Sphere-constrained ML detection for frequency-selective channels

The maximum-likelihood (ML) sequence detection problem for channels with memory is investigated. The Viterbi algorithm (VA) provides an exact solution. Its computational complexity is linear in the length of the transmitted sequence, but exponential in the channel memory length. On the other hand, the sphere decoding (SD) algorithm also solves the ML detection problem exactly, and has expected complexity which is a low-degree polynomial (often cubic) in the length of the transmitted sequence over a wide range of signal-to-noise ratios. We combine the sphere-constrained search strategy of SD with the dynamic programming principles of the VA. The resulting algorithm has the worst-case complexity determined by the VA, but often significantly lower expected complexity

On the sphere-decoding algorithm II. Generalizations, second-order statistics, and applications to communications

In Part 1, we found a closed-form expression for the expected complexity of the sphere-decoding algorithm, both for the infinite and finite lattice. We continue the discussion in this paper by generalizing the results to the complex version of the problem and using the expected complexity expressions to determine situations where sphere decoding is practically feasible. In particular, we consider applications of sphere decoding to detection in multiantenna systems. We show that, for a wide range of signal-to-noise ratios (SNRs), rates, and numbers of antennas, the expected complexity is polynomial, in fact, often roughly cubic. Since many communications systems operate at noise levels for which the expected complexity turns out to be polynomial, this suggests that maximum-likelihood decoding, which was hitherto thought to be computationally intractable, can, in fact, be implemented in real-time-a result with many practical implications. To provide complexity information beyond the mean, we derive a closed-form expression for the variance of the complexity of sphere-decoding algorithm in a finite lattice. Furthermore, we consider the expected complexity of sphere decoding for channels with memory, where the lattice-generating matrix has a special Toeplitz structure. Results indicate that the expected complexity in this case is, too, polynomial over a wide range of SNRs, rates, data blocks, and channel impulse response lengths

Joint data detection and channel estimation for OFDM systems

We develop new blind and semi-blind data detectors and channel estimators for orthogonal frequency-division multiplexing (OFDM) systems. Our data detectors require minimizing a complex, integer quadratic form in the data vector. The semi-blind detector uses both channel correlation and noise variance. The quadratic for the blind detector suffers from rank deficiency; for this, we give a low-complexity solution. Avoiding a computationally prohibitive exhaustive search, we solve our data detectors using sphere decoding (SD) and V-BLAST and provide simple adaptations of the SD algorithm. We consider how the blind detector performs under mismatch, generalize the basic data detectors to nonunitary constellations, and extend them to systems with pilots and virtual carriers. Simulations show that our data detectors perform well

Generalized feedback detection for spatial multiplexing multi-antenna systems

We present a unified detection framework for spatial multiplexing multiple-input multiple-output (MIMO) systems by generalizing Heller’s classical feedback decoding algorithm for convolutional codes. The resulting generalized feedback detector (GFD) is characterized by three parameters: window size, step size and branch factor. Many existing MIMO detectors are turned out to be special cases of the GFD. Moreover, different parameter choices can provide various performance-complexity tradeoffs. The connection between MIMO detectors and tree search algorithms is also established. To reduce redundant computations in the GFD, a shared computation technique is proposed by using a tree data structure. Using a union bound based analysis of the symbol error rates, the diversity order and signal-to-noise ratio (SNR) gain are derived analytically as functions of the three parameters; for example, the diversity order of the GFD varies between 1 and N. The complexity of the GFD varies between those of the maximum-likelihood (ML) detector and the zero-forcing decision feedback detector (ZFDFD). Extensive computer simulation results are also provided

MIMO Detection for High-Order QAM Based on a Gaussian Tree Approximation

This paper proposes a new detection algorithm for MIMO communication systems employing high order QAM constellations. The factor graph that corresponds to this problem is very loopy; in fact, it is a complete graph. Hence, a straightforward application of the Belief Propagation (BP) algorithm yields very poor results. Our algorithm is based on an optimal tree approximation of the Gaussian density of the unconstrained linear system. The finite-set constraint is then applied to obtain a loop-free discrete distribution. It is shown that even though the approximation is not directly applied to the exact discrete distribution, applying the BP algorithm to the loop-free factor graph outperforms current methods in terms of both performance and complexity. The improved performance of the proposed algorithm is demonstrated on the problem of MIMO detection

Semiblind Channel Estimation and Data Detection for OFDM Systems With Optimal Pilot Design

This paper considers semiblind channel estimation and data detection for orthogonal frequency-division multiplexing (OFDM) over frequency-selective fading channels. We show that the samples of an OFDM symbol are jointly complex Gaussian distributed, where the mean and covariance are determined by the locations and values of fixed pilot symbols. We exploit this distribution to derive a novel maximum-likelihood (ML) semiblind gradient-descent channel estimator. By exploiting the channel impulse response (CIR) statistics, we also derive a semiblind data detector for both Rayleigh and Ricean fading channels. Furthermore, we develop an enhanced data detector, which uses the estimator error statistics to mitigate the effect of channel estimation errors. Efficient implementation of both the semiblind and the improved data detectors is provided via sphere decoding and nulling-canceling detection. We also derive the Cramér-Rao bound (CRB) and design optimal pilots by minimizing the CRB. Our proposed channel estimator and data detector exhibit high bandwidth efficiency (requiring only a few pilot symbols), achieve the CRB, and also nearly reach the performance of an ideal reference receiver

Dispensing with channel estimation: differentially modulated cooperative wireless communications

As a benefit of bypassing the potentially excessive complexity and yet inaccurate channel estimation, differentially encoded modulation in conjunction with low-complexity noncoherent detection constitutes a viable candidate for user-cooperative systems, where estimating all the links by the relays is unrealistic. In order to stimulate further research on differentially modulated cooperative systems, a number of fundamental challenges encountered in their practical implementations are addressed, including the time-variant-channel-induced performance erosion, flexible cooperative protocol designs, resource allocation as well as its high-spectral-efficiency transceiver design. Our investigations demonstrate the quantitative benefits of cooperative wireless networks both from a pure capacity perspective as well as from a practical system design perspective