A decision feedback equalizer with time-reversal structure

This work describes the use of a receiver with a time-reversal structure for low-complexity decision feedback equalization of slowly fading dispersive indoor radio channels. Time-reversal is done by storing each block of received signal samples in a buffer and reversing the sequential order of the signal samples in time prior to equalization. As a result, the equivalent channel impulse response as seen by the equalizer is a time-reverse of the actual channel impulse response. Selective time-reversal operation, therefore, allows a decision feedback equalizer (DFE) with a small number of forward filter taps to perform equally well for both minimum-phase and maximum-phase channel characteristics. The author evaluates the theoretical performance bounds for such a receiver and quantifies the possible performance improvement for discrete multipath channels with Rayleigh fading statistics. Two extreme cases of DFE examples are considered: an infinite-length DFE; and a DFE with a single forward filter tap. Optimum burst and symbol timing recovery is addressed and several practical schemes are suggested. Simulation results are presented. The combined use of equalization and diversity reception is considered     

TURBO EQUALIZATION WITH JOINTLY GAUSSIAN EQUALIZER

A Jointly Gaussian (JG) equalizer is derived for turbo equalization based on an augmented real matrix representation of channel model and a Gaussian approximation of the received symbol sequence. Using matrix inversion lemma and Cholesky decomposition, a lowcomplexity implementation of JG equalizer is also presented. The simulation results and complexity comparison confirm that turbo equalization with JG equalizer has a better performance and a lower complexity than the existing turbo equalization with linear minimum mean squared error equalizer.     

Space–Time Turbo Equalization With Successive Interference Cancellation for Frequency-Selective MIMO Channels

This paper addresses the issue of iterative space–time equalization for multiple-input–multiple-output (MIMO) frequency-selective fading channels. A new soft equalization concept based on successive interference cancellation (SIC) is introduced for a space–time bit-interleaved coded modulation (STBICM) transmission. The proposed equalizer allows us to separate intersymbol interference (ISI) and multiantenna interference (MAI) functions. Soft ISI is successively suppressed using a low-complexity suboptimum minimum mean square error (MMSE) criterion. The decoupling of ISI and MAI offers more flexibility in the design of the whole space–time equalizer. Different multiantenna detection criteria can be considered, ranging from simple detectors to the optimal maximum a posteriori (MAP) criterion. In particular, we introduce two soft equalizers, which are called SIC/SIC and SIC/MAP, and we show that they can provide a good performance-to-complexity tradeoff for many system configurations, as compared with other turbo equalization schemes. This paper also introduces an MMSE-based iterative channel state information (CSI) estimation algorithm and shows that attractive performance can be achieved when the proposed soft SIC space–time equalizer iterates with the MMSE-based CSI estimator.      

Minimum mean squared error equalization using a priori information

A number of important advances have been made in the area of joint equalization and decoding of data transmitted over intersymbol interference (ISI) channels. Turbo equalization is an iterative approach to this problem, in which a maximum a posteriori probability (MAP) equalizer and a MAP decoder exchange soft information in the form of prior probabilities over the transmitted symbols. A number of reduced-complexity methods for turbo equalization have been introduced in which MAP equalization is replaced with suboptimal, low-complexity approaches. We explore a number of low-complexity soft-input/soft-output (SISO) equalization algorithms based on the minimum mean square error (MMSE) criterion. This includes the extension of existing approaches to general signal constellations and the derivation of a novel approach requiring less complexity than the MMSE-optimal solution. All approaches are qualitatively analyzed by observing the mean-square error averaged over a sequence of equalized data. We show that for the turbo equalization application, the MMSE-based SISO equalizers perform well compared with a MAP equalizer while providing a tremendous complexity reduction     

MLSE and MAP Equalization for Transmission Over Doubly Selective Channels

In this paper, equalization for transmission over doubly selective channels is discussed. The symbol-by-symbol maximum a posteriori probability (MAP) equalizer and the maximum-likelihood sequence estimation (MLSE) are discussed. The doubly selective channel is modeled using the basis expansion model (BEM). Using the BEM allows for an easy and low-complexity mechanism for constructing the channel trellis to implement the MLSE and the MAP equalizer. The MLSE and the MAP equalizer are implemented for single-carrier transmission and for multicarrier transmission implemented using orthogonal frequency-division multiplexing (OFDM). In this scenario, a complexity-diversity tradeoff can be observed. In addition, we propose a joint estimation and equalization technique for doubly selective channels. In this joint estimation and equalization technique, the channel state information (CSI) is obtained in an iterative manner. Simulation results show that the performance of the joint channel estimation and equalization approaches the performance when perfect CSI is available at the receiver.     

Low-Complexity Block Turbo Equalization for OFDM Systems in Time-Varying Channels

We propose low-complexity block turbo equalizers for orthogonal frequency-division multiplexing (OFDM) systems in time-varying channels. The presented work is based on a soft minimum mean-squared error (MMSE) block linear equalizer (BLE) that exploits the banded structure of the frequency-domain channel matrix, as well as a receiver window that enforces this banded structure. This equalization approach allows us to implement the proposed designs with a complexity that is only linear in the number of subcarriers. Three block turbo equalizers are discussed: two are based on a biased MMSE criterion, while the third is based on the unbiased MMSE criterion. Simulation results show that the proposed iterative MMSE BLE achieves a better bit error rate (BER) performance than a previously proposed iterative MMSE serial linear equalizer (SLE). The proposed equalization algorithms are also tested in the presence of channel estimation errors.      

Low-complexity MMSE turbo equalization: a possible solution for EDGE

This paper deals with a low complexity receiver scheme where equalization and channel decoding are jointly optimized in an iterative process. We derive the theoretical transfer function of the infinite length linear minimum mean square error (MMSE) equalizer with a priori information. A practical implementation is exposed which employs the fast Fourier transform (FFT) to compute the equalizer coefficients, resulting in a low-complexity receiver structure. The performance of the proposed scheme is investigated for the enhanced general packet radio service (EGPRS) radio link. Simulation results show that significant power gains may be achieved with only a few (3-4) iterations. These results demonstrate that MMSE turbo equalization is an attractive candidate for single-carrier broadband wireless transmissions in long delay-spread environments.     

Perfect equalization for DMT systems without guard interval

We propose a new, low-complexity frequency-domain equalizer for discrete multitone (DMT) systems, which, in the absence of a guard interval, utilizes existing redundancy in the frequency-domain to completely eliminate intersymbol and interchannel interference. A perfect reconstruction condition is derived for the noise-free case leading to a sparse equalizer matrix structure. It is furthermore shown that under realistic scenarios minimum mean square error adaptation of the equalizer coefficients allows for nearly perfect reconstruction already for a much smaller amount of redundancy than indicated by the perfect reconstruction condition. The new equalization scheme has at least the same potential compared with traditional DMT while offering new degrees of freedom for designing short-latency DMT systems     

Frequency domain decision feedback equalizer for time-reversal space-time block coding

In this paper,a frequency domain decision feedback equalizer is proposed for single carrier transmission with time-reversal space-time block coding (TR-STBC).It is shown that the diagonal decision feed...     

Adaptive analog equalization and receiver front-end control formultilevel partial-response transmission over metallic cables

This paper deals with multilevel partial-response class-IV (PRIV) transmission over unshielded twisted-pair (UTP) cables. Specifically, transmission at a rate of 155.52 Mb/s over data-grade UTP cables for local-area networking is considered. As a low-complexity method used to compensate for cable-length dependent signal distortion, adaptive analog equalization with two controlled parameters is proposed: one parameter determines a frequency-independent receiver gain, the other parameter controls the transfer characteristic of a variable analog receive-filter section. For the stepwise design of the transmit and receive filters, a combination of analytic techniques and simulated annealing is employed. First, the variable equalizer section, then the remaining fixed analog receive filter section are developed and finally the analog transmit filter is determined. The paper also describes the adjustment of the equalizer section, and the control of the sampling phase in the receiver front-end. The two equalizer parameters are controlled by an algorithm that operates on the sampled signals and adjusts these parameters to optimum settings independently of the sampling phase. The latter is controlled by a decision-directed phase-locked loop algorithm that becomes effective when equalization has been achieved. The dynamic behaviour and mean-square error in steady-state obtained with these control algorithms are investigated     

Determination of Tap Positions for Sparse Equalizers

Sparse equalizers, in which only a small subset of the filter taps is selected to be nonzero, were recently proposed as a low-complexity solution for receivers operating in wireless frequency-selective channels with sparse power profiles. The performance of the sparse equalizer heavily depends on its tap-positioning algorithm. This paper presents efficient low-complexity algorithms for determination of sparse equalizer tap positions based on a forward sequential search. We develop low-complexity metrics for the evaluation of the candidate tap positions in the search space as well as methods to effectively reduce the search space size. The proposed algorithms are shown to be superior over previously proposed algorithms in a wide range of channel conditions. Actually, the proposed algorithms yield, in most of the tested cases, performance identical to the optimal, prohibitively complex, tap-positioning algorithm. The main emphasis is on linear equalization suitable for wideband code-division multiple-access systems but the algorithm can be extended to a variety of equalization schemes and channels.     

A Hardware Efficient Passband Equalizer Structure for Data Transmission

A passband digital equalizer is proposed which combines the functions of bandpass filtering and phase splitting with that of adaptive equalization. The new equalizer also provides the in-phase and quadrature outputs required for demodulation. Although input sampling is required at several times the symbol rate (for voice-grade channel applications), outputs need be computed only once per baud. This structure economizes either on front-end analog (phase splitter) filtering or on the number of multiplications required in a digital implementation of a phase splitter and an equalizer. The performance of a receiver incorporating the new equalizer is compared, experimentally, with a receiver using a conventional fractionally spaced (T/2) equalizer.     

Iterative MAP Equalization and Decoding in Wireless Mobile Coded OFDM

Orthogonal frequency division multiplexing (OFDM) system suffers extra performance degradation in fast fading channels due to intercarrier interference (ICI). Combining frequency domain equalization and bit-interleaved coded modulation (BICM), the iterative receiver is able to harvest both temporal and frequency diversity. Realizing that ICI channels are intrinsically ISI channels, this paper proposes a soft-in soft-out (SISO) maximum a posteriori (MAP) equalizer by extending Ungerboeck's maximum likelihood sequence estimator (MLSE) formulation to ICI channels. The SISO MAP equalizer employs BCJR algorithm and computes the bit log-likelihood ratios (LLR) for the entire received sequence by efficiently constructing a trellis that takes into account of the ICI channel structure. A reduced state (RS) formulation of the SISO MAP equalizer which provides good performance/complexity tradeoff is also described. Utilizing the fact that ICI energy is clustered in adjacent subcarriers, frequency domain equalization is made localized. This paper further proposes two computational efficient linear minimum mean square error (LMMSE) based equalization methods: recursive q-tap SIC-LMMSE equalizer and recursive Sliding-Window (SW) SIC-LMMSE equalizer respectively. Simulations results demonstrate that the iterative SISO RS-MAP equalizer achieves the performance of no ICI with normalized Doppler frequency f_dT_s up to 20.46% in realistic mobile WiMAX environment.     

Improved spatial-temporal equalization for EDGE: a fastselective-direction MMSE timing recovery algorithm and two-stagesoft-output equalizer

The radio interface EDGE (Enhanced Data rates for Global Evolution) is currently being standardized as an evolutionary path from GSM and TDMA-IS136 for third-generation high-speed data wireless systems. For the EDGE system with multiple antennas, spatial-temporal equalization (STE) can reduce intersymbol interference and co-channel interference, thereby increasing the capacity and range. In this paper, we propose two new techniques to improve the performance of a previously proposed STE: a fast timing recovery algorithm for a selective time-reversal equalizer and a two-stage soft-output equalizer. The new timing recovery algorithm determines the estimated burst timing and processing direction by computing the minimum mean-square error (MMSE) for decision feedback equalizers in both the forward and reverse time directions. The two-stage soft-output equalizer is the cascade of a delayed decision-feedback sequence estimator (DDFSE) and maximum a posteriori probability (MAP) estimator. The DDFSE provides better noise variance estimation and channel truncation for the following MAP. The performance of the new STE is evaluated for the EDGE. At 10% block error rate, the two-branch receiver requires a 3-7-dB lower signal-to-interference ratio (SIR) than the previous approach. Compared with the one-branch receiver, the two-branch receiver requires a 4-dB lower SNR with noise only, and a 10-27-dB lower SIR with a single interferer     

A nonlinear electrical equalizer with decision feedback for OOK optical communication systems

In this paper we introduce a nonlinear equalizer using the Radial Basis Function (RBF) network with decision feedback equalizer (DFE) for electronic dispersion compensation in optical communication systems with on-off-keying and a direct detection receiver. The RBF method introduces a non-linear equalization technique suitable for optical communication direct detection systems that include nonlinear transformation at the photodetector. A bit error rate performance comparison shows that the RBF with DFE out performs the RBF without DFE and achieves similar results provided by maximum likelihood sequence estimator.     

基于DDEA算法的短波信道Turbo均衡研究

针对数据引导均衡算法（DDEA）的缺陷,受到Turbo均衡中迭代思想的启发,提出一种基于数据引导均衡技术的短波迭代信道估计、均衡和译码算法,不仅均衡和译码之间互相传递软信息,信道估计器使用的也是译码器反馈的软信息,通过每次迭代时软信息质量的改善,提高系统的可靠性;通过多次迭代信道估计器输出的信道参数很接近当前帧的实际信...     

Space-time block coding for single-carrier block transmission DS-CDMA downlink

The combination of space-time block coding (STBC) and direct-sequence code-division multiple access (DS-CDMA) has the potential to increase the performance of multiple users in a cellular network. However, if not carefully designed, the resulting transmission scheme suffers from increased multiuser interference (MUI), which dramatically deteriorates the performance. To tackle this MUI problem in the downlink, we combine two specific DS-CDMA and STBC techniques, namely single-carrier block transmission (SCBT) DS-CDMA and time-reversal STBC. The resulting transmission scheme allows for deterministic maximum-likelihood (ML) user separation through low-complexity code-matched filtering, as well as deterministic ML transmit stream separation through linear processing. Moreover, it can achieve maximum diversity gains of N/sub T/N/sub R/(L+1) for every user in the system, irrespective of the system load, where N/sub T/ is the number of transmit antennas, N/sub R/ the number of receive antennas, and L the order of the underlying multipath channels. In addition, it turns out that a low-complexity linear receiver based on frequency-domain equalization comes close to extracting the full diversity in reduced, as well as full load settings. In this perspective, we also develop two (recursive) least squares methods for direct equalizer design. Simulation results demonstrate the outstanding performance of the proposed transceiver compared to competing alternatives.     

A Novel Interpolation Equalization Technique for Multicarrier Modulation/Demodulation Systems

This paper presents a novel multitap interpolation equalization technique for filter bank-based multicarrier modulation/demodulation systems. The proposed technique is based on the equalization of the channel fractional delay in each subchannel in time synchronization with the constituent receiver side decimator. The proposed synchronization is achieved by combining a subset of the polyphase components of the analysis filter output signal after having passed through a bank of interpolation equalizers. The resulting multitap interpolation equalization permits a trade-off between various equalization parameters, such as the number of used polyphase components, the length of the equalizer, and the interchannel interference terms, making it possible to achieve a high signal-to-noise ratio (SNR) involving moderate equalization cost or a moderate SNR involving very low equalization cost. Simulation results for the standard carrier serving area loop show that the proposed equalization technique gives rise to 15 dB improvement in SNR compared to the output combiner equalization technique and can achieve an SNR close to the matched-filter bound for the channel by employing a reasonable equalizer length. Compared to the output combiner equalization technique, the proposed equalization technique involves around three times less the storage requirement at the same computational cost or around three times less the computational cost at the same storage requirement for equalizer training. Two suboptimal solutions are also proposed to simplify the equalizer training at only a minor loss in SNR.     

OFDM系统中低复杂度的时变信道迭代均衡算法

针对正交频分复用系统在时变信道中的均衡问题,提出了一种低复杂度的时变信道均衡算法。该算法首先运用一阶多项式基扩展模型对时变信道进行建模,利用频域信道矩阵能量主要集中在对角线附近的特点,将频域信道矩阵按梳状导频的位置沿对角线分块,然后运用高斯置信传播算法分别进行线性迫零均衡。算法避免了矩阵求逆运算,降低了计算复杂度,同时有效补偿了多普勒频移引起的载波间干扰,提高了系统性能。计算机仿真结果和算法复杂度分析表明,提出的分块迭代均衡算法有效降低了时变信道中系统的误码率,并且具有复杂度低,可分布式计算的特点,因此适用于专用集成电路等硬件实现。      

Turbo equalization: adaptive equalization and channel decodingjointly optimized

This paper deals with a receiver scheme where adaptive equalization and channel decoding are jointly optimized in an iterative process. This receiver scheme is well suited for transmissions over a frequency-selective channel with large delay spread and for high spectral efficiency modulations. A low-complexity soft-input soft-output M-ary channel decoder is proposed. Turbo equalization allows intersymbol interference to be reduced drastically. For most time-invariant discrete channels, the turbo-equalizer performance is close to the coded Gaussian channel performance, even for low signal-to-noise ratios. Finally, results over a time-varying frequency-selective channel proves the excellent behavior of the turbo equalizer