Christos Komninakis

Multi-input multi-output fading channel tracking and equalization using Kalman estimation

This paper addresses the problem of channel tracking and equalization for multi-input multi-output (MIMO) time-varying frequency-selective channels. These channels model the effects of inter-symbol interference (ISI), co-channel interference (CCI), and noise. A low-order autoregressive model approximates the MIMO channel variation and facilitates tracking via a Kalman filter. Hard decisions to aid Kalman tracking come from a MIMO finite-length minimum-mean-squared-error decision-feedback equalizer (MMSE-DFE), which performs the equalization task. Since the optimum DFE for a wide range of channels produces decisions with a delay /spl Delta/ > 0, the Kalman filter tracks the channel with a delay. A channel prediction module bridges the time gap between the channel estimates produced by the Kalman filter and those needed for the DFE adaptation. The proposed algorithm offers good tracking behavior for multiuser fading ISI channels at the expense of higher complexity than conventional adaptive algorithms. Applications include synchronous multiuser detection of independent transmitters, as well as coordinated transmission through many transmitter/receiver antennas, for increased data rate.

Joint iterative channel estimation and decoding in flat correlated Rayleigh fading

This paper addresses the design and performance evaluation with respect to capacity of M-PSK turbo-coded systems operating in frequency-flat time-selective Rayleigh fading. The receiver jointly performs channel estimation and turbo decoding, allowing the two processes to benefit from each other. To this end, we introduce a suitable Markov model with a finite number of states, designed to approximate both the values and the statistical properties of the correlated flat fading channel phase, which poses a more severe challenge to PSK transmission than amplitude hiding. Then, the forward-backward algorithm determines both the maximum a posteriori probability (MAP) value for each symbol in the data sequence and the MAP channel phase in each iteration. Simulations show good performance in standard correlated Rayleigh fading channels. A sequence of progressively tighter upper bounds to the capacity of a simplified Markov-phase channel is derived, and performance of a turbo code with joint iterative channel estimation and decoding is demonstrated to approach these capacity bounds.

Constellation labeling for linear encoders

This paper investigates optimal constellation labeling in the context of the edge profile. A constellations edge profile lists the minimum-distance edge for each binary symbol error. The paper introduces the symmetric-ultracomposite (SU) labeling structure and shows that this structure provides undominated edge profiles for 2/sup n/-PSK, 2/sup n/-PAM, and 2/sup 2n/-point square QAM. The SU structure is a generalization of the commonly used reflected binary Gray code. With the proper choice of basis vectors, SU labeling can support either set-partition or Gray-code labeling of 2/sup n/-PSK, 2/sup n/-PAM, and 2/sup 2n/-point square QAM. Notably, there are Gray-code and set-partition labelings that do not have the SU structure. These labelings yield inferior edge profiles. The SU structure does not apply to cross constellations. However, for any standard cross constellation with 32 or more points, a quasi-SU labeling structure can approximate the SU structure. With the correct choice of basis, quasi-SU labelings produce quasi-Gray labelings. However, the quasi-SU structure cannot support set-partition labeling. In fact, the quasi-SU structure provides a better edge profile than standard set-partition labeling. Thus, for cross constellations there is a choice between edge profile optimality and the group structure provided by set-partitioning. Here, the correct choice depends on whether the encoder trellis has parallel branches.

Channel estimation and equalization in fading

This paper addresses the problem of channel tracking and equalization in frequency-selective fading channels. Low-order autoregressive models approximate the channel taps, where each tap is a circular complex Gaussian random process with the typical U-shaped spectrum, and uncorrelated with each other. A Kalman filter tracks the time-varying channel, using the decisions of an adaptive minimum-mean-squared-error decision-feedback equalizer (DFE). The DFE is optimized for decision delay /spl Delta/>0, which exhibits performance advantages over decision delay /spl Delta/=0 for a wide range of channels. The DFE staggered decisions cause the Kalman filter to also track the channel with a delay. The receiver also uses a channel prediction module to bridge the time gap between the Kalman channel estimation and the channel estimates needed for the DFE adaptation. The proposed algorithm offers good tracking behavior thus allowing for reduction in the amount of training symbols needed to effectively track a time-varying frequency selective channel.

Adaptive multi-input multi-output fading channel equalization using Kalman estimation

This paper addresses the problem of adaptive channel tracking and equalization for multi-input multi-output (MIMO) time-variant frequency-selective channels. A finite-length minimum-mean-squared-error decision-feedback equalizer (MMSE-DFE) performs the equalization task, while a Kalman filter tracks the MIMO channel, which models the corrupting effects of inter-symbol interference (ISI), inter-user interference (IUI), and noise. The Kalman tracking is aided by previous hard decisions produced by the DFE, with a decision delay /spl Delta/>0, which causes the Kalman filter to track the channel with a delay. A channel prediction module bridges the time gap between the channel estimates produced by the Kalman filter and those needed for the DFE adaptation. The proposed algorithm offers good tracking behavior for multi-user fading ISI channels at the expense of higher complexity.

Pilot-aided joint data and channel estimation in flat correlated fading

This paper addresses the design and performance evaluation of a pilot-aided turbo-coded system to achieve reliable PSK communication in frequency-flat, time-selective fading, with a relatively high Doppler rate. We introduce a suitable Markov model with a finite number of states, designed to approximate both the values and the statistical properties of the correlated flat fading channel phase, which poses a more severe challenge to PSK transmission than amplitude fading. The forward-backward algorithm is used to determine both the maximum a posteriori probability (MAP) value for each bit in the data sequence, and the MAP channel phase in each iteration. Soft information is exchanged between the phase and data estimation modules. Using a turbo-code and joint iterative decoding and channel estimation, performance is demonstrated to approach an upper bound to the capacity of a Markov-phase channel.

Minimality for punctured convolutional codes

This paper investigates encoders optimization for the Hamming weight after periodic puncturing, and discusses minimality issues that may affect the performance of the punctured encoders. Periodically puncturing a minimal encoder produces a higher rate encoder that may or may not be minimal. If it is not minimal, it may have a zero-output loop and it may be catastrophic. A code search can use a fast algorithm to determine whether an encoders state diagram has a zero-output loop under periodic symbol puncturing, and a proposed method to assess the performance of codes with a zero-output loop that are not catastrophic. As an example, the paper optimizes rate-1/4 unpunctured codes for Hamming weight under both bit-wise and symbol-wise periodic puncturing. Code tables and simulation results are included.

Capacity of the binomial channel, or minimax redundancy for memoryless sources

This paper computes the capacity of the binomial channel of order n, for any finite n via convex optimization and duality. The binomial channel capacity is also the minimax coding redundancy for a class of memoryless sources. The exact capacity for finite n computed here is compared to the asymptotic expression found by Xie and Barron (see IEEE Trans. Inform. Theory, vol.43, no.2, p.646-57 (March 1997)).

Robustness of space-time turbo codes

We consider the performance of a turbo code with 2 transmit antennas and 2 receive antennas for flat fading channels. We consider robustness within and among families of channels with the same singular values (SVs). When the two SVs are similar, the bit error rate performance is robust in terms of proximity to the channel capacity. When the 2 SVs differ significantly, robust performance can be achieved by a time-varying linear transformation (TVLT). Iterative decoding is the same as for standard parallel concatenated convolutional codes, except that the extrinsic information about encoder outputs are also exchanged.

Trellis turbo-codes in flat Rayleigh fading with diversity

This paper compares the performance of two schemes for joint channel estimation and turbo-decoding of high-rate trellis turbo-codes in flat Rayleigh fading, where antenna diversity is available at the receiver. The first method relies on iterative quantized phase estimation, and the second on optimum filtering of pilot and coded symbols. For Doppler rates of practical interest, simulations indicate that optimum pilot filtering is superior to approximating the channel phase with a quantized Markov model. The optimum filtering approach also has lower complexity. For an absolute measure of performance, proximity to channel capacity is also discussed. Iterative joint channel estimation and turbo-decoding with either method is demonstrated to achieve almost all the capacity gain due to receiver antenna diversity.