Low-complexity iterative channel estimation for serially concatenated systems over frequency-nonselective Rayleigh fading channels

A low-complexity iterative maximum a posteriori (MAP) channel estimator is proposed whose complexity increases linearly with the symbol alphabet size 'M. Prediction-based MAP channel estimation is not appropriate with a high-order prediction filter or a large modulation alphabet size, since the computational complexity increases with M^L , where L is the predictor order. In contrast, the proposed channel estimator has a constant number of trellis states regardless of the prediction filter order, and is shown to provide comparable error performance to the prediction-based MAP estimator     

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     

Timing Synchronization for Cooperative Communications with Detect and Forward Relaying

A non-data-aided near maximum likelihood (NDA-NML) symbol timing estimator is presented, which is applied to a cooperative communication system with a source, relay and destination. A Cramer rao bound (CRB) for the estimator for asymptotically low signal-to-noise (SNR) ratio case is derived. The timing complexity of the NDA-NML estimator is derived and compared with the correlation based data-aided maximum likelihood (DA-ML) estimator. It is demonstrated that the complexity of the NDA-NML estimator is much less than that of correlation based DA-ML estimator. The bit-error-rate (BER) performance of this system operating in a detect-and-forward (DAF) mode is studied where the channel state information (CSI) is available at the receiver and the symbol timings are estimated independently for each channel. SNR combining (SNRC) and equal ratio combining (ERC) methods are considered. It is found that timing estimation error has a significant effect on BER performance. It is also found that for large timing error the benefit of cooperative diversity could vanish. It is demonstrated that significant gains can be made with both combining methods with cooperation and timing estimation, where the gains are the same for both estimators.     

Receiver structures for time-varying frequency-selective fadingchannels

Several receiver structures for linearly modulated signals are proposed for time-varying frequency-selective channels. Their channel estimators explicitly model the time variation of the channel taps via polynomials. These structures are constructed from the following building blocks: (i) sliding or fixed block channel estimators; (ii) maximum likelihood sequence detectors (MLSDs) or decision feedback equalizers (DFEs); and (iii) single or multiple passes. A sliding window channel estimator uses a window of received samples to estimate the channel taps within or at the end of the window. Every symbol period, the window of samples is slid along another symbol period, and a new estimate is calculated. A fixed block channel estimator uses all received samples to estimate the channel taps throughout the packet, all at once. A single pass receiver estimates the channel and detects data once only. A multipass receiver performs channel estimation and data detection repetitively. The effect of the training symbol positions on the performance of the block multipass approach is studied. The bit error rate (BER) performance of the MLSD structures is characterized through simulation and analysis. The proposed receivers offer a range of performance/complexity tradeoffs, but all are well suited to time-varying channels. In fast fading channels, as the signal-to-noise ratio (SNR) increases, they begin to significantly outperform the per-survivor processing-based MLSD receivers which employ the least mean-squares (LMS) algorithm for channel estimation     

A low-complexity ML channel estimator for OFDM

Orthogonal frequency-division multiplexing with cyclic prefix enables low-cost frequency-domain mitigation of multipath distortion. However, to determine the equalizer coefficients, knowledge of the channel frequency response is required. While a straightforward approach is to measure the response to a known pilot symbol sequence, existing literature reports a significant performance gain when exploiting the frequency correlation properties of the channel. Expressing this correlation by the finite delay spread, we build a deterministic model parametrized by the channel impulse response and, based on this model, derive the maximum-likelihood channel estimator. In addition to being optimal (up to the modeling error), this estimator receives an elegant time-frequency interpretation. As a result, it has a significantly lower complexity than previously published methods.     

Sequential sequence estimation for multiple-channel systems withintersymbol and interchannel interference

A vector sequential sequence estimator is proposed for multiple-channel systems with both intersymbol interference (ISI) and interchannel interference (ICI). Both finite ISI-ICI and infinite ISI-ICI are considered. The estimator consists of a multiple-dimensional whitened matched filter and a vector sequential decoder. The metric of the sequential algorithm is derived, and the algorithm's performance is analyzed. Computer simulation results for a two-dimensional finite ISI-ICI channel and a two-dimensional infinite ISI-ICI channel are presented. Analysis and simulation show that the symbol error probability of the vector sequential algorithm is essentially the same as for maximum-likelihood sequence estimation using the vector Viterbi algorithm, while its average computational complexity is much less, although computation per symbol is a random variable with the Pareto distribution. There exists a signal-to-noise ratio above which the ensemble average computation is bounded. An upper bound on this ratio is found     

Lower Bounds on Error Probability in the Presence of Large Intersymbol Interference

A lower bound on the symbol error probability achieved by any estimator of a digital pulse-amplitude-modulated sequence in the presence of white Gaussian noise and intersymbol interference is presented. The bound reduces to the well-known single-pulse error probability bound when intersymbol interference is small, but is tighter when interference is large. For example, on the singlepole (RC) channel, the effective signal-to-noise ratio for any estimator is shown to decrease by at least 3 dB for every doubling in pulse rate T^-1asT rightarrow 0and, on the double-pole channel, by at least 9 dB, thus disproving a recent conjecture [2] on the performance of nonlinear receivers.     

Bias in a stress-strength problem

The bias of the maximum likelihood estimator for R≠Pr{ X<Y} where X and Y are independent normal random variables with unknown parameters is discussed. The bias is an odd function with respect to δ=gauf^-1 (R), where gauf(·) is the Cdf of the standard normal distribution, so the study is restricted to R ⩾0.5, or equivalently, δ⩾0. There exists δ₀>0 such that the bias is positive in the interval 0<δ<δ₀. R has a positive bias at least in the interval 0.84<R<0.94     

MIMO Receiver Using Reduced Complexity Sequence Estimation With Channel Estimation and Tracking

A sequence-based multiple-input–multiple-output receiver incorporating channel estimation and tracking for a frequency selective fading environment is developed. It employs near-maximum likelihood sequence estimation using the partitioned Viterbi algorithm and offers linearly increasing complexity with the number of transmit antennas. The receiver implements channel estimation and tracking using a vector-polynomial-based generalized recursive least squares algorithm. The resulting integrated receiver can operate in a continuously time-varying Rayleigh or Rician fading environment. Simulation results show that it offers a good tradeoff between complexity and performance. Further complexity reduction can be achieved using tentative decisions as reference signals to the estimator and a reduced complexity form of the estimator.      

An Accurate and Very Low Complexity LMMSE Channel Estimation Technique for OFDM Systems

In this paper, we propose a very low linear minimum mean square error (LMMSE) channel estimation technique for orthogonal frequency division multiplexing (OFDM) systems. The conventional LMMSE, based on the autocorrelation channel matrix, requires \(O(N_P^3)\) operations (\(N_P\) represents the total number pilot in one OFDM symbol). By exploiting the structure of the channel autocorrelation matrix, we propose a very low complexity LMMSE channel estimator which requires only \(O(N_PlogN_P)\) operations. Simulation results show that the proposed technique yields the same performances as well as the classical LMMSE in terms of bit error rate and mean square error.     

The error performance of CD900-like cellular mobile radio systems

The symbol error performance of CD900-like digital cellular mobile radio systems over narrowband and urban wideband transmission channels was investigated. The basic performance is presented for Gaussian, flat-fading Rayleigh, and log-normal channels in the presence of selection and ratio combining space diversity schemes. For wideband channels having more than one resolvable fading path, a CD900-like system without diversity reception suffers from large residual symbol error probabilities P_R(≈10^-1). The introduction of adaptive correlation diversity (ACD) mitigates the effects of multipath, yielding a P_R of 6×10^-5. Although this P_R value is relatively low, the probability of symbol error (P_e) versus signal-to-noise ratio (SNR) is significantly poorer than for the Gaussian channel. By combining the ACD scheme with space diversity, the P_R is eliminated by P_e >10^-5, and the channel SNR is within 5 dB of the Gaussian channel performance when P_e is 10^-10     

Frequency-Domain Channel Estimation for SC-FDE in UWB Communications

Recently, single-carrier block transmission with frequency-domain equalization (SC-FDE) has been shown to be a promising candidate for ultra-wideband (UWB) communications. In this paper, we address the channel estimation problem for SC-FDE transmission over UWB channels. A mean-square error (MSE) lower bound for the frequency-domain linear minimum mean-squared error (LMMSE) channel estimator is derived, and the optimal pilot sequence that achieves this lower bound is obtained. Further simplification leads to a frequency-domain channel estimator with reduced computational complexity. The performance of the simplified estimator for SC-FDE over UWB channels is evaluated and compared with that with perfect channel state information. The effects of nonoptimal and optimal pilot symbols are also investigated. Our results show that the proposed frequency-domain channel estimator performs well over UWB channels with only small performance degradation, compared with that with perfect channel estimation     

基于Kaczmarz迭代的大规模MIMO系统低复杂度软输出信号检测

大规模MIMO系统上行链路中,最小均方误差（MMSE）算法能获得接近最优的线性检测性能,但是涉及复杂度较高的矩阵求逆运算.本文基于Kaczmarz迭代提出一种低复杂度软输出信号检测算法,在算法实现中避免了矩阵求逆运算,将实现复杂度由O（K³）降为O（K²）.同时,引入了最优松弛参数进一步加快算法收敛,最后给出了两种用于信道译码的LLR的近似计算方法.仿真结果表明：所提出的Kaczmarz迭代软输出信号检测算法经过两到三次简单的迭代即可较快地收敛,并达到接近MMSE检测算法的误码率性能的水平,其性能与复杂度均优于基于矩阵近似求逆的一类检测算法.     

Study on adaptive modulation in D2D communications over Nakagami-m fading channel

A novel adaptive modulation based on nondata-aided error vector magnitude (NDA-EVM) was proposed to solve the problem of lower spectral efficiency in device to device (D2D) communication over Nakagami-m fading channel.The NDA-EVM was used to evaluate the channel quality.The relationship between NDA-EVM and symbol error ratio (SER) was derived according to the maximum likelihood method.Thereafter,the adaptive modulation mechanism of MQAM with the SER constraint was designed.Considering the joint effect of finite-length queuing and fading channel,the system packet loss rate and spectral efficiency was analyzed.Theoretical analysis and simulation experiments show that NDA-EVM based adaptive modulation accurately gives the modulation threshold and evaluates the relationship between QoS and packet loss rate,the proposed algorithm improves system spectral efficiency while maintaining low algorithm complexity,spectral efficiency improves by 0.752 bit·(s·Hz)^-1,compared with traditional algorithm.     

Adaptive Bayesian decision feedback equalizer for dispersive mobileradio channels

The paper investigates adaptive equalization of time-dispersive mobile radio fading channels and develops a robust high performance Bayesian decision feedback equalizer (DFE). The characteristics and implementation aspects of this Bayesian DFE are analyzed, and its performance is compared with those of the conventional symbol or fractional spaced DFE and the maximum likelihood sequence estimator (MLSE). In terms of computational complexity, the adaptive Bayesian DFE is slightly more complex than the conventional DFE but is much simpler than the adaptive MLSE. In terms of error rate in symbol detection, the adaptive Bayesian DFE outperforms the conventional DFE dramatically. Moreover, for severely fading multipath channels, the adaptive MLSE exhibits significant degradation from the theoretical optimal performance and becomes inferior to the adaptive Bayesian DFE     

New-user identification in a CDMA system

We present three detector/estimators (DEs) which allow multiuser detection and parameter estimation without a side channel in a dynamic asynchronous code-division multiple-access (CDMA) system in which users are entering and leaving the system. These DEs optimally detect a new user given only the chip rate and the spreading factor of the new user. Two of these DEs, the maximum-likelihood detector/estimator (MLDE) and the generalized maximum-likelihood detector/estimator (GMLDE), produce maximum-likelihood estimates of the new user's signature sequence, delay, and amplitude, which are then incorporated into a multiuser detector. The third DE, the cyclic detector/estimator (CDE), is the most computationally efficient of the three processors. This DE detects the new user by testing for cyclostationarity and then uses suboptimal schemes to estimate the new user's signature sequence, delay, and amplitude. Simulations indicate that all three DEs reliably detect a new user for an E_s/σ² (symbol-energy-to-noise ratio) of 5 dB. The MLDE and GMLDE produce signature sequence and delay estimates with probability of error less than 0.07 for an E_s/σ² of 10 dB, and the CDE produces signature sequence and delay estimates with probability of error less than 0.13 for an E_s/σ² of 15 dB     

A new adaptive equalizer with channel estimator for mobile radiocommunication

For unknown mobile radio channels with severe intersymbol interference (ISI), a maximum likelihood sequence estimator, such as a decision feedback equalizer (DFE) having both feedforward and feedback filters, needs to handle both precursors and postcursors. Consequently, such an equalizer is too complex to be practical. This paper presents a new reduced-state, soft decision feedback Viterbi equalizer (RSSDFVE) with a channel estimator and predictor. The RSSDFVE uses maximum likelihood sequence estimation (MLSE) to handle the precursors and truncates the overall postcursors with the soft decision of the MLSE to reduce the implementation complexity. A multiray fading channel model with a Doppler frequency shift is used in the simulation. For fast convergence, a channel estimator with fast start-up is proposed. The channel estimator obtains the sampled channel impulse response (CIR) from the training sequence and updates the RSSDFVE during the bursts in order to track changes of the fading channel. Simulation results show the RSSDFVE has nearly the same performance as the MLSE for time-invariant multipath fading channels and better performance than the DFE for time-variant multipath fading channels with less implementation complexity than the MLSE. The fast start-up (FS) channel estimator gives faster convergence than a Kalman channel estimator. The proposed RSSDFVE retains the MLSE structure to obtain good performance and only uses soft decisions to subtract the postcursor interference. It provides the best tradeoff between complexity and performance of any Viterbi equalizers     

A universal predictor based on pattern matching

We consider a universal predictor based on pattern matching. Given a sequence X₁, ..., X_n drawn from a stationary mixing source, it predicts the next symbol X_n+1 based on selecting a context of X_n+1. The predictor, called the sampled pattern matching (SPM), is a modification of the Ehrenfeucht-Mycielski (1992) pseudorandom generator algorithm. It predicts the value of the most frequent symbol appearing at the so-called sampled positions. These positions follow the occurrences of a fraction of the longest suffix of the original sequence that has another copy inside X₁X₂···X_n ; that is, in SPM, the context selection consists of taking certain fraction of the longest match. The study of the longest match for lossless data compression was initiated by Wyner and Ziv in their 1989 seminal paper. Here, we estimate the redundancy of the SPM universal predictor, that is, we prove that the probability the SPM predictor makes worse decisions than the optimal predictor is O(n^-ν) for some 0<ν<½ as n→∞. As a matter of fact, we show that we can predict K=O(1) symbols with the same probability of error     

The sublinear relationship between index change and carrier densityin 1.5 and 1.3 μm semiconductor lasers

The carrier-induced index change was measured using a novel injection-reflection technique in combination with differential carrier lifetime data. The observed relation between index change and injected carrier density at bandgap wavelength is nonlinear and is approximately given by δn_act=-6.1×10^-14 ( N)^0.66 for a 1.5-μm laser and δn _act=-1.3×10^-14 (N)^0.68 for a 1.3-μm laser. The carrier-induced index change for a 1.3-μm laser at 1.53-μm wavelength is smaller and is given by δn _act=-9.2×10^-16 (N)^0.72      

Decoding, Performance Analysis, and Optimal Signal Designs for Coordinate Interleaved Orthogonal Designs

Space-time block codes (STBC) using coordinate interleaved orthogonal designs (CIOD) proposed recently by Khan and Rajan allow single-complex symbol decoding and offer higher data rates than orthogonal STBC. In this paper, we present the channel decoupling property of CIOD codes. A new general maximum likelihood method is derived, enabling the calculation of the symbol pair-wise error probability and union bound (UB) on symbol error rate (SER). Extensive simulation results show that the UB is within 0.1 dB from the simulated SER when SER < 10^-2. The UB thus can be used to accurately predict and optimize the performance of CIOD codes. Furthermore, a new signal design combining signal rotation and power allocation is presented for constellations with uneven powers of real and imaginary parts such as rectangular quadrature amplitude modulation.