Dominik Seethaler

Efficient detection algorithms for MIMO channels: a geometrical approach to approximate ML detection

It is well known that suboptimal detection schemes for multiple-input multiple-output (MIMO) spatial multiplexing systems (equalization-based schemes as well as nulling-and-cancelling schemes) are unable to exploit all of the available diversity, and thus, their performance is inferior to ML detection. Motivated by experimental evidence that this inferior performance is primarily caused by the inability of suboptimal schemes to deal with bad (i.e., poorly conditioned) channel realizations, we study the decision regions of suboptimal schemes for bad channels. Based on a simplified model for bad channels, we then develop two computationally efficient detection algorithms that are robust to bad channels. In particular, the novel sphere-projection algorithm (SPA) is a simple add-on to standard suboptimal detectors that is able to achieve near-ML performance and significantly increased diversity gains. The SPAs computational complexity is comparable with that of nulling-and-cancelling detectors and only a fraction of that of the Fincke-Phost sphere-decoding algorithm for ML detection.

ASIC Implementation of Soft-Input Soft-Output MIMO Detection Using MMSE Parallel Interference Cancellation

Multiple-input multiple-output (MIMO) technology is the key to meet the demands for data rate and link reliability of modern wireless communication systems, such as IEEE 802.11n or 3GPP-LTE. The full potential of MIMO systems can, however, only be achieved by means iterative MIMO decoding relying on soft-input soft-output (SISO) data detection. In this paper, we describe the first ASIC implementation of a SISO detector for iterative MIMO decoding. To this end, we propose a low-complexity minimum mean-squared error (MMSE) based parallel interference cancellation algorithm, develop a suitable VLSI architecture, and present a corresponding four-stream 1.5 mm2 detector chip in 90 nm CMOS technology. The fabricated ASIC includes all necessary preprocessing circuitry and exceeds the 600 Mb/s peak data-rate of IEEE 802.11n. A comparison with state-of-the-art MIMO-detector implementations demonstrates the performance benefits of our ASIC prototype in practical system-scenarios.

Worst- and average-case complexity of LLL lattice reduction in MIMO wireless systems

Lattice reduction by means of the LLL algorithm has been previously suggested as a powerful preprocessing tool that allows to improve the performance of suboptimal detectors and to reduce the complexity of optimal MIMO detectors. The complexity of the LLL algorithm is often cited as polynomial in the dimension of the lattice. In this paper we argue that this statement is not correct when made in the MIMO context. Specifically, we demonstrate that in typical communication scenarios the worst-case complexity of the LLL algorithm is not even finite. For i.i.d. Rayleigh fading channels, we further prove that the average LLL complexity is polynomial and that the probability for an atypically large number of LLL iterations decays exponentially.

An efficient MMSE-based demodulator for MIMO bit-interleaved coded modulation

In bit-interleaved coded modulation (BICM) systems employing maximum-likelihood decoding, a demodulator (demapper) calculates a log-likelihood ratio (LLR) for each coded bit, which is then used as a bit metric for Viterbi decoding. In the MIMO case, the computational complexity of LLR calculation tends to be excessively high, even if the log-sum approximation is used. Thus, there is a strong demand for efficient suboptimum MIMO-BICM demodulation algorithms with near-optimum performance. We propose an efficient MIMO-BICM demodulator that is derived by means of a Gaussian approximation for the post-detection interference. Our derivation results in an MMSE equalizer followed by per-layer LLR calculation (i.e., LLRs are calculated separately for each layer). The novel demodulator can be interpreted as an MMSE analogue of a recently proposed ZF-equalization based demodulator, as well as an extension of ZF-equalization based demodulation to correlated post-detection interference. Because it performs per-layer LLR calculation, it has the same (low) computational complexity as the ZF-equalization based demodulator. Simulation results demonstrate that the performance of our demodulator is close to that of LLR calculation using all layers jointly, and significantly better than that of the ZF-equalization based demodulator.

Low-Complexity and Full-Diversity MIMO Detection Based on Condition Number Thresholding

In this paper, we consider MIMO spatial multiplexing systems and elaborate the impact of the channel condition number on the performance of ML and ZF detection. In particular, we show that for channels with bounded condition number ZF detection achieves the same diversity as ML detection. Motivated by this, we propose a novel threshold receiver that uses simple ZF detection for well-conditioned channels and ML detection for poorly conditioned channels. We show that this receiver achieves full diversity and we provide an upper bound on its SNR gap to ML detection. We further investigate cost-reduced versions of the threshold receiver and examine their performance in terms of simulation results.

Low-Complexity MIMO Data Detection using Seysen's Lattice Reduction Algorithm

Lattice reduction (LR) is a powerful technique for improving the performance of suboptimum MIMO data detection methods. For LR-assisted data detection, the LLL algorithm has been considered almost exclusively so far. In this paper, we propose and develop the application of Seysens algorithm (SA) to LR-assisted MIMO detection, and we show that the SA is a promising alternative to the LLL algorithm. Specifically, the SA outperforms the LLL algorithm in that it finds better lattice bases for MIMO systems of practical interest, which is reflected by an improved performance of SA-assisted detectors relative to their LLL-assisted counterparts. We present an efficient implementation of the SA whose per-iteration complexity is linear in the number of antennas, and we demonstrate that the SA requires significantly fewer iterations than the LLL algorithm.

On the Complexity Distribution of Sphere Decoding

We analyze the (computational) complexity distribution of sphere decoding (SD) for random infinite lattices. In particular, we show that under fairly general assumptions on the statistics of the lattice basis matrix, the tail behavior of the SD complexity distribution is fully determined by the inverse volume of the fundamental regions of the underlying lattice. Particularizing this result to N x M, N ≥ M, i.i.d. circularly symmetric complex Gaussian lattice basis matrices, we find that the corresponding complexity distribution is of Pareto-type with tail exponent given by N-M+1. A more refined analysis reveals that the corresponding average complexity of SD is infinite for N = M and finite for N >; M. Finally, for i.i.d. circularly symmetric complex Gaussian lattice basis matrices, we analyze SD preprocessing techniques based on lattice-reduction (such as the LLL algorithm or layer-sorting according to the V-BLAST algorithm) and regularization. In particular, we show that lattice-reduction does not improve the tail exponent of the complexity distribution while regularization results in a SD complexity distribution with tails that decrease faster than polynomial.

Vector Perturbation Precoding Revisited

We consider the downlink of a multiuser system with multiple antennas at the base station. Vector perturbation (VP) precoding is a promising variant of transmit-side channel inversion allowing the users to detect their data in a simple, noncooperative manner. VP precoding has so far been developed and analyzed under the assumptions that the transmitter has perfect channel state information (CSI) and that the receivers know perfectly a channel-dependent transmit power normalization factor and have infinite dynamic range. We demonstrate that the violation of any of these idealizing assumptions degrades the performance of VP significantly and almost always results in an error floor. Motivated by this observation, we propose a novel scheme which we term transmit outage precoding (TOP). With TOP, the transmitter uses a prearranged power scaling known by the receivers and refrains from transmitting when channel conditions are poor. We further show how to augment TOP and conventional VP to deal with a finite dynamic range at the receiver. The performance of the proposed schemes under various levels of transmit CSI is studied in terms of a theoretical diversity analysis and illustrated by numerical results.

Improved MMSE estimation of correlated MIMO channels using a structured correlation estimator

Channel estimation is an important and challenging task in MIMO communications. The minimum mean-square-error (MMSE) channel estimator is able to exploit spatial correlation of the MIMO channel but requires prior estimation of the channel correlation matrix. In this paper, we investigate pilot-based MMSE channel estimation including channel correlation estimation. We propose an MMSE channel estimator using a structured correlation estimator and demonstrate its advantages over conventional MMSE estimators. Simulation results show that the proposed channel estimator outperforms conventional channel estimators in the case of strong spatial correlation and at low SNR.

Performance and Complexity Analysis of Infinity-Norm Sphere-Decoding

Promising approaches for efficient detection in multiple-input multiple-output (MIMO) wireless systems are based on sphere-decoding (SD). The conventional (and optimum) norm that is used to conduct the tree traversal step in SD is the l 2 -norm. It was, however, recently observed that using the l ¿-norm instead reduces the hardware complexity of SD considerably at only a marginal performance loss. These savings result from a reduction in the length of the critical path in the circuit and the silicon area required for metric computation, but are also, as observed previously through simulation results, a consequence of a reduction in the computational (i.e., algorithmic) complexity. The aim of this paper is an analytical performance and computational complexity analysis of l ¿-norm SD. For independent and identically distributed (i.i.d.) Rayleigh fading MIMO channels, we show that l ¿-norm SD achieves full diversity order with an asymptotic SNR gap, compared to l 2-norm SD, that increases at most linearly in the number of receive antennas. Moreover, we provide a closed-form expression for the computational complexity of l ¿-norm SD based on which we establish that its complexity scales exponentially in the system size. Finally, we characterize the tree pruning behavior of l ¿-norm SD and show that it behaves fundamentally different from that of l 2-norm SD.