Conjugate gradient based MMSE Decision Feedback Equalization

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.

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.

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).

The combination of multitone modulation with direct sequence spectrum spreading (DS/SS) has been introduced in the past. The performance of a correlation receiver has been evaluated for a multipath channel and in the presence of an additional multiple access interference. We analyze the problem of decision feedback equalization (DFE) for such a system. In order to understand the potential of the system with equalization, we first study the steady-state behavior of the equalizer for a minimum mean square error (MMSE) criterion. The investigation is carried out for a receiver made of a bank of filters matched to both the symbol shape and the channel, and for a two path channel. Assuming transmission of binary phase shift keying (BPSK) symbols, an exact expression of the bit error probability is obtained in the form of an integral. Then adaptive least mean square (LMS) and recursive least square (RLS) structures are derived. The performance of the adaptive RLS algorithm is demonstrated by means of computer simulations.

A well-known receiver strategy for a linearly modulated signal transmitted over a frequency-selective channel is channel equalization. Recently it was proposed to employ a minimum mean-squared error (MMSE) channel equalizer for the downlink of CDMA. In this paper, we introduce a new receiver concept using MMSE channel equalization as a first stage and MMSE decision-feedback equalization (DFE) utilizing soft feedback from the decoding unit as a second stage. Both schemes are compared for the downlink of CDMA. It turns out, that after channel decoding we gain about 1 dB compared to conventional MMSE channel equalization.

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.

We investigate the use of the minimum mean-squared- error decision-feedback-equalizer (MMSE-DFE) as a preprocessor to reduce the computational complexity of symbol detection in frequency-selective multiple- input multiple-output (MIMO) channels. The preprocessor delays and focuses the received signal energy which reduces the effects of inter-symbol- interference and multiple-access-interference. This property of the MMSE-DFE preprocessor is exploited to order and to reduce the number of symbol candidates considered by an iterative maximum- likelihood (ML) detector. Simulations show that the proposed detection scheme can achieve lower bit- error-rates than existing reduced-complexity algorithms in overdetermined and underdetermined receive scenarios. Near-optimum performance is achieved when the number of symbol candidates is increased.

SUMMARY This paper proposes an iterative maximum a posteriori probability (MAP) receiver for multiple-input-multiple-output (MIMO) and orthogonal frequency-division multiplexing (OFDM) mobile communications. For exploiting the space, time, and frequency diversity, the lowdensity parity-check code (LDPC) is used as a channel coding with a builtin interleaver. The receiver employs the expectation maximization (EM) algorithm so as to perform the MAP symbol detection with reasonable computational complexity. The minimum mean square error (MMSE), recursive least squares (RLS), and least mean square (LMS) algorithms are theoretically derived for the channel estimation within this framework. Furthermore, the proposed receiver performs a new scheme called backward symbol detection (BSD), in which the signal detection uses the channel impulse response that is estimated one OFDM symbol later. The advantage of BSD, which is explained from the viewpoint of the message passing algorithm, is that BSD can exploit information on the both precedent and subsequent OFDM symbols, similarly to RLS with smoothing and removing (SR-RLS) [25]. In comparison with SR-RLS, BSD reduces the complexity at the cost of packet error rate (PER) performance. Computer simulations show that the receiver employing RLS for the channel estimation outperforms the ones employing MMSE or LMS, and that BSD can improve the PER performance of the ones employing RLS or LMS.

Several researches investigate the performance of the conventional adaptive equalizers for the medium data rates HF waveforms (up to 8 PSK) and show that they are suitable for mitigating the HF channel. However, the performance of these types of equalizers is very bad for the high data rates HF waveforms (up to 64QAM). Most of the later researches in the high data rates HF waveforms are based on the soft turbo equalizers which are very complicated. In this paper, we try to design the lowest complex equalizer can mitigate the HF channel for the high data rates waveforms. We investigate the performance of the minimum mean square error decision feedback equalizer (MMSE-DFE) indirectly adaptive through channel estimation based on least square estimation (LS). We show that the basic performance of the MMSE-DFE cannot satisfy the standard requirements, and then we introduce two additional enhancements. First, an effective channel estimation technique (double estimation) is proposed. The new estimator shows a clear performance enhancement over simple least square estimation with linear interpolation (about 3 dB gain at 1e-5 BER for the 64QAM). The second enhancement is to use the iterative structure through decoder using the same conventional equalizer and decoder and this gives another 3 dB gain at 1e-5 BER for the 64QAM. Iterative structure is less complicated than turbo equalizers for sure, as turbo equalizers require a lot of changes in the equalizer, decoder and demapper blocks to be SISO modules. Final equalizer model satisfies all the strict requirements of both (STANAG 4539 annex B) and (MIL-STD-188-110B app. C) standards under the ITU-R Poor channel conditions. In addition, we compare our performance with two different vendors of HF modems and other different research and show that our performance is very competitive.

Transmitter optimization for a multicarrier system with Gaussian pulse as transmit filter is studied in this paper. Symbol duration T and /spl alpha/ are optimization parameters, where /spl alpha/ is a parameter in Gaussian pulse function. 2-D minimum mean square error decision-feedback equalizer (MMSE-DFE) is used in the receiver and cost function is the output unbiased signal-to-noise ratio (SNR) of 2-D MMSE-DFE. Four kinds of deterministic channels are discussed. Analysis shows that the problem for time-selective channel is the dual problem for frequency-selective channel. If doubly-selective channel is deterministic separable, we obtain a general result, which is highly symmetric in time and frequency domains. Finally, we propose balanced design for practical purposes.

A major complaint of individuals with normal hearing and hearing impairments is a reduced ability to understand speech in a noisy environment. This paper is proposed to remove the noise from the speech signal in various real time environments and to make the hearing impaired to understand the information by transforming speech in to text format. The quality of audio signal can be improved by filtering the degraded speech signal through adaptive filters. For Noise cancellation widrow & hoff’s Least Mean Square (LMS) algorithms are being used for simplicity in implementation. The LMS algorithm was simple in it's derivation and robust in a number of applications but it also have limitation in selection of a certain values such as step size and results in computational complexity. Hence to overcome all the limitations and to present an enhanced speech signal, a novel approach named VSSNDLMS algorithm is proposed. The performance of algorithms like Variable Step Size Normalised LMS , Normalised Differential LMS with proposed VSSNDLMS with different input signals are analysed in this paper . Finally, through simulation results the proposed VSSNDLMS algorithm converges fastly with minimum mean square error and it is useful in predicting the adaptive filter performance of various algorithms and the implementation indicate the improvement in quality of the speech signal and it appears to be favourable for hearing impaired. Keywords: VSSNDLMS, LMS Algorithm, Noise Cancellation, Speech Processing, Adaptive Filter

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.

This paper proposes an enhanced decision feedback equalizer (DFE) for filter bank multicarrier (FBMC) systems over offset quadrature amplitude modulation (OQAM) based on a minimal mean square error (MMSE) criterion. For each subcarrier, besides one feedforward (FF) filter and one feedback (FB) filter, we add two intercarrier interference (ICI)-suppressing filters, which feed back detected precursors extracted from neighboring subchannels to enhance ICI suppression in the presence of multipath channels. Our simulation results indicate our proposal makes a considerable improvement comparing with MMSE-DFE under a severe ICI and ISI scenario despite few extra costs in computational complexity.

In a TDMA mobile communication system, an adaptive decision feedback equalizer (DFE) is the common device to compensate the intersymbol interference caused by the multipath effect. Due to the fast fading characteristic of channels, most conventional DFEs use the recursive least square (RLS) algorithm. However, it is known that the RLS algorithm is computationally intensive and not easy to implement. The LMS is well known for its simple structure, however, due to its poor tracking property, it cannot be used. Recently, a multiple-training and multiple-tracking LMS (MTT-LMS) algorithm was developed. It was shown that the DFE trained by the MTT-LMS algorithm can yield a satisfactory result at moderate mobile speed. The MTT-LMS algorithm retains the simple structure of the LMS algorithm and is suitable for hardware implementation. In this paper, we consider the ASIC design of the MTT-LMS DFE for application to North American IS-54 systems. We have designed an efficient architecture which not only has small chip area but low clock rate. We also develop a new decision device to provide the desired signal for the MTT-LMS algorithm and the implementation of the device is simpler than the conventional one.

In orthogonal frequency-division multiplexing (OFDM) systems, it is generally assumed that the channel response is static in an OFDM symbol period. However, the assumption does not hold in high-mobility environments. As a result, intercarrier interference (ICI) is induced and the system performance is degraded. A simple remedy for this problem is the application of the zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. Unfortunately, the direct ZF method requires the inversion of an NxN ICI matrix, where N is the number of subcarriers. When N is large, the computational complexity can become prohibitively high. As for the direct MMSE method, in addition to an NxN matrix inverse, it requires an extra NxN matrix multiplication, making the required computational complexity higher compared to the direct ZF method. In this dissertation, we first propose a low-complexity ZF method to solve the problem in single-input-single-output (SISO) OFDM systems. The main idea is to explore the special structure inherent in the ICI matrix and to apply Newton's iteration for matrix inversion. With our formulation, fast Fourier transforms (FFTs) can be used in the iterative process, reducing the complexity from O(N^3) to O(Nlog_2 N) . Also, the required number of the iteration is typically one or two. We also analyze the convergence behavior of the proposed method and derive the theoretical output signal-to-interference-noise-ratio (SINR). For the MMSE method, we first reformulate the MMSE solution in a way that the extra matrix multiplication can be avoided. Similar to the ZF method, we then exploit the structure of the ICI matrix and apply Newton's iteration to reduce the complexity of the matrix inversion. For a multiple-input-multiple-output (MIMO) OFDM system, the required complexity of the ZF and MMSE methods becomes more intractable. We then manage to extend the proposed ZF and MMSE methods for SISO-OFDM systems to MIMO-OFDM systems. It turns out that the computational complexity can be reduced even more significantly. Simulation results show that the performance of the proposed methods is almost as good as that of the direct ZF and MMSE methods, while the required computational complexity is reduced dramatically. Finally, we explore the application of the proposed methods in mobility-induced ICI mitigation for OFDM multiple access (OFDMA) systems, and in carrier frequency offset (CFO) induced ICI mitigation for OFDMA uplink systems. As that in OFDM systems, the proposed methods can reduce the required computational complexity, effectively.