Space-time trellis codes over rapid rayleigh fading channels with channel estimation?part ii: performance analysis and code design for non-identical channels

We consider the maximum likelihood (ML) receiver design, performance analysis and code design for space-time trellis codes (STTC) over non-identical, rapid fading channels with imperfect channel state information (CSI). The exact pairwise error probability (PEP) and PEP bounds for the ML receiver are obtained. A new code design criterion exploiting the statistical information of the channel estimates is proposed, which can minimize the performance loss caused by channel estimation error. New codes are obtained via an iterative search algorithm with reduced complexity. Under actual channel estimation conditions, our codes perform better than the existing codes in the literature which are designed on the assumption of identical channels, and perfect CSI at the receiver. More performance gain can be achieved by our codes when the degree of imbalance among the links is higher.     

Closed-form blind MIMO channel estimation for orthogonal space-time block codes

In this paper, a new computationally simple approach to blind decoding of orthogonal space-time block codes (OSTBCs) is proposed. Using specific properties of OSTBCs, the authors' approach estimates the channel matrix in a closed form and in a fully blind fashion. This channel estimate is then used in the maximum-likelihood (ML) receiver to decode the information symbols. The proposed estimation technique provides consistent channel estimates, and, as a result, the performance of the authors' blind ML receiver approaches that of the coherent ML receiver, which exploits the exact channel state information (CSI). Simulation results demonstrate the performance improvements achieved by the proposed blind decoding algorithm relative to the popular differential space-time modulation scheme.     

Performance of STTC-MC-CDMA Systems with Imperfect Channel Estimation

Since, in a practical system perfect channel state information (CSI) is not possible due to presence of noise. This paper deals with the performance of space-time trellis code (STTC) in multi-carrier code-division multiple-access systems in presence of channel estimation (CE) error and results are compared with perfect CSI at the receiver. The pilot symbol assisted (PSA) technique is used for CE employing minimum mean-square error method. The symbol error rate (SER) performance is observed by employing Viterbi decoding algorithm to decode STTC code at the receiver in multi-path fading channel. The simulated SER performances in presence of CE error and with perfect CSI are compared with the theoretical performances to validate the theoretical analysis.     

Performance Analysis of Space-Time Coded CDMA System Over Nakagami Fading Channels with Perfect and Imperfect CSI

In this paper, the performance of multiuser CDMA systems with different space time code schemes is investigated over Nakagami fading channel. Low-complexity multiuser receiver schemes are developed for space-time coded CDMA systems with perfect and imperfect channel state information (CSI). The schemes can make full use of the complex orthogonality of space-time coding to obtain the linear decoding complexity, and thus simplify the exponential decoding complexity of the existing scheme greatly. Moreover, it can achieve almost the same performance as the existing scheme. Based on the bit error rate (BER) analysis of the systems, the theoretical calculation expressions of average BER are derived in detail for both perfect CSI and imperfect CSI, respectively. As a result, tight closed-form BER expressions are obtained for space-time coded CDMA with orthogonal spreading code, and approximate closed-form BER expressions are attained for space-time coded CDMA with quasi-orthogonal spreading code. Computer simulation for BER shows that the theoretical analysis and simulation are in good agreement. The results show that the space-time coded CDMA systems have BER performance degradation for imperfect CSI.     

Blind estimation and detection of space-time trellis coded transmissions over the Rayleigh fading MIMO channel

We present a joint channel estimation and detection method of space-time trellis codes (STTC) in the context of an unknown flat fading multiple-input multiple-output (MIMO) channel. A combined state-space model for the space-time code and the Rayleigh fading MIMO channel is introduced, in order to use deterministic particle filtering at the receiver side. An important feature of the proposed method is that the fading rate need not be known to the receiver. Monte-Carlo simulations show that the performances of the proposed scheme are close to decoding with perfect channel state information (CSI) using the Viterbi algorithm (VA).     

Doubly iterative receiver for block transmissions with EM-based channel estimation

Cyclic-prefix code division multiple access (CP-CDMA), multicarrier CDMA (MC-CDMA) and single carrier cyclic-prefix (SCCP) transmission are some schemes that could support the increasing demand of future high data rate applications. The linear and nonlinear equalizers used to detect the transmitted signal are always far from the Maximum-Likelihood (ML) detection bound. The block iterative generalized decision feedback equalizer (BI-GDFE) is an iterative and effective interference cancelation scheme which could provide near-ML performance yet with very low complexity. In order to deploy this scheme, the channel state information (CSI) must be available at the receiver. In practice, this information has to be estimated by using pilot and data symbols. This paper investigates the problem of channel estimation using the Expectation Maximization (EM) algorithm. The BI-GDFE provides the soft information of the transmitted signals to the EM-based algorithm in the form a combination of hard decision and a coefficient so-called the input-decision correlation (IDC). The resultant receiver becomes a doubly iterative scheme. To evaluate the performance of the proposed estimation algorithm, the Cramér-Rao Lower Bound (CRLB) is also derived. Computer simulations show that the bit error rate (BER) performance of the proposed receiver for joint channel estimation and signal detection can reach the performance of the BI-GDFE with perfect CSI.     

Extended MLSE diversity receiver for the time- andfrequency-selective channel

This paper develops a maximum-likelihood sequence estimation (MLSE) diversity receiver for the time- and frequency-selective channel corrupted by additive Gaussian noise when linear constellations (M-ASK, M-PSK, M-QAM) are employed. The paper extends Ungerboeck's derivation of the extended MLSE receiver for the purely frequency-selective channel to the more general channel. Although the new receiver structure and metric assume ideal channel-state information (CSI), the receiver can be used wherever high-quality CSI is available, such as a comb of pilot tones or time-isolated symbols. The major contributions of this paper are as follows: (1) the derivation of a finite-complexity diversity receiver that is maximum likelihood (ML) for all linear channel models and sources of diversity, as long as ideal CSI is available; (2) a benchmark, in that the new receiver's performance is a lower bound on the performance of practical systems, which either lack ideal CSI or are not ML; (3) insight into matched filtering and ML diversity receiver processing for the time- and frequency-selective channels; and (4) bounds on the new receiver's bit-error rate (BER) for ideal CSI and pilot tone CSI, in a fast Rayleigh-fading channel with multiple independently faded paths. The new receiver can seamlessly tolerate square-root Nyquist pulses without a fading-induced ISI error floor     

Soft quasi-maximum-likelihood detection for multiple-antenna wireless channels

The paper addresses soft maximum-likelihood (ML) detection for multiple-antenna wireless communication channels. We propose a soft quasi-ML detector that maximizes the log-likelihood function by deploying a semi-definite relaxation (SDR). Given perfect channel state information at the receiver, the quasi-ML SDR detector closely approximates the performance of the optimal ML detector in both coded and uncoded multiple-input, multiple-output (MIMO) channels with quadrature phase-shift keying (QPSK) modulation and frequency-flat Rayleigh fading. The complexity of the quasi-ML SDR detector is much less than that of the optimal ML detector, thus offering more favorable performance/complexity characteristics. In contrast to the existing sphere decoder, the new quasi-ML detector enjoys guaranteed polynomial worst-case complexity. The two detectors exhibit quite comparable performance in a variety of ergodic QPSK MIMO channels, but the complexity of the quasi-ML detector scales better with increasing number of transmit and receive antennas, especially in the region of low signal-to-noise ratio (SNR).     

Iterative Estimation and Equalization for SCCP Over Doubly Selective Channels

In time varying channels, symbol recovery for single carrier cyclic prefix (SCCP) systems becomes complicated, because the orthogonality of channel frequency response (CFR) matrix is destroyed. In response, we propose a block turbo equalization algorithm in the time domain for SCCP to cope with channel time variations. In particular, the band structure of the channel time response (CTR) matrix is exploited to reduce the computational complexity of matrix inversion. In order to use this equalization scheme, accurate channel state information (CSI) must be available. Accordingly, we present a doubly selective channel estimation method for SCCP block transmissions with the aid of a Karhunen-Loeve basis expansion model (KL-BEM). In this method, the channel estimates are firstly obtained by using the cyclic prefix (CP) of each block, and then further refined by employing an expectation maximization (EM) based iterative algorithm. Combining the iterative estimator with the proposed equalizer naturally results in a doubly iterative receiver, the performance of which is shown to come close to the performance with perfect CSI.     

空时频移键控(ST-FSK)的分离ML信号检测方法

该文提出一种分离最大似然(ML)信号检测方法,在信道状态信息已知的假设下,利用信号的正交性特点,使多个接收矢量的ML联合检测问题分离为若干个矢量的单独ML检测问题。若采用合适的信道估值算法,在运算量上不仅大大低于非相干检测,还能获得性能的提高。仿真实验验证了算法的有效性。     

Mitigation of channel estimation error in TR–UWB system based on a novel MMSE equalizer

The time reversal (TR) technique combined with the ultra-wideband (UWB) system offers a new potential for decreasing the cost and complexity of the UWB receivers. In spite of TR–UWB's good performance in perfect channel state information (CSI), it is very sensitive to the channel estimation error. The effect of channel imperfection on the TR–UWB system is considered in this paper. At first, based on a minimum mean square error (MMSE) equalizer receiver, a prefilter is calculated in closed form to improve the performance of the TR–UWB system in an imperfect CSI scenario. Furthermore, for comparison purposes, a similar calculation for prefilter is carried out based on a simple matched filter (MF) receiver. Then, in order to improve the MF receiver performance, a two-stage iteration-based algorithm is developed. The initial value for this iteration-based improved algorithm is considered to be a prefilter which is calculated in the TR–UWB system with MMSE equalizer. This optimized algorithm causes the channel estimation error in the TR–UWB system to become zero in some steps. Finally, exhaustive simulations are done to demonstrate the performance advantage attained by the improved algorithm.     

Matrix Coded Modulation: A New Non-coherent MIMO Scheme

This paper describes a new space-time coding scheme for non-coherent multi-antenna multi-input multi-output (MIMO) systems. This new MIMO scheme merges error-correcting and space-time coding functions by transmitting invertible matrices, so this scheme has been called “Matrix Coded Modulation” or “MCM”. Coherent systems require channel state information (CSI) at the transmitters and/or at the receivers, and their performances strongly depend on the channel estimation. For example, in systems using Orthogonal frequency division multiplexing, the channel estimation requires the insertion of pilot-symbols in the transmitted frame which implies a spectral efficiency loss of the global system that increase with the number of transmit antennas. The existing non-coherent schemes such as the differential space-time modulation leads to performance degradation compared to coherent systems in which perfect CSI is assumed. Decoding in the MCM scheme is performed iteratively, based on a specified detection criteria. In the proposed MCM scheme, decoding can be achieved with or without CSI at the receiving antennas. As the space-time coding function is merged with the error-correcting code, the euclidean distances distribution between modulated signals based on the detection criteria is strongly linked to the Hamming weights distribution of the channel error-correcting code used in the MCM scheme. Moreover, a low-complexity decoding algorithm is described and compared to the existing differential schemes.     

Multiple-Antenna Signaling Over Fading Channels With Estimated Channel State Information: Performance Analysis

Multiple-antenna concepts for wireless communication systems promise high spectral efficiency and low error rates by proper exploitation of the randomness in multipath propagation. In this paper, we investigate the impact of channel uncertainty caused by channel estimation errors on the error rate performance. We consider a training-based multiple-antenna system that reserves a portion of time to sound the channel. Training symbols are used to estimate the channel by means of an arbitrary linear filter at the receiver. No channel state information (CSI) is assumed at the transmitter. We present a new framework to analyze training-based multiple-antenna systems by introducing an equivalent system model that specifies the channel by the estimated (and hence, known) channel coefficients and an uncorrelated, data-dependent, multiplicative noise. We derive the maximum-likelihood (ML) detector and highlight its behavior in the limiting cases of perfect CSI and no CSI, and its relation to several mismatched detectors. We deduce new exact expressions and Chernoff bounds of the pairwise error probability (PEP) used to assess word-error and bit-error rate bounds for ML and mismatched detection. Finally, we review the code design guidelines in terms of the deleterious effect of channel uncertainty for coherent and noncoherent signaling schemes, and present numerical results.     

Differential and coherent decorrelating multiuser receivers for space-time-coded CDMA systems

Previously, we proposed a differential space-code modulation (DSCM) scheme that integrates the strength of differential space-time coding and spreading to achieve interference suppression and resistance to time-varying channel fading in single-user environments. In this paper, we consider the problem of multiuser receiver design for code-division multiple-access (CDMA) systems that utilize DSCM for transmission. In particular, we propose two differential receivers for such systems. These differential receivers do not require the channel state information (CSI) for detection and, still, are resistant to multiuser interference (MUI) and time-varying channel fading. We also propose a coherent receiver that requires only the CSI of the desired user for detection. The coherent receiver yields improved performance over the differential receivers when reliable channel estimates are available (e.g., in slowly fading channels). The proposed differential/coherent receivers are decorrelative schemes that decouple the detection of different users. Both long and short spreading codes can be employed in these schemes. Numerical examples are presented to demonstrate the effectiveness of the proposed receivers.     

Practical robust uniform channel decomposition scheme for CSI mismatch in limited feedback MIMO systems

Uniform channel decomposition (UCD) has been proven to be optimal in bit error rate (BER) performance and strictly capacity lossless when perfect channel state information (CSI) is assumed to be available at both the transmitter and receiver side. In practice, CSI can be obtained by channel estimation at receiver and conveyed to transmitter via a limited-rate feedback channel. In such case, the implementation of traditional UCD by treating the imperfect CSI as perfect CSI cause significant performance degradation due to inevitable channel estimation error and vector quantization error. To overcome this problem, a practical robust UCD scheme was proposed in this paper, which includes two steps, firstly, a matching architecture was proposed to eliminate the mismatch between CSI at receiver (CSIR) and CSI at transmitter (CSIT), secondly, an MMSE based robust UCD scheme considering channel estimation error and vector quantization error as an integral part of the design was derived. Simulation results show that the proposed practical robust UCD scheme is capable of improving the BER performance greatly in the context of channel estimation error and vector quantization error compared with the traditional UCD scheme.     

Exact bit-error rate analysis for the combined system of beamforming and Alamouti's space-time block code

The simplest Alamouti's space-time block code can be coupled with more than two transmit antennas via the beamforming technique to enhance the performance gain without code rate reduction. Beamforming is performed at the transmitter, dependent on the channel state information (CSI) which is obtained by using feedback through a feedback link or estimated using reciprocity in duplexing schemes. In this letter, we derived the exact bit-error rate for the combined system with two transmit and one receive antennas in slow Rayleigh flat fading channels. It is assumed that the receiver has the perfect CSI. The expression can be easily extended to more than two transmit antennas.     

A VERTICAL LAYERED SPACE—TIME CODE AND ITS CLOSED—FORM BLIND SYMBOL DETECTION

Vertical layered space-time codes have demonstrated the snormous potential to accommodate rapid flow data.Thus far,vertical layered space-time codes assumed that perfect estimates of current channel fading conditions are available at the receiver.However,increasing the number of transmit antennas increases the required training interval and reduces the available time in which data may be transmitted before the fading coefficients change.In this paper,a vertical layered space-time code is proposed.By applying the subupace method to the layered space-time code,the symbols can be detected without training symbols and channel estimates at the transmitter or the receiver.Monte Carlo simulations show that performance can approach that of the detection method with the knowledge of the channel.     

Matrix Coded Modulation: A New Non-coherent MIMO Scheme

This paper describes a new space-time coding scheme for non-coherent multi-antenna Multi-Input Multi-Output (MIMO) systems. This new MIMO scheme merges error-correcting and space-time coding functions by transmitting invertible matrices, so this scheme has been called “Matrix Coded Modulation” or “MCM”. Coherent systems require Channel State Information (CSI) at the transmitters and/or at the receivers, and their performances strongly depend on the channel estimation. For example, in systems using Orthogonal Frequency Division Multiplexing, the channel estimation requires the insertion of pilot-symbols in the transmitted frame which implies a spectral efficiency loss of the global system that increase with the number of transmit antennas. The existing non-coherent schemes such as the Differential Space-Time Modulation leads to performance degradation compared to coherent systems in which perfect CSI is assumed. Decoding in the MCM scheme is performed iteratively, based on a specified detection criteria. In the proposed MCM scheme, decoding can be achieved with or without CSI at the receiving antennas. As the space-time coding function is merged with the error-correcting code, the euclidean distances distribution between modulated signals based on the detection criteria is strongly linked to the Hamming weights distribution of the channel error-correcting code used in the MCM scheme. Moreover, a low-complexity decoding algorithm is described and compared to the existing differential schemes.     

On Multiple Symbol Detection for Diagonal DUSTM Over Ricean Channels

This letter considers multiple symbol differential detection for multiple-antenna systems over flat Ricean-fading channels when partial channel state information (CSI) is available at the transmitter. Using the maximum likelihood (ML) principle, and assuming perfect knowledge of the channel mean, we derive the optimal multiple symbol detection (MSD) rule for diagonal differential unitary space-time modulation (DUSTM). This rule is used to develop a sphere decoding bound intersection detector (SD-BID) with low complexity. A suboptimal MSD based decision feedback DD (DF-DD) algorithm is also derived. The simulation results show that our proposed MSD algorithms reduce the error floor of conventional differential detection and that the computational complexity of these new algorithms is reasonably low.     

Error probability of coded STBC systems in block fading environments

In this letter, a union bound on the error probability of coded multi-antenna systems over block fading channels is derived. The bound is based on uniform interleaving of the coded sequence prior to transmission over the channel. Using this argument the distribution of error bits over the fading blocks is computed and the corresponding pair wise error probability (PEP) is derived. We consider coded systems that concatenate a binary code with a space-time block code (STBC). Coherent detection is assumed with perfect and imperfect channel state information (CSI) at the receiver, where imperfect CSI is obtained using pilot-aided estimation. Under channel estimation environments, the tradeoff between channel diversity and channel estimation is investigated and the optimal channel memory is approximated analytically. Results show that the performance degradation due to channel memory decreases as the number of transmit antennas is increased. Moreover, the optimal channel memory increases with increasing the number of transmit antennas.