Equalization and semi-blind channel estimation for space-time block coded signals over a frequency-selective fading channel

In this paper, we investigate the equalization and channel identification for space-time block coded signals over a frequency-selective multiple-input multiple-output (MIMO) channel. The equalization has been considered by taking into account the cyclostationarity of space-time block coded signals. The minimum mean square error (MMSE) solutions have been derived for the linear and decision feedback (DF) equalizers. The channel estimation is required for the equalization. With known symbols (as pilot symbols), MIMO channels can be estimated. In addition, due to the redundancy induced by space-time block code, it is possible to identify MIMO channels blindly using the subspace method. We consider both blind and semi-blind channel estimation for MIMO channels. It is shown that the semi-blind channel estimate has fewer estimation errors, and it results in less (bit error rate) performance degradation of the MMSE linear and DF equalizers.     

Downlink Specific Linear Equalization for Frequency Selective CDMA Cellular Systems

We derive and compare several linear equalizers for the CDMA downlink under frequency selective multipath conditions: minimum mean-square error (MMSE), zero-forcing (ZF), and RAKE. MMSE and ZF equalizers are designed based on perfect knowledge of the channel. The downlink specific structure involves first inverting the multipath channel to restore the synchronous multi-user signal transmitted from the base-station at the chip-rate, and then correlating with the product of the desired user's channel code times the base-station specific scrambling code once per symbol to decode the symbols. ZF equalization restores orthogonality of the Walsh-Hadamard channel codes on the downlink but often suffers from noise gain because certain channel conditions (no common zeros) are not met; MMSE restores orthogonality only approximately but avoids excessive noise gain. We compare MMSE and ZF to the traditional matched filter (also known as the RAKE receiver). Our formulation generalizes for the multi-channel case as might be derived from multiple antennas and/or over-sampling with respect to the chip-rate. The optimal symbol-level MMSE equalizer is derived and slightly out-performs the chip-level but at greater computational cost. An MMSE soft hand-off receiver is derived and simulated. Average BER for a class of multi-path channels is presented under varying operating conditions of single-cell and edge-of-cell, coded and un-coded BPSK data symbols, and uncoded 16-QAM. These simulations indicate large performance gains compared to the RAKE receiver, especially when the cell is fully loaded with users. Bit error rate (BER) performance for the chip-level equalizers is well predicted by approximate SINR expressions and a Gaussian interference assumption.     

Blind estimation and equalization of MIMO channels via multidelaywhitening

Blind channel estimation and blind minimum mean square error (MMSE) equalization of multiple-input multiple-output (MIMO) communications channels arising in multiuser systems is considered, using primarily the second-order statistics of the data. The basis of the approach is the design of multiple zero-forcing equalizers that whiten the noise-free data at multiple delays. In the past such an approach has been considered using just one zero-forcing equalizer at zero-delay. Infinite impulse response (IIR) channels are allowed. Moreover, the multichannel transfer function need not be column-reduced. The proposed approach also works when the “subchannel” transfer functions have common zeros so long as the common zeros are minimum-phase zeros. The channel length or model orders need not be known. Using second-order statistics, the sources are recovered up to a unitary mixing matrix, and are further “unmixed” using higher order statistics of the data. Two illustrative simulation examples are provided where the proposed method is compared with its predecessors and an existing method to show its efficacy     

Adaptive algorithms for channel equalization with soft decisionfeedback

A new approach based on joint entropy maximization (JEM) is taken and adaptive algorithms are developed for channel equalization with a decision feedback equalizer (DFE). The proposed work generalizes the existing algorithms for DFE with a hard decision device. Previous research has shown that when the hard decisions in a DFE are replaced with soft decisions, the performance of the adaptive algorithms [e.g., minimum mean square error (MMSE)] improves dramatically. The soft decisions can be introduced naturally via the viewpoint taken here. Additionally, constant modulus and other (blind) algorithms for DFE with soft decisions can be derived from this JEM approach     

On a whitening approach to partial channel estimation and blindequalization of FIR/IIR multiple-input multiple-output channels

Channel estimation and blind equalization of multiple-input multiple-output (MIMO) communications channels is considered using primarily the second-order statistics of the data. Such models arise when a single receiver data from multiple sources is fractionally sampled (assuming that there is excess bandwidth) or when an antenna array is used with or without fractional sampling. We consider estimation of (partial) channel impulse response and design of finite-length minimum mean-square error (MMSE) blind equalizers. The basis of the approach is the design of a zero-forcing equalizer that whitens the noise-free data. We allow infinite impulse response (IIR) channels. Moreover, the multichannel transfer function need not be column reduced. Our approaches also work when the “subchannel” transfer functions have common zeros as long as the common zeros are minimum-phase zeros. The channel length or model orders need not be known. The sources are recovered up to a unitary mixing matrix and are further “unmixed” using higher order statistics of the data. A linear prediction approach is also considered under the above conditions of possibly IIR channels, common subchannel zeros/factors, and not-necessarily column reduced channels. Four illustrative simulation examples are provided     

Blind chip-level equalizer for the downlink of cyclic-prefix CDMA systems

The authors present a chip-level blind frequency domain equalizer (FEQ) for the forward-link channel of a cyclic-prefix code division multiple access system. The FEQ coefficients are obtained without the need of training symbols or knowledge of channel state information. The coefficients are instead acquired by solving a constraint energy minimization problem involving the subspace spanned by the active and passive spreading codewords. They also prove that the random scrambling code sequences is required for the operation of the proposed equalization algorithm. Results from computer simulations are provided to verify the performance of the proposed FEQ.     

Multistep linear predictors-based blind identification andequalization of multiple-input multiple-output channels

Channel estimation and blind equalization of multiple-input multiple-output (MIMO) communications channels is considered using primarily the second-order statistics of the data. Such models arise when single receiver data from multiple sources is fractionally sampled (assuming that there is excess bandwidth) or when an antenna array is used with or without fractional sampling. We consider the estimation of (partial) channel impulse response and design of finite-length minimum mean-square error (MMSE) blind equalizers. We extend the multistep linear prediction approach to MIMO channels where the multichannel transfer function need not be column reduced. Moreover, we allow infinite impulse response (IIR) channels as well as the case where the “subchannel” transfer functions have common zeros. In the past, this approach has been confined to SIMO finite impulse response (FIR) channels with no common subchannel zeros. A related existing approach applicable to MIMO channels is restricted to FIR column-reduced systems with equal length subchannels. In our approach, the knowledge of the nature of the underlying model (FIR or IIR) or the model order is not required. Our approach works when the “subchannel” transfer functions have common zeros, as long as the common zeros are minimum-phase zeros. The sources are recovered up to a unitary mixing matrix and are further “unmixed” using higher order statistics of the data. Illustrative computer simulation examples are provided     

A multidelay whitening approach to blind identification andequalization of SIMO channels

Blind channel estimation and blind equalization of single-input multiple-output communications channels is considered using only the second-order statistics of the data. Estimation of (partial) channel impulse response and design of finite-length minimum mean-square error blind equalizers is investigated. The basis of the approach is the design of multiple zero-forcing equalizers that whiten the noise-free data at multiple delays. In the past such an approach has been considered using just one zero-forcing equalizer at zero-delay. Infinite-impulse response channels are allowed. The proposed approach also works when the "subchannel" transfer functions have common zeros so long as the common zeros are minimum-phase zeros. The channel length or model orders need not be known. Three illustrative simulation examples using 4-QAM and 16-QAM signals are provided where the proposed approach is compared with several existing approaches     

Design of multiple MMSE subequalizers for faster-than-Nyquist-rate transmission

We consider an equalization problem when the transmitted symbol rate is higher than the available channel bandwidth. This situation can happen in the uplink of the voiceband pulse-code modulation (PCM) modems whose transmit signal bandwidth is larger than the available channel bandwidth. Although the use of a minimum mean-squared error (MMSE) pre-equalizer is considered in the International Telecommunications Union (ITU)-T V.92 Recommendation, it may not provide an acceptable performance unless the channel condition is mild. As another approach to this problem, we consider the use of a bank of subequalizers, each of which compensates the part of the channel distortion, enabling the PCM-mode transmission over the channel where the V.92 scheme may fail. In this paper, a multiple subequalizer scheme is optimally designed in the MMSE sense, and its performance is compared with the MMSE pre-equalizer of V.92 in terms of the bit-rate-normalized signal-to-noise ratio.     

基于Turbo均衡和信道估计的单通道盲信号恢复算法

定时同步是单通道盲信号接收端处理的难点,提出了一种无需定时同步基于Turbo均衡的单通道盲信号恢复算法。该算法将定时同步偏差等效为符号间干扰（ISI,inter-symbol interference）信道,通过信道估计和Turbo均衡相互反馈软信息来改善源信号信息恢复性能。重点研究了初始盲均衡算法、信道估计算法、混合信号的MMSE均衡算法以及三者间的软信息交互。算法复杂度低、计算量小,适用于高阶调制信号。仿真结果表明,对BPSK、QPSK和8PSK信号,该算法都能得到较好的性能,且对等功率和不等功率信号同样适用。     

Fractionally spaced equalization of linear polyphase channels andrelated blind techniques based on multichannel linear prediction

We consider the problem of linear equalization of polyphase channels and its blind implementation. These channels may result from oversampling the single output of a transmission channel or/and by receiving multiple outputs of an antenna array. A number of previous contributions in the field of blind channel identification have shown that polyphase channels can be blindly identified using only second-order statistics (SOS) of the output. In this work, we are mostly interested in the blind linear equalization of these channels. After some elaboration on the specifics of the equalization problem for polyphase channels, we show how optimal settings of various well-known types of linear equalization structures can be obtained blindly using only the output's SOS by using multichannel linear prediction or related techniques     

Basis expansion models and diversity techniques for blindidentification and equalization of time-varying channels

The time-varying impulse response of rapidly fading mobile communication channels is expanded over a basis of complex exponentials that arise due to Doppler effects encountered with multipath propagation. Blind methods are reviewed for estimating the bases' parameters and the model orders. Existing second-order methods are critiqued and novel algorithms are developed for blind identification, direct, zero-forcing equalization and minimum mean square error (MMSE) equalization by combining channel diversity with temporal (fractional sampling) and/or spatial diversity which becomes available with multiple receivers. Illustrative simulations are also presented     

Direct blind MMSE channel equalization based on second-orderstatistics

A family of new MMSE blind channel equalization algorithms based on second-order statistics are proposed. Instead of estimating the channel impulse response, we directly estimate the cross-correlation function needed in Wiener-Hopf filters. We develop several different schemes to estimate the cross-correlation vector, with which different Wiener filters are derived according to minimum mean square error (MMSE). Unlike many known sub-space methods, these equalization algorithms do not rely on signal and noise subspace separation and are consequently more robust to channel order estimation errors. Their implementation requires no adjustment for either single- or multiple-user systems. They can effectively equalize single-input multiple-output (SIMO) systems and can reduce the multiple-input multiple-output (MIMO) systems into a memoryless signal mixing system for source separation. The implementations of these algorithms on SIMO system are given, and simulation examples are provided to demonstrate their superior performance over some existing algorithms     

Blind equalization and multiuser detection in dispersive CDMAchannels

The problem of blind demodulation of multiuser information symbols in a high-rate code-division multiple-access (CDMA) network in the presence of both multiple-access interference (MAI) and intersymbol interference (ISI) is considered. The dispersive CDMA channel is first cast into a multiple-input multiple-output (MIMO) signal model framework. By applying the theory of blind MIMO channel identification and equalization, it is then shown that under certain conditions the multiuser information symbols can be recovered without any prior knowledge of the channel or the users' signature waveforms (including the desired user's signature waveform), although the algorithmic complexity of such an approach is prohibitively high. However, in practice, the signature waveform of the user of interest is always available at the receiver. It is shown that by incorporating this knowledge, the impulse response of each user's dispersive channel can be identified using a subspace method. It is further shown that based on the identified signal subspace parameters and the channel response, two linear detectors that are capable of suppressing both MAI and ISI, i.e., a zero-forcing detector and a minimum-mean-square-error (MMSE) detector, can be constructed in closed form, at almost no extra computational cost. Data detection can then be furnished by applying these linear detectors (obtained blindly) to the received signal. The major contribution of this paper is the development of these subspace-based blind techniques for joint suppression of MAI and ISI in the dispersive CDMA channels     

Computationally efficient equalization for asynchronous cooperative communications with multiple frequency offsets

In cooperative communications, time and frequency synchronization is an important issue needed to be addressed in practice. Due to the nature of cooperative communications, multiple frequency offsets may occur and the traditional frequency offset compensations may not apply. For this problem, equalization for the time-varying channel has been used in the literature, where the equalization matrix inverse needs to be retaken every symbol. In this paper, we propose computationally efficient minimum mean square error (MMSE) and MMSE decision feedback equalizers (MMSE-DFE) when multiple frequency offsets are present, where the equalization matrix inverses do not need to be retaken every symbol. Our proposed equalization methods apply to linear convolutively coded cooperative systems, where linear convolutive space-time coding is used to achieve the full cooperative diversity when there are timing errors from the cooperative users or relay nodes, i.e., asynchronous cooperative communication systems.     

Blind channel identification and equalization using periodicmodulation precoders: performance analysis

The paper deals with blind identification and equalization of communication channels within the so-called modulation induced cyclostationarity (MIC) framework, where the input symbol stream is modulated by a P periodic precoder with the purpose of inducing cyclostationarity in the transmit sequence. By exploiting the cyclostationarity induced by the periodic precoder, a subspace-based channel identification algorithm that is resilient to the location of channel zeros, channel order overestimation errors, and color of additive stationary noise, is developed. The asymptotic performance of the subspace-based identification approach is analyzed and compared with the asymptotic lower bound provided by the nonlinear cyclic correlation matching approach. Criteria for optimally designing the periodic precoder are also presented. The performance of MMSE-FIR and MMSE-DFE equalizers is quantified for the proposed cyclostationarity-induced framework in terms of the MMSE. Although cyclostationarity-inducing transmitters present several advantages relative to their stationary counterparts from a channel estimation viewpoint, it is shown that from an equalization viewpoint, MIC-based systems exhibit a slightly increased MMSE/BER when compared with the stationary case     

Atmospheric Optical CDMA Communication Systems via Optical Orthogonal Codes

We propose and consider using a class of multiple-access sequences, namely, optical orthogonal codes (OOCs) in atmospheric optical code-division multiple-access systems. We obtain analytical solutions to the error probability for various channel models using positive-intrinsic-negative diode and avalanche photodiode photodetectors. In our analysis, the effects of atmospheric turbulence, ambient light, thermal noise, and multiuser interference are considered, in the context of a semiclassical photon-counting approach. The performance of the systems taking advantage of space diversity and error-correcting codes are also evaluated. Two common and widely used optical modulations, on–off keying and pulse-position modulation, are considered. Receiver structures based on correlator and chip level are used for OOC detection. Unlike the traditional chip-level receiver, here a generalized form of chip-level structure with two threshold levels is considered. Upper and lower bounds on the error probability for the above-chip-level receiver structure is obtained. From our analytical results, we can deduce that the chip-level receiver outperforms a simple correlator in the absence or weak atmospheric fading; however, in a strong fading environment, the simple correlator outperforms the chip-level receiver.     

Performance of blind equalization with higher order statistics inindoor radio environments

This paper analyzes the performance of blind equalization using the complex cepstrum of third-order moments applied to 4-QAM time division multiple access (TDMA) indoor radio communication systems. In particular, we have modeled a dispersive indoor channel with Rice statistics. We used the blind algorithms to estimate the channel-impulse response, and from this, we computed the equalizer coefficients using a classical minimum mean square error (MMSE) algorithm. In order to evaluate the system performance, we calculated the bit error rate (BER) of a decision feedback equalizer (DFE) that uses a tricepstrum algorithm to estimate the channel-impulse response. The results are compared with those obtained using a least sum of square errors (LSSE) algorithm as a channel estimator and considering the exact channel response. The results obtained show that this kind of blind equalizer performs better than the more classically trained equalizer when Rice channels with a strong direct path and signal-to-noise ratios (SNRs) lower than 20 dB are taken into account. However, some problems relating to the length of time needed for convergence must be solved     

Blind detection of multirate asynchronous CDMA signals in multipath channels

Blind detection of a desired user's signal in a multirate direct sequence code division multiple access (DS-CDMA) system [using either variable sequence length (VSL) or multicode (MC) access] is considered. A code-constrained inverse filter criterion (IFC)-based blind detector for equal-rate CDMA signals to detect a desired user's signal was presented by Tugnait and Li (2001). The IFC method exploits the higher order statistics of the data. In multirate CDMA systems, a high-rate user signal may be treated as the superposition of several virtual basic-rate signals. The code-constrained IFC-based detector may be used to detect a given basic-rate virtual signal. This, however, does not solve the problem of combining the detected virtual basic-rate signals to yield the original high-rate signal since the former may be delayed by different equalization delays, may be multiply extracted, and may be in different "order." In this paper, novel approaches combining the code-constrained IFC and a penalty function are developed to cope with this problem for VSL and MC multirate access methods. Global minima of the proposed cost functions are analyzed. Three illustrative simulation examples are presented, including an example where the proposed algorithms are compared with an existing subspace approach (and its modifications), a clairvoyant matched filter receiver, and a known channel linear minimum mean-square error (MMSE) receiver.     

OFDM调制系统中一种鲁棒的MMSE信道均衡算法

在OFDM调制系统中,由于多载波的存在,载波间ICI对信道均衡结果影响很大,同时,采用MMSE信道均衡算法对不同的信道模型也存在均衡误差不稳定的情况。本文提出一种鲁棒的MMSE信道均衡算法,该算法的核心是针对不同信道对信道的PDP进行归一化处理,从而得到在不同类型信道下稳定且鲁棒的信道均衡性能。