Block data transmission: a comparison of performance for the mber precoder designs

In a companion paper, we have studied the zero-forcing (ZF) transceiver with decision feedback equalizer (DFE) over slowly time-varying narrowband multiinput multioutput (MIMO) channels. The space-time generalized triangular decomposition (ST-GTD) was used for the design of ZF-DFE transceivers. The space-time geometric mean decomposition (ST-GMD) ZF transceiver minimizes both the arithmetic mean square error (MSE) at the feedback detector and the average uncoded bit error rate (BER) in moderate high signal-to-noise ratio (SNR). This paper addresses the design problem of DFE transceiver without zero-forcing constraint. In the first part, a channel independent temporal precoder is superimposed on the conventional block-wise GMD-based minimum mean square error (MMSE) DFE transceiver to take advantage of the temporal diversity. In the second part, ST-GTD is applied for the design of MMSE DFE transceivers. With accurate channel prediction and space-time powerloading, the proposed ST-GMD MMSE transceiver minimizes the arithmetic MSE at the feedack detector, and maximizes Gaussian mutual information. For practical applications, the ST-GTD MMSE transceiver which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD MMSE system is also developed. In the convex region, our analysis shows that the proposed MMSE transceivers has better BER performance than the conventional GMD-based MMSE transceiver; the average BERs of the proposed systems are nonincreasing functions of the ST-block size. The superior performance of ST-GMD MMSE transceiver over the ST-GMD ZF transceiver is also verified analytically.

The paper considers the problem of constructing adaptive minimum bit error rate (MBER) neural network equalisers for binary signalling. Motivated from a kernel density estimation of the bit error rate (BER) as a smooth function of training data, a stochastic gradient algorithm called the least bit error rate (LBER) is developed for adaptive nonlinear equalisers. This LBER algorithm is applied to adaptive training of a radial basis function (RBF) equaliser in a channel intersymbol interference (ISI) plus co-channel interference setting. A simulation study shows that the proposed algorithm has good convergence speed, and a small-size RBF equaliser trained by the LBER can closely approximate the performance of the optimal Bayesian equaliser. The results also demonstrate that the standard adaptive algorithm, the least mean square (LMS), performs poorly for neural network equalisers because the minimum mean square error (MMSE) is clearly suboptimal in the equalisation setting.

In recent times, there has been growing interests in integration of voice, data and video traffic in wireless communication networks. With these growing interests, WCDMA has immerged as an attractive access technique. The performance of WCDMA system is deteriorated in presence of multipath fading environment. The paper presents space-time coded minimum mean square error (MMSE) Decision Feedback Equalizer (DFE) for wideband code division multiple access (WCDMA) in a frequency selective channel. The filter coefficients in MMSE DFE are optimized to suppress noise, intersymbol interference (ISI), and multiple access interference (MAI) with reasonable system complexity. For the above structure, we have presented the estimation of BER for a MMSE DFE using computer simulation experiments. The simulation includes the effects of additive white Gaussian noise, multipath fading and multiple access interference (MAI). Furthermore, the performance is compared with standard linear equalizer (LE) and RAKE receiver. Numerical and simulation results show that the MMSE DFE exhibits significant performance improvement over the standard linear equalizer (LE) and RAKE receiver.

Adaptive beamforming for binary phase shift keying communication systems

The paper derives a minimum bit error rate (BER) solution for the decision feedback equaliser (DFE) that employs a linear combination of the channel observations and the past decisions. We show that by using a geometric translation the DFE is reduced to a simpler linear equaliser. A BER expression for the linear equaliser is obtained under the assumption of linearly separable decision regions, and a method is proposed to optimally set the linear-combiner coefficients of the DFE. This minimum BER solution is superior to the usual minimum mean square error (MSE) solution.

The conventional decision feedback equaliser (DFE) that employs a linear combination of channel observations and past decisions is considered. The design of this class of DFE is to construct a hyperplane that separates the different signal classes. It is well known that the popular minimum mean square error (MMSE) design is generally not the optimal minimum bit error rate (MBER) solution. A strategy is proposed for designing the DFE based on support vector machines (SVMs). The SVM design achieves asymptotically the MBER solution and is superior in performance to the usual MMSE solution. Unlike the exact MBER solution, this SVM solution can be computed very efficiently.

The performance of linear filters degrade drastically when applied to mitigate intersymbol interference caused by channels with frequent nulls in their spectral characteristics like, e.g., time-dispersive radio channels. In such cases, the well-known decision feedback equalizer (DFE) is one possible nonlinear approach to improve the quality of the receiver. However, adapting the DFE filter coefficients to equalize time-varying channels is computationally intense, especially if the dimension of the observation vector is very high. In this paper, we apply the conjugate gradient (CG) algorithm to a conventional minimum mean square error (MMSE) DFE in order to reduce its computational complexity. Moreover, we compare its performance to the one of MMSE DFE versions which are based on the computationally efficient least-mean-square (LMS) or recursive least-squares (RLS) algorithm, respectively. The analysis additionally includes a detailed investigation of computational complexity with respect to the required number of floating point operations (FLOPs). Simulation results when applied to a digital communications system show the ability of the CG based MMSE DFE to outperform either the LMS and the RLS based MMSE DFE although its computational complexity is even smaller in most of the cases.

We investigate the equalization and channel identification for space-time block coded signals over a frequency-selective multiple-input multiple output (MIMO) channels. The equalization is considered by taking into account the cyclostationarity of space-time block coded signals. The minimum mean square error (MMSE) solutions are derived for linear and decision feedback (DF) equalizers. Due to the redundancy induced by space-time block coding, a blind estimation for MIMO channels is investigated by using the subspace method. Together with pilot symbols, the semi-blind channel estimation can be used and it can result in less (bit error rate) performance degradation of the MMSE linear and DF equalizers.

Compared to wired channels, time dispersive radio channels possess more frequent nulls in their spectral characteristics. Thus, the performance of linear filters to compensate intersymbol interference degrades dramatically. The well-known nonlinear decision feedback equalizer (DFE) is one approach to improve this behavior. However, in systems with observations of high dimensionality, the optimum DFE structure is computational intensive. In this paper, we apply the method of the multi-stage Wiener filter (MSWF) to a conventional minimum mean square error (MMSE) DFE in order to reduce computational complexity. The application of the new algorithm to an Enhanced Data rates for GSM Evolution (EDGE) system demonstrates the ability to outperform the even more computational intensive linear Wiener filter (WF).

In orthogonal frequency division multiplexing (OFDM), Fourier Transform (FT) is used as a modulation technique. To avoid inter-symbol interference (ISI) in OFDM by a time dispersive channel, a cyclic prefix (CP) is used which also reduces its spectral efficiency. wavelet packet transform (WPT) as a modulation scheme has been proposed for wireless communication. In this paper, WPT based OFDM is presented and proposed using minimum mean square error (MMSE) equalizer. Equalization is a major factor in wavelets. MMSE is proposed for wavelet based OFDM (WOFDM) based on WPT and compared with zero forcing equalizer (ZFE). The performance is measured for arbitrary magnitude finite impulse response (FIR) channels in the presence of additive white Gaussian noise (AWGN) and impulse noise. Simulation results show a clear improvement in bit error rate (BER) for MMSE over ZFE equalization technique in the presence of noise.

The paper proposes a receiver scheme for multicarrier-CDMA (MC-CDMA) that while not making use of the well known technique of guard interval is able to combat the effects of intersymbol as well as intercarrier interference (ISI, ICI). This is achieved by means of an adaptive multiple input multiple output (MIMO) fractionally spaced (FS) decision feedback equaliser (DFE) receiver scheme performing joint detection (JD). The forward section of the equaliser is designed to operate at a fractional rate, while the feedback section is symbol spaced. The analysis and design of the MIMO FS/DFE scheme is made for the minimum mean square error (MMSE) criterion. In this context, the steady state behaviour is analysed and the receivers performance are computed by means of the residual mean square error (MSE). Using Gaussian approximation an expression of the bit error rate (BER) for binary phase shift keying (BPSK) modulation is derived for both the down link (DL) and up link (UL) communication scenarios.

This paper presents a linear complexity iterative rake detector for the recently proposed orthogonal time frequency space (OTFS) modulation scheme. The basic idea is to extract and combine the received multipath components of the transmitted symbols in the delay-Doppler grid using linear diversity combining schemes like maximal ratio combining (MRC), equal gain combining and selection combining to improve the SNR of the combined signal. We reformulate the OTFS input-output relation in the vector form by placing some null symbols in the delay-Doppler grid thereby exploiting the block circulant property of the channel matrix. Using the new input-output relation we propose a low complexity iterative detector based on the MRC scheme. The bit error rate (BER) performance of the proposed detector will be compared with the state of the art message passing detector and orthogonal frequency division multiplexing (OFDM) scheme employing a single tap minimum mean square error (MMSE) equalizer. We also show that the frame error rate (FER) performance of the MRC detector can be improved by employing error correcting codes operating in the form of a turbo decision feedback equalizer (DFE).

The two major obstacles toward high-capacity indoor wireless networks are distortion due to the indoor channel and the limited availability of bandwidth which necessitates a high spectral efficiency. A combined orthogonal-frequency division multiplexing/spatial-diversity multiple access (OFDM/SDMA) approach can effectively tackle both obstacles. The channel distortion due to multipath propagation is easily mitigated with OFDM while the bandwidth efficiency can be increased with the use of SDMA. In order to keep the network's cost acceptable, simplified SDMA processors are preferred over the exponentially complex optimal maximum-likelihood processors. However, these simplified processors perform significantly worse than the optimal ones in terms of average bit error rate (BER). In this paper, we show that by adapting the constellation sizes applied on the individual subcarriers to the channel conditions, the performance of OFDM/SDMA processors can be significantly enhanced. In the uplink, we derive simple closed-form equations for the optimal constellation sizes for both a simple linear minimum mean-square error (MMSE) detector and for a nonlinear MMSE decision feedback equalizer (DFE) detector. Furthermore, for each detector, we introduce a simplified loading algorithm which lowers the computational and signaling complexity substantially at a small performance penalty. In the downlink, we study the dual precoders of the uplink detectors, respectively, the linear MMSE precoder and the nonlinear Tomlinson-Harashima (TH) MMSE-based precoder. For both precoders, we derive expressions for the optimal and the simplified constellation sizes. Additionally, we show that in time-division duplexing systems, the constellation distribution of a set of dual detectors/precoders is identical for up- and downlink, which effectively halves the computational complexity of adaptive loading. In the fully loaded uplink, the proposed adaptive loading algorithm results in a gain of 9 dB for a BER=10/sup -3/ for the linear MMSE detector and a gain of 4.5 dB for the nonlinear MMSE-DFE detector. In the fully loaded downlink, a gain of 6.3 dB is achieved for the MMSE precoder and 5.5 dB for the TH-MMSE precoder.

In this paper, we consider the design of a full-rate linear space-time block code for coherent multiple-input multiple-output (MIMO) communication systems under a quasi-static Rayleigh flat-fading environment. Our design targets specifically at the use of a linear minimum mean-square error (MMSE) receiver that minimizes the asymptotic average bit error rate (BER) when the transmitted signal is selected from a 4-QAM constellation. This optimization problem is solved in two main stages: 1) a lower bound on the BER is first minimized, and 2)how this minimized lower bound can be achieved is then shown. By exploiting a rigorous convex optimization technique without any assumption on the code, we prove that individual unitary and trace-orthogonal structures are the necessary and sufficient conditions to assure the minimum asymptotic average BER with an MMSE detector. An algorithm is provided for an efficient generation of our codes, and simulation results confirm that our optimally designed codes are indeed superior in performance compared to some other commonly used codes

In this brief, decision-feedback equalization (DFE) receiver for multidrop single-ended signaling is described. The proposed DFE receiver adopts a reference voltage having equalization information to remove channel intersymbol interference. It uses a smaller number of DFE tap elements than the conventional DFE receiver for the same level of equalization, resulting in reduced power consumption and silicon area, particularly for multi-input/output interface. The proposed DFE receiver was fabricated in a 0.13- μm CMOS process, whose evaluation results indicate a reliable operation up to 3.40-Gb/s data rate with reduced power consumption.