Efficient decision feedback blind equalizer with multi-level modulus algorithm and two-stage feedback scheme for high-order QAM cable receivers

Intersymbol interference (ISI) of the radio propagation through multipath fading channels is a major factor that limits the performance of mobile communication systems. Blind decision feedback equalization (DFE) is one of major methods for channel equalization. We propose a new method, based on a Hammerstein filter instead of DFE filters, for enhancing the performance of DFE, hence, blind HDFE. In this paper, we show the bit error rate (BER) performance of blind DFE and blind HDFE, in order to prove the superiority of BHDFE.

Decision Feedback Equalizer (DFE) offers a good compromise between complexity and performance for channels with strong Intersymbol Interference (ISI). However, their blind or Decision-Directed (DD) adaptation may endure the inherent limitation from blind equalization algorithm or DD algorithm, i.e., 1) the blind equalization such as Constant Modulus Algorithm (CMA) has the ¿eye-opened¿ ability, but moderate convergence rate and steady state Mean Square Error (MSE); 2) the DD algorithm has faster convergence rate and lower steady state MSE, but it always cannot work unless the MSE of received signals is very low. So for overcoming above disadvantages we study the geometrical relation between CMA1-2 and DD algorithm and obtain the method of soft switch between CMA1-2 and DD algorithm. Consequently a new DFE based on CMA1-2 and DD algorithm is proposed. Based on theoretical analysis and computer simulations, the proposed approach is shown to be much more effective than the conventional DFE.

In this paper, an efficient blind equalization with two‐stage single/multilevel modulus and decision directed (DD) least mean square (LMS)‐like algorithm is proposed for high‐order QAM (64/256/1024QAM) cable modem systems. In wire‐lined cable systems, it seems that the cable channel may display a nearly invariant multi‐path effect over a considerable time, and then the blind equalizer can have the capability to recover the received high‐order QAM symbols on wired cables. The proposed blind equalization algorithm applies a two‐stage convergence scheme, which results from the multi‐modulus algorithm (MMA), sometimes called the modified constant modulus algorithm (MCMA), and the DD LMS‐like method. In the first equalization stage, the joint MMA and DD LMS‐like methods are applied for the purpose of fast convergence. When the convergence process reaches an acceptably steady condition, the convergence detector changes the process into the second stage. In the second equalization stage, the enhanced DD LMS‐like method with the generalized multi‐modulus is applied to reduce the mean square error (MSE) of equalizations further. For high‐order QAM cable systems, the proposed method performs faster than the previous well‐known blind methods do. Simultaneously, the proposed algorithm also provides less MSE and lower symbol error rate (SER) than the other blind methods do at the same signal‐to‐noise ratio (SNR).

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 this paper, a fast blind equalization with a two-stage generalized multilevel modulus algorithm (GMMA) and soft decision-directed (SDD) scheme is proposed for high-order QAM (64/256/1024QAM) systems on the downstream wired cable channel. The proposed fast blind equalization algorithm applies the two-stage convergence scheme and the SDD part uses the scheme with an adaptively selected decision region. In the first convergence stage, the joint GMMA and modified SDD equalization is applied for the purpose of the fast convergence. When the convergence process reaches the enough steady state, the convergence detector changes the first stage equalization to the second stage. In the second stage, the modified SDD scheme is applied to reduce the mean square error (MSE) further. On the wired cable channel at the 64/256/1024QAM modes, the proposed blind algorithm performs faster convergence speed than the previous blind methods do; meanwhile, the proposed algorithm also achieves smaller MSE than the other methods at the same signal-to-noise ratio (SNR).

We report a very efficient semianalytical approach for the performance evaluation of differential detection schemes for GMSK signals of the DECT standard. Precisely, for a given channel, the performance is determined by means of an analytical procedure which includes the saddlepoint approximation. We consider both static channels (with impulse response generated by the simulation program SIRCIM) and two-ray Rayleigh and log-normal fading channels. As a departure from previous works, our receiver includes an all-digital part after the analog differential detection scheme. The digital part includes: (1) a block for the estimation of both the optimum sampling phase and the nonlinear channel coefficients (by making use of the DECT training sequence), (2) a one-tap decision feedback (DF) equalizer, and (3) a block for the evaluation of the approximate optimum bias level (/spl gamma//sub e/) in the threshold detector. Both the DF equalizer coefficient and /spl gamma//sub e/ are based on the nonlinear channel coefficients estimate. For channels with a normalized delay spread up to 0.2, the use of the optimum threshold together with the DF equalizer permits a gain of about 2 dB at BER=10/sup -6/ with respect to a receiver without equalization and a zero-level decision threshold. In addition, we discover that, in indoor environments, the 2-bit GMSK detector performs roughly the same as the 1-bit detector. The threshold optimization is also effective in the presence of channels affected by fading. To support this statement, we report the performance of the 1-bit differential detection scheme combined with antenna selection diversity in the presence of a two-ray log-normal and Rayleigh fading channel.

This paper presents a QPSK/16 QAM down stream receiver ASIC chip for LMDS (Local Multipoint Distribution Services) applications. The proposed LMDS chip consists of a blind equalizer, a timing recovery block and a carrier recovery block. The blind equalizer uses a DFE (Decision Feedback Equalizer) structure using CMA (Constant Modulus Algorithm). The symbol timing recovery uses the modified parabolic interpolator and the decision-directed carrier recovery is used to remove the carrier frequency offset, phase offset and phase jitter. The implemented LMDS receiver can support four data rates, 10, 20, 30 and 40 Mbps and can accommodate the symbol rate up to 10 Mbaud. This symbol rate is faster than existing QAM receivers.

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.

Up to now, the Mean Square Error (MSE) criteria, the residual Inter-Symbol Interference (ISI) and the Bit-Error-Rate (BER) were used to analyze the equalization performance of a blind adaptive equalizer in its convergence state. In this paper, we propose an additional tool (additional to the ISI, MSE and BER) for analyzing the equalization performance in the convergence region based on the Maximum Time Interval Error (MTIE) criterion that is used for the specification of clock stability requirements in telecommunications standards. This new tool preserves the short term statistical information unlike the already known tools (BER, ISI, MSE) that lack this information. Simulation results will show that the equalization performance of a blind adaptive equalizer obtained in the convergence region for two different channels is seen to be approximately the same from the residual ISI and MSE point of view while this is not the case with our new proposed tool. Thus, our new proposed tool might be considered as a more sensitive tool compared to the ISI and MSE method.

Radial basis function (RBF) network based channel equalisers have a close relationship with Bayesian schemes. Decision feedback is introduced in the design of the RBF equaliser in order to reduce its computational complexity. The RBF decision feedback equaliser (DFE) was found to give similar performance to the conventional mean square error (MSE) DFE over Gaussian channels using various quadrature amplitude modulation (QAM) schemes, while requiring a lower feedforward and feedback order. Over Rayleigh-fading channels similar findings were valid for binary modulation, while for higher order modems the RBF based DFE requires increased feedforward and feedback orders in order to outperform the conventional MSE DFE scheme.

The central theme is the study of error propagation effects in decision feedback equalizers (DFEs). The thesis contains: a stochastic analysis of error propagation in a tuned DFE; an analysis of the effects of error propagation in a blindly adapted DFE; a deterministic analysis of error propagation through input-output stability ideas; and testing procedures for establishing correct tap convergence in blind adaptation. To a lesser extent, the decision directed equalizer (DDE) is also treated. Characterizing error propagation using finite state Markov process (FSMP) techniques is first considered. We classify how the channel and DFE parameters affect the FSMP model and establish tight bounds on the error probability and mean error recovery time of a tuned DFE. These bounds are shown to be too conservative for practical use and highlight the need for imposing stronger hypotheses on the class of channels for which a DFE may be effectively used. In blind DFE adaptation we show the effect of decision errors is to distort the adaptation relative to the use of a training sequence. The mean square error surface in a LMS type setting is shown to be a concatenation of quadratic functions exposing the possibility of false tap convergence to undesirable DFE parameter settings. Averaging analysis and simulation are used to verify this behaviour on some examples. Error propagation in a tuned DFE is also examined in a deterministic setting. A finite error recovery time problem is set up as an input-output stability problem. Passivity theory is invoked to prove that a DFE can be effectively used on a channel satisfying a simple frequency domain condition. These results give performance bounds which relate well with practice. Testing for false tap convergence in blind adaptation concludes our study. Simple statistic output tests are shown to be capable of discerning correct operation of a DDE. Similar tests are conjectured for the DFE, supported by proofs for the low dimensional cases.

WiMAX is a coming forth broadband wireless technology that considered as one of the most prominent solution to provide high speed data services. This paper addresses the design of WiMAX end to end physical layer (PHY) in Simulink with channel equalization and space time block coding techniques. The authors analyzed the performance of WiMAX PHY with decision feedback equalizers (DFE), linear equalizers and blind equalizers over AWGN and multipath faded channels. Results include MISO channel power spectral density (PSD), antenna amplitude/PSD/phase difference, multipath faded and AWGN channel's effect on the transmitted signal and the performance of proposed equalizers on the received signals. This paper concluded that the linear equalizers have higher frame error rates (FER) than DFE. However, blind equalizers have higher FERs compared to conventional equalizers with better spectral efficiency as they need no training sequence.

Adopting the amplify-and-forward (AF) relay protocol, this paper focuses on the design of a multiuser multiple-input multiple-output (MIMO) multi-relay system with direct source-destination links taken into consideration. In order to improve the quality of signal detection at the receiver, we make use of the minimal mean-squared error (MMSE)-decision feedback equalization (DFE) technique. With the constraints of the signal transmission power at both source and relay nodes, the minimization of the sum mean-squared error (MSE) for the signal waveform estimation of all users' data streams is employed as our design criterion. Through the block coordinate descent (BCD) method of Gauss-Seidel type, we develop an iterative algorithm with guaranteed convergence to conduct the joint optimization of all the source precoding, relay amplifying, feed-forward and decision feedback matrices, where each step we take is to solve a convex problem. It is shown from simulation results that, in comparison to the linear MMSE receiver-based algorithm, the proposed nonlinear one achieves better performance in terms of both MSE and bit-error-rate (BER). Moreover, the system reliability can be significantly improved when the signal-to-noise ratios (SNRs) of direct links become relatively good.

A plethora of approaches have been proposed for blind equalization to date. In this contribution a new blind equalizer is proposed, extending the concept of trained turbo equalizers to the blind scenario by using per-survivor processing (PSP). This equalizer exploits the enhanced data protection offered by channel coding and exhibits good performance in terms of its output bit error rate (BER). Explicitly, a BER comparable to that of a trained turbo equalizer is attained at the cost of a modest complexity increase.

The constant modulus algorithm (CMA) for blind equalization requires a separate carrier-recovery system for phase recovery. A modified CMA, called the multimodulus algorithm (MMA), which may perform joint blind equalization and carrier recovery without the need for a separate carrier-recovery system for quadrature amplitude modulation (QAM) signal constellations. This letter mathematically analyzes the steady-state mean square error (MSE) of MMA. Analysis results indicate that MMA produces 50% fewer steady-state MSE than CMA.