On channel estimation and sequence detection of interleaved codedsignals over frequency nonselective Rayleigh fading channels

Due to the receiver complexity introduced by interleaving, the implementation of maximum likelihood (IML) decoding of interleaved coded signals transmitted over frequency nonselective Rayleigh fading channels has been shown to be practically impossible. As an alternative, a two-stage receiver structure has been proposed, where the channel estimation and sequence decoding are done separately. The channel estimation issue in a two-stage receiver is examined in detail in this paper. It is shown that although an optimum (maximum a posteriori (MAP)) channel estimation is not possible in practice, it can be approached asymptotically by joint MAP estimation of the channel and the coded data sequence. The implementation of the joint MAP estimation is shown to be an ML sequence estimator followed by an minimum mean-square error (MMSE) channel estimator. Approximate fill sequence estimation using pilot symbol interpolation is also studied, and through computer simulations, its performance is compared to receivers using hit sequence estimation. The effect of decision delay (DD), prediction order, and pilot insertion rate (PIR) on the reduced complexity ML sequence estimation is investigated as well. Finally, a practical receiver is proposed that makes the best compromise among the error performance, receiver complexity, DD, and power (or bandwidth) expansion due to pilot insertion     

Decision-feedback MAP receiver for time-selective fading CDMAchannels

A decision-feedback maximum a posteriori (MAP) receiver is proposed for code-division multiple-access channels with time-selective fading. The receiver consists of a sequence-matched filter and a MAP demodulator. Output samples (more than one per symbol) from the matched filter are fed into the MAP demodulator. The MAP demodulator exploits the channel memory by delaying the decision and using a sequence of observations. This receiver also rejects multiple-access interference and estimates channel fading coefficients implicitly to give good demodulation decisions. Moreover, computer simulations are performed to evaluate the bit-error rate performance of the receiver under various channel conditions     

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.     

Error Rate Analysis of Uplink MC-CDMA Systems under Imperfect Channel Estimation

Theoretical error rate performance of wireless communication systems are usually determined assuming that the perfect channel state information (CSI) is available at the receiver. However, in actual practice, the channel gains at the receiver are obtained via using some channel estimation (CE) techniques. Due to inherent presence of noise, the CE is not perfect resulting in the performance degradation. In this paper, we evaluate the error rate performance of an uplink multicarrier code-division multiple-access (MC-CDMA) system, considering different modulation techniques, where CE is performed using pilot symbol assisted (PSA) minimum mean-square error (MMSE) CE technique. The symbol error rate (SER) analysis of an uplink MC-CDMA system using multiuser detection techniques, such as MMSE and zero forcing (ZF), is presented under imperfect CE. Simulated results for SER are also shown to confirm the accuracy of the analytically derived results.     

Low-Complexity Map Channel Estimation for Mobile MIMO-OFDM Systems

This paper presents a reduced-complexity maximum a posteriori probability (MAP) channel estimator with iterative data detection for orthogonal frequency division multiplexing (OFDM) systems over mobile multiple-input multiple- output channels. The optimal MAP estimator needs to invert an NN_T x NN_T data-dependent matrix each in OFDM symbol interval, where N is the number of subcarriers and N_T is the number of transmit antennas. We derive an expectation maximization (EM) algorithm with low-rank approximation to avoid inverting large-size matrices, and thus drastically reduce the receiver complexity. In the iterative process, channel parameters are initially obtained by a least square (LS) estimator for temporary symbol decisions. Then, inter-carrier interference (ICI) due to fast fading is approximated and canceled. Finally, the temporary symbol decisions and the ICI-canceled received signals are processed by the EM-based MAP estimator to refine the channel state information for improved detection. The proposed scheme achieves about 2 dB gain over the LS scheme in channels with medium to high normalized Doppler shifts.     

A sequential Monte Carlo blind receiver for OFDM systems infrequency-selective fading channels

We consider the application of the sequential Monte Carlo (SMC) methodology to the problem of blind symbol detection in a wireless orthogonal frequency-division multiplexing (OFDM) system over a frequency-selective fading channel. Bayesian inference of the unknown data symbols in the presence of an unknown multipath fading channel is made only from the observations over one OFDM symbol duration. A novel blind SMC detector built on the techniques of importance sampling and resampling is developed for differentially encoded OFDM systems. The performance of different schemes of delayed-weight estimation methods is studied. Furthermore, being soft-input and soft-output in nature, the proposed SMC detector is employed as the first-stage demodulator in a turbo receiver for a coded OFDM system. Such a turbo receiver successively improves the receiver performance by iteratively exchanging the so-called extrinsic information with the maximum a posteriori (MAP) outer channel decoder. Finally, the performance of the proposed sequential Monte Carlo receiver is demonstrated through computer simulations     

瑞利衰落信道下的Turbo均衡

Turbo均衡是一种将Turbo原理和均衡技术结合起来的技术。他通过反复均衡和信道译码来提高接收机性能。针时瑞利衰落信道，采用基于线性滤波器的软输入／软输出均衡器来消除码间干扰，其系数由最小均方误差准则确定。译码器采用最大后验概率算法时卷积码译码。考虑到瑞利衰落信道为随机信道，用非相干检测时信道进行估计。接收机通过联合均衡和译码以充分利用已经获得的信息，实现信道估计及信道均衡与信道译码的迭代更新。仿真结果表明其性能不仅远远优于非迭代系统．而且在信噪比高于4dB时几乎可以完全消除符号间干扰的影响，与MAPSE相比其复杂度大大降低。     

Channel Independent Precoder for OFDM-Based Systems Over Fading Channels

In this paper we propose an independent channel precoder for orthogonal frequency division multiplexing (OFDM) systems over fading channels. The design of the precoder is based on the information redistribution of the input modulated symbols among the output precoded symbols. The proposed precoder decreases the variance of the instantaneous noise power at the receiver produced by the channel variability. The employment of an interleaver together with a precoding matrix whose size does not depend on the number of data carriers in an OFDM symbol allows different configurations of time-frequency diversity which can be easily adapted to the channel conditions. The precoder is evaluated with a modified Zero Forcing (ZF) equalizer whose maximum gain is constrained by means of a clipping factor. Thus, the clipping factor limits the noise power transfer in the receiver deprecoding block in low SNR conditions.      

Space–Time Block Codes Achieving Full Diversity With Linear Receivers

In most of the existing space–time code designs, achieving full diversity is based on maximum-likelihood (ML) decoding at the receiver that is usually computationally expensive and may not have soft outputs. Recently, Zhang–Liu–Wong introduced Toeplitz codes and showed that Toeplitz codes achieve full diversity when a linear receiver, zero-forcing (ZF) or minimum mean square error (MMSE) receiver, is used. Motivated from Zhang–Liu–Wong's results on Toeplitz codes, in this paper, we propose a design criterion for space–time block codes (STBC), in which information symbols and their complex conjugates are linearly embedded, to achieve full diversity when ZF or MMSE receiver is used. The (complex) orthogonal STBC (OSTBC) satisfy the criterion as one may expect. We also show that the symbol rates of STBC under this criterion are upper bounded by 1. Subsequently, we propose a novel family of STBC that satisfy the criterion and thus achieve full diversity with ZF or MMSE receiver. Our newly proposed STBC are constructed by overlapping the $2,times,2$ Alamouti code and hence named overlapped Alamouti codes in this paper. The new codes are close to orthogonal and their symbol rates can approach 1 for any number of transmit antennas. Simulation results show that overlapped Alamouti codes significantly outperform Toeplitz codes for all numbers of transmit antennas and also outperform OSTBC when the number of transmit antennas is above $4$.      

Coherent Transmission Direct Detection MIMO Over Short-Range Optical Interconnects and Passive Optical Networks

Building on a recently introduced quadratic multiple-input multiple-output (Q-MIMO) channel model making use of quadratic forms instead of linear channel matrices, we explore diverse signaling formats over the Q-MIMO channel in the frequency flat regime, highlighting the unique characteristics of optical multimode fiber (MMF) systems versus their wireless counterparts. In particular, we treat multiple-input single-output multimode fiber systems, comparing them with single-input single-output MMF systems and obtaining insight into the possibility of efficiently coupling the output of an MMF into a single-mode fiber. We further treat vector amplitude modulation over MMF MIMO and study the receiver zero-forcing (ZF) technique for MMF MIMO transmission, deriving its performance and comparing with a recently introduced ZF beamforming technique based on precoding at the transmitter, which is shown to be superior to receiver ZF.      

Zero forcing and minimum mean-square-error equalization formultiuser detection in code-division multiple-access channels

In code-division multiple-access (CDMA) systems transmitting over time-varying multipath channels, both intersymbol interference (ISI) and multiple-access interference (MAI) arise. The conventional suboptimum receiver consisting of a bank of matched filters is often inefficient because interference is treated as noise. The optimum multiuser detector is too complex to be implemented at present. Four suboptimum detection techniques based on zero forcing (ZF) and minimum mean-square-error (MMSE) equalization with and without decision feedback (DF) are presented and compared. They combat both ISI and MAI. The computational complexity of all four equalizers is essentially the same. All four equalizers are independent of the size of the data symbol alphabet. It is shown that the performance of the MMSE equalizers is better than that of the corresponding ZF equalizers. Furthermore, the performance of the equalizers with DF is better than that of the corresponding equalizers without DF. The impairing effect of error propagation on the equalizers with DF is reduced by channel sorting     

Full-Diversity Codes for MISO Systems Equipped With Linear or ML Detectors

In this paper, a general criterion for space-time block codes (STBC) to achieve full diversity with a linear receiver is proposed for a wireless communication system having multiple transmitter and single receiver antennas [multiple-input–single-output (MISO)]. Particularly, the STBC with Toeplitz structure satisfies this criterion, and therefore, enables full diversity. Further examination of this Toeplitz STBC reveals the following important properties: 1) the symbol transmission rate can be made to approach unity; 2) applying the Toeplitz code to any signalling scheme having nonzero distance between the nearest constellation points results in a nonvanishing determinant. In addition, if quadratic-amplitude modulation (QAM) is used as the signalling scheme, then for independent MISO flat-fading channels, the Toeplitz codes is proved to approach the optimal diversity-versus-multiplexing tradeoff with a zero-forcing (ZF) receiver when the number of channel uses is large. This is, so far, the first nonorthogonal STBC shown to achieve the optimal tradeoff for such a receiver. On the other hand, when maximum-likelihood (ML) detection is employed in a MISO system, the Toeplitz STBC achieves the maximum coding gain for independent channels. When the channel fading coefficients are correlated, the inherent transmission matrix in the Toeplitz STBC can be designed to minimize the average worst case pairwise error probability.      

Improving differential detection of MDPSK by nonlinear noiseprediction and sequence estimation

A new technique is proposed to improve the performance of differential detection (DD) of M-ary differential phase-shift keying (MDPSK) significantly, applying sequence estimation. In order to obtain an appropriate representation of the received signal, a nonlinear time-variant finite impulse response or infinite impulse response prediction-error filter is used. For both filter structures the optimum coefficients are derived, assuming transmission over an additive white Gaussian noise (AWGN) channel. Delayed decision-feedback sequence estimation (DDFSE) is employed to estimate the transmitted symbol sequence. It is shown by simulations that even for decision-feedback equalization, which is a simple special case of DDFSE, a significant performance improvement of conventional DD under AWGN conditions results. In contrast to other noncoherent low-complexity receivers proposed in literature, this receiver is very robust under flat fading (Rayleigh and Ricean) conditions     

Symbol-by-symbol MAP demodulation of CPM and PSK signals onRayleigh flat-fading channels

Demodulation using the symbol-by-symbol maximum a posteriori probability (MAP) algorithm is presented. The algorithm is derived for the case of continuous phase modulation (CPM) signals transmitted over Rayleigh flat-fading channels, and a corresponding receiver structure is specified. It is shown that the MAP algorithm requires computing, for each trellis branch, the sum of the products of the weights of all paths through the trellis which pass through that branch, and that this generic computational problem can be solved efficiently by an approach that uses a forward and backward recursion through the trellis. Simulation results are presented which show both the hard and soft decision performance of the MAP receiver to be robust, even in the presence of fade rates of up to 30% of the symbol rate. The application of the receiver concept to phase-shift keying (PSK) signals is also discussed, and then evaluated via simulation. The concept of joint demodulation and decoding using iterative processing techniques is introduced. It is shown that the MAP receiver is well suited for iterative processing applications due to its use of a priori symbol probabilities and its production of optimal soft decisions. Simulation results for the reception of quaternary PSK (QPSK) show that the bit error rate (BER) performance of the iterative MAP receiver can approach that of a receiver operating with perfect knowledge of the fading process     

Joint channel estimation and data detection for high rate orthogonal time frequency space systems

This paper proposes a new pilot pattern in the delay-Doppler (DD) domain for the orthogonal time frequency space (OTFS) system. In contrast to the embedded-pilot schemes, guard intervals are not used so as increase the spectral efficiency. Also, compared to the superimposed design where data symbols and pilots are arranged on the entire DD grid, in the proposed rearrangement, the number of pilots used is only spread over a subgrid of the DD grid. Hence, the interference of pilots with data symbols is reduced. Afterwards, an algorithm for channel estimation (CE) and symbol detection in the DD domain benefiting from the sparsity of the DD channel is designed. The sparse CE step is formulated as a specific marginalization of the maximum a posteriori (MAP) criterion by providing a Bayesian approach via the mean-field approximation that involves the variational Bayesian expectation maximization (VB-EM) algorithm. Detection of data symbols is done using a low complexity MP algorithm. We also propose an interference cancellation (IC) scheme to mitigate contamination of data by pilots that is run after each CE step. To achieve a high CE accuracy, based on the mean mutual incoherence property (MIP), a pilot optimization problem for OTFS is formulated and develop a simulated annealing-based algorithm to solve it. Finally, simulation results show that the proposed scheme achieves a good compromise between spectral efficiency, complexity, and performance in terms of bit error rate (BER) and normalized mean square error (NMSE) when compared to literature benchmarks.     

A systematic approach to carrier recovery and detection ofdigitally phase modulated signals of fading channels

The problem of optimal carrier recovery and detection of digitally phase modulated signals on fading channels by using a nonstructured approach is presented, i.e. no constraint is placed on the receiver structure. First, the optimal receiver is derived for digitally phase-modulated signals when transmitted over a frequency-nonselective fading channel with memory. The memory results from the fact that usually the coherence time of the channel is larger than the symbol period. Symbols adjacent in time cannot be detected independently and therefore the well-known quadratic receiver is not optimal in this case. A maximum a posteriori (MAP) detector is derived and explicitly utilizes the channel memory for carrier recovery. The derivation shows that the optimal carrier recovery is, under certain conditions, a Kalman filter. Some attractive properties of this carrier recovery unit (including the absence of hang up) are discussed. Then the error rate of several digital modulation schemes is calculated taking the performance of the filter into account. The differences in susceptibility of the modulation schemes to carrier phase jitter are specified     

Joint iterative channel estimation and decoding in flat correlatedRayleigh fading

This paper addresses the design and performance evaluation with respect to capacity of M-PSK turbo-coded systems operating in frequency-flat time-selective Rayleigh fading. The receiver jointly performs channel estimation and turbo decoding, allowing the two processes to benefit from each other. To this end, we introduce a suitable Markov model with a finite number of states, designed to approximate both the values and the statistical properties of the correlated flat fading channel phase, which poses a more severe challenge to PSK transmission than amplitude hiding. Then, the forward-backward algorithm determines both the maximum a posteriori probability (MAP) value for each symbol in the data sequence and the MAP channel phase in each iteration. Simulations show good performance in standard correlated Rayleigh fading channels. A sequence of progressively tighter upper bounds to the capacity of a simplified Markov-phase channel is derived, and performance of a turbo code with joint iterative channel estimation and decoding is demonstrated to approach these capacity bounds     

Effect Investigation of Channel Estimation Deviation on STBC Performance in CDMA System

1　Introduction　Inrecentyears ,Space Timecode (STC) [3,8～ 11] hasattractedmuchattentionfrommanyscholarsinthefieldofwirelesscommunicationsasaneffectivetransmitdi versitytechniquecombatingfadinginwirelesscommuni cations.SpaceTimeBlockCode (STBC) [3] ,whichisproposedbyS .M .Alamoutiin 1998asasub optimaltransmitdiversitytechnique ,canobtain gainthroughemployingtwoantennasattransmitend .However,STBChastheassumptionofflatfadingchannelcondi tionthatlimitsitsuseonbroadbandwirelesscommuni cat…     

Fast adaptive equalization/diversity combining for time-varyingdispersive channels

We examine adaptive equalization and diversity combining methods for fast Rayleigh-fading frequency selective channels. We assume a block adaptive receiver in which the receiver coefficients are obtained from feedforward channel estimation. For the feedforward channel estimation, we propose a novel reduced dimension channel estimation procedure, where the number of unknown parameters are reduced using a priori information of the transmit shaping filter's impulse response. Fewer unknown parameters require a shorter training sequence. We obtain least-squares, maximum-likelihood, and maximum a posteriori (MAP) estimators for the reduced dimension channel estimation problem. For symbol detection, we propose the use of a matched filtered diversity combining decision feedback equalizer (DFE) instead of a straightforward diversity combining DFE. The matched filter form has lower computational complexity and provides a well-conditioned matrix inversion. To cope with fast time-varying channels, we introduce a new DFE coefficient computation algorithm which is obtained by incorporating the channel variation during the decision delay into the minimum mean square error (MMSE) criterion. We refer to this as the non-Toeplitz DFE (NT-DFE). We also show the feasibility of a suboptimal receiver which has a lower complexity than a recursive least squares adaptation, with performance close to the optimal NT-DFE     

Optimized Delay Diversity for Suboptimum Equalization

The optimization of delay diversity (DD) for linear equalization (LE) and decision-feedback equalization (DFE) is presented. The general case of transmission over a correlated multiple-input–multiple-output frequency-selective fading channel is considered. The proposed optimization requires the knowledge of the statistical properties of the wireless channel at the transmitter, but channel state information is only required at the receiver side. Based on an approximation of the bit error rate for LE and DFE, a stochastic gradient algorithm for optimization of the DD transmit filters is derived. Simulation results for the Global System for Mobile Communications (GSM)/Enhanced Data Rates for GSM Evolution system show significant performance gains of the proposed optimized DD scheme over the DD schemes reported by Gore (Proc. IEEE Inter. Conf. Commun., 2002) and Hehn (IEEE Trans. Wireless Commun., vol. 4, p. 2289, 2005) if LE and DFE are used at the receiver.