Layered MAP algorithm for MIMO ISI channels

The layered maximum a posteriori （L-MAP） algorithm has been proposed to detect signals under frequency selective fading multiple input multiple output （MIMO） channels. Compared to the optimum MAP detector, the L-MAP algorithm can efficiently identify signal bits, and the complexity grows linearly with the number of input antennas. The basic idea of L-MAP is to operate on each input sub-stream with an optimum MAP sequential detector separately by assuming the other streams are Gaussian noise. The soft output can also be forwarded to outer channel decoder for iterative decoding. Simulation results show that the proposed method can converge with a small number of iterations under different channel conditions and outperforms other sub-optimum detectors for rank-deficient channels.     

Linear turbo equalization for parallel ISI channels

We propose a method for exploiting transmit diversity using parallel independent intersymbol interference channels together with an iterative equalizing receiver. Linear iterative turbo equalization (LITE) employs an interleaver in the transmitter and passes a priori information on the transmitted symbols between multiple soft-input/soft-output minimum mean-square error linear equalizers in the receiver. We describe the LITE algorithm, present simulations for both stationary and fading channels, and develop a framework for analyzing the evolution of the a priori information as the algorithm iterates.     

FIR channel-shortening equalizers for MIMO ISI channels

Finite-length delay-optimized multi-input multi-output (MIMO) equalizers that optimally shorten the impulse response memory of frequency-selective MIMO channels are derived. The MIMO equalizers are designed to minimize the average energy of the error sequence between the equalized MIMO channel impulse response and an MIMO target impulse response (TIR) with shorter memory. Two criteria for optimizing the MIMO TIR are analyzed and compared. The presented analytical framework encompasses a multitude of previously-studied finite-length equalization techniques     

Optimum soft decision demodulation for ISI channels

Two different methods of soft-decision demodulation for channels with finite intersymbol interference (ISI) in the presence of additive white Gaussian noise (AWGN) are analyzed. In both schemes, the cutoff rate R₀ of the discrete channel created by the demodulator output quantization is chosen as the design criterion. Expressions for the optimal thresholds of the quantizer associated with the demodulation of binary signals are derived. Results for the channel with memory equal to one symbol duration are presented. As a special case, the (1-D) channel with soft decision demodulation is analyzed. Closed-form solutions show that a 4-b quantizer improves performance substantially in this case     

Sequence detection for binary ISI channels using signal-spacepartitioning

Binary symbol detection based on a sequence of finite observation signals is formulated in the multidimensional signal space. A systematic space partitioning method is proposed to divide the entire space into two decision regions using a set of hyperplanes. The resulting detector structure consists of K parallel linear classifiers followed by a K-to-1 Boolean mapper, and is well suited to high-speed implementation. Compared to direct implementation of the fixed-delay tree search (FDTS) detection rule, the proposed signal-space formulation results in a considerable saving in digital hardware. Examples taken from binary-input intersymbol interference (ISI) channels are used to demonstrate the proposed technique. Block processing strategies suitable for high-speed applications are also discussed     

On the application of factor graphs and the sum-product algorithm to ISI channels

In this paper, based on the application of the sum-product (SP) algorithm to factor graphs (FGs) representing the joint a posteriori probability (APP) of the transmitted symbols, we propose new iterative soft-input soft-output (SISO) detection schemes for intersymbol interference (ISI) channels. We have verified by computer simulations that the SP algorithm converges to a good approximation of the exact marginal APPs of the transmitted symbols if the FG has girth at least 6. For ISI channels whose corresponding FG has girth 4, the application of a stretching technique allows us to obtain an equivalent girth-6 graph. For sparse ISI channels, the proposed algorithms have advantages in terms of complexity over optimal detection schemes based on the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. They also allow a parallel implementation of the receiver and the possibility of a more efficient complexity reduction. The application to joint detection and decoding of low-density parity-check (LDPC) codes is also considered and results are shown for some partial-response magnetic channels. Also in these cases, we show that the proposed algorithms have a limited performance loss with respect to that can be obtained when the optimal "serial" BCJR algorithm is used for detection. Therefore, for their parallel implementation, they represent a favorable alternative to the modified "parallel" BCJR algorithm proposed in the literature for the application to magnetic channels.     

Performance of trellis-coded modulation for equalized multipathfading ISI channels

The performance of TCM on equalized multipath fading ISI channels with different equalization schemes is examined. Trellis codes that are effective for AWGN channels and flat fading channels with interleaving are evaluated for equalized multipath fading channels. For joint MLSE equalization and decoding the equivalent uncoded system outperforms all the trellis-coded systems that are examined. Trellis codes that are designed for flat fading channels with interleaving perform well if interleaving is used and an MLSE equalizer is used before deinterleaving. An effective interleaver-deinterleaver is identified that allows joint DDFSE equalization and decoding to be used without the need for equalization before decoding     

Efficient Viterbi algorithm for signals with ISI

The authors propose an efficient method of implementing the Viterbi algorithm at Nyquist-rate, for linearly modulated signals corrupted by ISI and AWGN. When signalling is M-ary and ISI extends over L-1 symbols, this scheme results in M+CL (complex multiplications, C is the number of samples per symbol), whereas the whitened-matched-filter based Viterbi algorithm requires M^L complex multiplications     

On the performance evaluation of ISI channels

The performance of finite intersymbol interference (ISI) channels in the presence of additive white Gaussian noise is evaluated by interpreting the ISI channel as a trellis code. Closed form results are obtained for ISI channels with one and two symbols of interference. An efficient algorithm is also introduced to evaluate the minimum free Euclidean distance of any ISI channel     

Adaptive combined DFE/MLSE techniques for ISI channels

By embedding a decision-feedback equalizer (DFE) into the structure of a maximum-likelihood sequence estimator (MLSE), an adaptive combined DFE/MLSE scheme is proposed. In this combined DFE/MLSE, the embedded DFE has three functions: (i) prefiltering the received signals and truncating the equivalent channel response into the desired one, (ii) compensating for channel distortions, and (iii) providing the MLSE detector with predicted values of input signals. Since the embedded MLSE detector operates on the predicted signals the detected symbols at the output of the DFE/MLSE do not suffer any delay and can be directly fed back into the embedded DFE so that the error propagation, which usually takes place in a conventional DFE, can be greatly reduced. Analytical and simulation results indicate that the performance is significantly improved by the DFE/MLSE compared to the conventional DFE while its computation complexity is much less than that of the conventional MLSE receiver. The combined DFE/MLSE can use different adaptive structures (block-updating, sliding window updating or symbol-by-symbol updating) to meet different performance objectives. Moreover, the proposed DFE/MLSE provides a trade-off between performance and complexity with a parameter m representing the MLSE detection depth as well as the number of predicting steps of the embedded DFE. For some particular values of m, this scheme is capable of emulating the conventional DFE, MLSE-VA, adaptive LE-MLSE equalizer, adaptive DDFSE, and adaptive BDFE without detection delay     

Combined turbo detection and decoding for unknown ISI channels

We present two decoding structures which combine turbo detection and decoding, allowing communication in the presence of intersymbol interference (ISI). The first one treats the ISI as another constituent decoder which participates in the exchange of extrinsic information, and performs slightly worse than the second structure, which combines the trellis representing each one of the constituent encoders with the ISI trellis. We show that for both methods, it is possible to obtain good performance, even when no a priori information about the ISI channel is available to the decoder.     

Transceiver optimization for block-based multiple access through ISI channels

In this paper, we describe a formulation of the minimum mean square error (MMSE) joint transmitter-receiver design problem for block-based multiple access communication over intersymbol interference (ISI) channels. Since the direct formulation of this problem turns out to be nonconvex, we develop various alternative convex formulations using techniques of linear matrix inequalities (LMIs) and second-order cone programming (SOCP). In particular, we show that the optimal MMSE transceiver design problem can be reformulated as a semidefinite program (SDP), which can be solved using highly efficient interior point methods. When the channel matrices are diagonal (as in cyclic prefixed multicarrier systems), we show that the optimal MMSE transceivers can be obtained by subcarrier allocation and optimal power loading to each subcarrier for all the users. Moreover, the optimal subcarrier allocation and power-loading can be computed fairly simply (in polynomial time) by the relative ratios of the magnitudes of the subchannel gains corresponding to all subcarriers. We also prove that any two users can share no more than one subcarrier in the optimal MMSE transceivers. By exploiting this property, we design an efficient strongly polynomial time algorithm for the determination of optimal powerloading and subcarrier allocation in the two-user case.     

On the performance of turbo equalization for precoded ISI channels

In this paper, we present a semi‐analytical approach for analyzing the serial concatenation (SCC) of a high rate convolutional code and a precoded intersymbol interference (ISI) channel. The significance of the proposed approach is that it can be used to identify, for a given outer high rate code and fixed ISI channel, the precoder that results in the lowest error rate floor. In estimating the bit error performance in the floor region, we use analytical techniques developed for trellis codes to compute the overall system minimum squared Euclidean distance, and then use a semi‐analytical approach to find the corresponding multiplicity. We also demonstrate via simulations that the proposed technique may be extended to fading ISI channels with favorable results. We give examples that support our analysis. Copyright © 2006 John Wiley & Sons, Ltd.     

Sequential sequence estimation for trellis-coded modulation onmultipath fading ISI channels

A new receiver structure is proposed for trellis-coded modulation on multipath fading intersymbol interference (ISI) channels that permits the use of large-state trellis codes. The receiver uses a sequential sequence estimator with the Fano algorithm, and a channel estimator consisting of a fast nonrecursive start-up algorithm for training and the LMS algorithm for tracking. During the tracking mode, the channel estimates are updated dynamically by using recent tentative decisions produced by the sequential sequence estimator. This approach results in good tracking even on rapidly varying channels, and reduces the degradation in performance of the sequential sequence estimator due to channel estimation error. The effect of fading is mitigated using both implicit time diversity in the form of interleaved trellis-coded modulation and explicit antenna diversity     

Multistage block-spreading for impulse radio multiple access through ISI channels

Transmitting digital information using ultra-short pulses, impulse radio (IR) has received increasing interest for multiple access (MA). When IRMA systems have to operate in dense multipath environments, the multiple user interference (MUI) and intersymbol interference (ISI) induced, adversely affect system capacity and performance. Analog IRMA utilizes pulse position modulation (PPM) and random time-hopping codes to mitigate ISI and suppress MUI statistically. We develop an all-digital IRMA scheme that relies on multistage block-spreading (MS-BS), and judiciously designed transceiver pairs to eliminate MUI deterministically, and regardless of ISI multipath effects. Our proposed MS-BS-IRMA system can accommodate a large number of users and is capable of providing different users with variable transmission rates, which is important for multimedia applications. Unlike conventional IRMA systems, MS-BS-IRMA exhibits no degradation in bit-error rate performance, as the number of users increases.     

Blind asynchronous multiuser CDMA receivers for ISI channels usingcode-aided CMA

A code-aided constant modulus algorithm (CMA) based approach is presented for blind detection of asynchronous short-code DS-CDMA (direct sequence code division multiple access) signals in intersymbol interference (ISI)/multipath channels. Only the spreading code of the desired user is assumed to be known; its transmission delay may be unknown. A linear equalizer is designed by minimizing the Godard/CMA cost function of the equalizer output with respect to the equalizer coefficients subject to the fact that the equalizer lies in a subspace associated with the desired user's code sequence. Constrained CMA leads to the extraction of the desired user's signal whereas unconstrained minimization leads to the extraction of any one of the active users. The results are further improved by using unconstrained CMA initialized by the results of the code-aided CMA. Identifiability properties of the approach are analyzed. Illustrative simulation examples are provided     

Blind OFDM symbol synchronization in ISI channels

We present a new algorithm for blind symbol synchronization in orthogonal frequency division multiplexing (OFDM) systems. The new algorithm declares symbol synchronization when a certain autocorrelation matrix, constructed from the received signal, achieves minimum rank. Unlike previously proposed blind algorithms, the new rank method guarantees correct symbol synchronization, even in the presence of intersymbol interference. Also, it does not assume that the OFDM time samples are i.i.d. In particular, the rank method works even with OFDM systems that employ pulse shaping. The increased complexity of the algorithm would be acceptable for systems, such as fixed-receiver broadcast systems, that require guaranteed synchronization under all conditions.     

Blind multiuser MMSE detector for CDMA signals in ISI channels

A technique is introduced that allows the blind and direct estimation of an optimal, in the minimum mean-squared error sense, linear multiuser receiver for direct-sequence code-division multiple-access signals. We consider the case of an asynchronous multiple access channel in the presence of possibly large intersymbol-interference. Our approach does not require channel estimation and uses the knowledge of the code for the user of interest only, Unlike other comparable techniques, this method converges to the true optimum receiver as the sample size increases, regardless of signal-to-noise ratio     

FDMA capacity of Gaussian multiple-access channels with ISI

This paper proposes a numerical method for characterizing the rate region achievable with frequency-division multiple access (FDMA) for a Gaussian multiple-access channel with intersymbol interference. The frequency spectrum is divided into discrete frequency bins and the discrete bin-assignment problem is shown to have a convex relaxation, making it tractable to numerical optimization algorithms. A practical low-complexity algorithm for the two-user case is also proposed. The algorithm is based on the observation that the optimal frequency partition has a two-band structure when the two channels are identical or when the signal-to-noise ratio is high. The simulation result shows that the algorithm performs well in other cases as well. The FDMA-capacity algorithm is used to devise the optimal frequency-division duplex plan for very-high-speed digital subscriber lines     

On the capacity and normalization of ISI channels

We investigate the capacity of various intersymbol interference (ISI) channels with additive white Gaussian noise (AWGN). Previous papers showed a minimum E/sub b//N/sub 0/ of -4.6 dB, 3 dB below the capacity of a flat channel, is obtained using water-pouring capacity formulas for the 1+D channel. However, these papers did not take into account that the channel power gain can be greater than one when water-pouring is used. We present a generic power normalization method of the channel frequency response, namely, peak bandwidth normalization (PBN), to facilitate the fair capacity comparison of various ISI channels. Three types of ISI channel, i.e., adder channels, RC channels, and magnetic recording channels, are examined. By using our channel power gain normalization, the capacity curves of these ISI channels are shown.