Soft Interference Cancellation Minimum Mean-squared Error Research Articles

Min-Sum Soft Symbol Estimation for Iterative MMSE Detection

Soft symbol estimation (SSE) is the first process in soft interference cancellation minimum mean squared error (SIC-MMSE) detection for multiple-input multiple-output (MIMO) systems. SSE requires the sum of exhaustive multiplications of probability that occupies a non-negligible amount of the entire SIC-MMSE complexity. This paper proposes two approaches to reduce the complexity of SSE. The first is to find the approximation of SSE by investigating the estimation in the log-domain, which leads to a simple min-sum operation. The second is to approximate the hyperbolic tangent with low-order piecewise polynomial functions. These two approaches are then integrated. The simulation results show that the proposed methods do not degrade the performance in terms of bit error rate (BER), and that they can greatly reduce the number of multiplications, from $O(K2^{K})$ to $O(K)$ .

Turbo equalization based on joint Gaussian, SIC-MMSE and LMMSE for nonlinear satellite channels

The nonlinear distortion of wideband signal due to the filtering and efficiently operated high power amplifiers limits the performance of satellite communications. Volterra series can be used to describe the nonlinear satellite channels effectively. Most existing equalizers simply ignore the nonlinear terms or treat all the nonlinear combinations of symbols as interference. In this study, by properly exploiting information from nonlinear terms, we propose three turbo equalizers for nonlinear satellite channels, namely, joint Gaussian (JG), soft interference cancellation-minimum mean square error (SIC-MMSE) and linear minimum mean square error (LMMSE) equalizers. In JG and SIC-MMSE-based equalizers, both the linear and nonlinear terms that contain the symbol of interest are considered as desired signals. Accordingly, the required statistics are calculated based on the a priori probabilities of coded bits from output of channel decoder. For LMMSE-based equalizer, we propose to calculate the extrinsic information from output of equalizer by excluding the prior information in both the linear and nonlinear terms. Simulation results demonstrate that the proposed equalizers significantly outperform the method which ignores the presence of nonlinear interferences. Moreover, the nonlinear terms that contain the symbol of interest can be exploited to further improve the performance of turbo equalization.

Low-complexity SIC-MMSE for joint multiple-input multiple-output detection

Iterative detection and decoding based on a soft interference cancellation–minimum mean squared error (SIC-MMSE) scheme provides efficient performance for coded MIMO systems. The critical computational burden for a SIC-MMSE detector in a MIMO system lies in the multiple inverse operations of the complex matrix. In this paper, we present a new method to reduce the complexity of the SIC-MMSE scheme based on a MIMO detection scheme that uses a single universal matrix with a non-layer-dependent inversion process. We apply the Taylor series expansion approach and derive a simple non-layer-dependent inverse matrix. The simulation results reveal that the utilization of the universal matrices presented in this paper produces almost the same performance as the conventional SIC-MMSE scheme but with low computational complexity.

Efficient SIC-MMSE MIMO detection with three iterative loops

In this paper, we propose an efficient joint iterative detection and decoding (JIDD) scheme with a soft interference cancellation minimum mean squared error (SIC-MMSE) based method for a turbo coded multiple-input multiple-output (MIMO) system. In the proposed method, we activate a loop inside the SIC-MMSE based MIMO detection process in addition to the iterative loop between the MIMO detector and turbo decoder, so that the iteration inside the SIC-MMSE detection can be performed in parallel to the iterations inside the turbo decoder. Subsequently, soft outputs from each loop is exchanged for next further iteration, and this makes three iterative loops in total. In comparison with the conventional JIDD schemes, employing additional loop inside the MIMO detection process largely contributes to enhance the performance. In addition, the additional loop speeds up the performance convergence and eventually requires smaller overall computational complexity at the same performance.

Efficient soft bit estimation for joint iterative multiple‐input multiple‐output detection

In this study, the authors propose a joint iterative detection and decoding (JIDD) method for a turbo coded multiple-input multiple-output (MIMO) system, with a linear order of complexity. Accurate estimation of soft information should be conditioned for excellent performance of the JIDD, but it usually requires an exponential order of complexity. They propose a method which improves the performance of soft interference cancellation minimum mean-squared error (SIC-MMSE) method by increasing the reliability of the soft information utilised for interference cancellation. The proposed method utilises a posteriori probabilities from the MIMO detector as well as a priori probabilities from the turbo decoder, and perform soft minimum mean-squared error filtering for symbol level detection. With this approach, soft information is fully fed into the symbol detection process, and thus the reliability of soft symbol is increased. In addition, they can separate out the bit-level soft estimation process by using a simple linear method. Simulation results show that the proposed method provides substantial complexity reduction, with a bit error rate performance comparable to the conventional SIC-MMSE methods.

Low-Complexity Butterfly Integration Structure for MMSE-SIC SISO Detector

In this paper, we propose a low-complexity butterfly integration structure (LCBIS) for the minimum mean square error-soft interference cancellation (MMSE-SIC) soft-in soft-out (SISO) detector, which is widely used for MIMO systems. Unlike the conventional MMSE-SIC SISO detector which performs matrix inverse operations, the LCBIS performs butterfly integration operations with low complexity. To develop the LCBIS SISO detector, we derive an integral expression for the extrinsic information of the conventional MMSE-SIC SISO detector, and then propose a butterfly integration structure to compute the integral expression efficiently. Without matrix inverse operations, LCBIS significantly reduces the complexity of the MMSE-SIC SISO detector. In addition, simulation results show that LCBIS can offer much better BER than the other SISO detectors which do not perform matrix inverse operations.

Simple and Accurate Design of Low-Density Parity-Check Codes for Multi-Input Multi-Output Systems

In this paper we design an irregular low-density parity-check (LDPC) code for multiple-input multiple-output (MIMO) systems, using a simple extrinsic information transfer (EXIT) chart method. The MIMO systems considered are the optimal maximum a posteriori probability (MAP) detector and the suboptimal minimum mean square error soft-interference cancellation (MMSE-SIC) detector. The MIMO detector and the LDPC decoder exchange soft information and form a turbo iterative receiver. The EXIT charts are used to obtain the edge degree distribution of the irregular LDPC code which is optimized for the MIMO detector. It is shown that the performance of the designed LDPC code is better than that of conventional LDPC code which was optimized for either the Additive White Gaussian Noise (AWGN) channel or the MIMO channel without an explicit consideration of the given detector structure.

Low complexity iterative detection for OFDMA uplink with frequency offsets

In this work, we propose an iterative algorithm for the detection of transmitted symbols at the uplink of an orthogonal frequency-division multiple access (OFDMA) system. The algorithm allows distinct frequency-offsets (FO)s from each user that cause multiple-access and self interference. The proposed algorithm squeezes the interference of subcarrier k into 2D + 1 nearby subcarriers by preprocessing the received signal and yields a banded structure interference matrix. Here, the value of D depends on the FO and determines the squeezing depth. The proposed algorithm exploits this banded structure and realizes a low complexity iterative soft-interference-cancellation minimum mean-squared error (SIC-MMSE) equalizer that can be used in Turbo equalization. Simulation results show that the bit-error-rate (BER) performance of the proposed algorithm outperforms existing detection algorithms and is very much close to the zero-FO frequency-domain-equalization (zero-FO-FDE).

Iterative Receivers for MIMO-OFDM and Their Convergence Behavior

In this paper, we investigate two reduced-complexity iterative soft interference cancellation minimum mean square error (SIC-MMSE) receivers for frequency-selective multiple-input-multiple-output (MIMO) channels. In the first receiver, the extrinsic information is exchanged between the SIC-MMSE equalizer and the channel decoding stages at each iteration. In the second receiver, the extrinsic information obtained from the SIC-MMSE equalizer is fed back to itself only up to a certain number of iterations and then passed to the channel decoder at the end of the last iteration only to reduce the computational complexity. Moreover, to better understand the convergence behavior of the proposed iterative receivers, we study the notion of extrinsic information transfer (EXIT) characteristics. Using simulations, we derive the extrinsic information trajectory on the EXIT chart at various bit-energy-to-noise-spectral-density ratio ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Eb</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">No</i> ) ranges to predict the number of iterations required to converge and the turbo cliff region. The predicted behavior of the proposed receivers is then confirmed by the bit-error-rate (BER) performance curves.

Reduced-Complexity Iterative Equalization for Severe Time-Dispersive MIMO Channels

In this paper, a reduced-complexity soft-interference-cancellation minimum mean-square-error (SIC-MMSE) iterative equalization method for severe time-dispersive multiple-input-multiple-output (MIMO) channels is proposed. To mitigate the severe time dispersiveness of the channel, a single carrier with cyclic prefix is employed, and the equalization is performed in the frequency domain. This simplifies the challenging problem of equalization in MIMO channels due to both the intersymbol interference (ISI) and the coantenna interference (CAI). The proposed iterative algorithm works in two stages. The first stage estimates the transmitted frequency-domain symbols using a low-complexity SIC-MMSE equalizer. The second stage converts the estimated frequency-domain symbols in the time domain and finds their means and variances to incorporate in the SIC-MMSE equalizer in the next iteration. Simulation results show the bit-/symbol-error-rate performance of the SIC-MMSE equalizer, with and without coding, for various modulation schemes.

Coding-Spreading Tradeoff in LDPC-Coded CDMA With Turbo Multiuser Detection

We consider the problem of coding-spreading tradeoff in code-division multiple-access (CDMA) systems employing multiuser joint decoding. In particular, we assume the users employing the capacity-achieving low-density parity-check (LDPC) codes and at the receiver, turbo multiuser detection is used to implement joint decoding. We solve the coding-spreading optimization based on the extrinsic information signal-to-noise ratio (SNR) evolution curves for the soft-input soft-output (SISO) multiuser detectors and the SISO LDPC decoders. Two types of SISO multiuser detectors are treated, namely, the soft interference cancellation minimum mean-square-error (SIC-MMSE) detector and the soft interference cancellation matched filter (SIC-MF) detector. Moreover, both single-cell and multicell scenarios are considered. For each of these cases, we are able to characterize the extrinsic information SNR analytically, for both finite-size systems and for the so-called large systems where asymptotic performance results must be evoked. Our analysis indicates that the SIC-MMSE-based system offers a significant gain in spectral efficiency compared with the SIC-MF counterpart, in both single-cell and multicell scenarios. This is in contrast to the single-user decoding case, where it has been shown that the MMSE detector offers little advantage over the conventional matched-filter in terms of capacity in multicell scenario. Moreover, the results on coding-spreading tradeoff for finite-size systems and large systems match very well.