Space-time coding and Kalman filtering for diversity transmissions through time-selective fading channels

Most existing space-time coding (STC) schemes have been developed for flat fading channels. To obtain antenna diversity gain, they rely on channel state information (CSl) required at the receiver through channel estimation techniques. This paper proposes a new decision feedback decoding scheme for Alamouti-based space-time block coding (STBC) transmission over time-selective fading channels. In wireless channels, time-selective fading effects arise mainly due to Doppler shift and carrier frequency offset. Modelling the time-selective fading channels as the first-order Gauss-Markov processes, we use recursive algorithms such as Kalman filtering, LMS and RLS algorithms for channel tracking. The proposed scheme consists of the symbol decoding stage and channel tracking algorithms. Computer simulations confirm that the proposed scheme shows the better performance and robustness to time-selectivity.

The application of maximum a posteriori (MAP) detection to DS-CDMA systems in time-selective fading channels is investigated. By sampling the outputs of a matched filter and combining antenna array elements, strong multiple-access interference (MAI) is estimated and suppressed. By incorporating channel approximations, Kalman filtering, and the probability density of the prediction error, a joint channel estimation and MAP detection algorithm is developed. Unknown channel parameters are identified by using an algorithm similar to the extended Kalman filter (EKF). Also, differential modulation is applied to eliminate the need for pilot insertion. Through computer simulations, a near-optimum bit-error-rate (BER) performance is found.

This letter considers the effect of channel estimation errors on the performance of space-time coded (STC) systems with transmit and receive antenna selection over quasi-static flat fading channels. By performing pairwise error probability analysis and presenting numerical examples, we show that the diversity order achieved with perfect channel state information (CSI) is still achievable with imperfect CSI used both at the antenna selection and the space-time decoding processes. We note that our results apply to general STC systems with both transmit and/or receive antenna selection based on largest received powers which can be estimated by any channel estimator.

It is well known that the performance of the wireless communication systems can be enhanced by using multiple transmit and receive antennas, which is generally referred to as the MIMO technique, and has been incorporated into the IEEE 802.11n standard, i.e. one of the Wi-Fi systems. The MIMO technique has also been adopted by the 3GPP Long Term Evolution (LTE) and the 3GPP2 Ultra Mobile Broadband (UMB) standards. The space-time coding is a promising way to realize the gain in the wireless communications system using MIMO. The space time block code, and the orthogonal space time block code in particular have been proposed in research and implemented in practical wireless communication systems due to their low computational complexity in maximum likelihood decoding implementation. However, the code rates of the orthogonal space time block codes are usually lower than $3/4$ when the number of transmit antennas is greater than two, which limit their throughput. To increase the code rate and the throughput of the orthogonal space time block code for more than two transmit antennas, a family of new space-time block codes (STBC) for 3 and 4 transmit antennas in a MIMO wireless communication system have been proposed in this Ph.D. research. These new codes are orthogonal and achieve full diversity, full rate using Triple QPSK'' modulation, which is proposed in this research. We investigated the performance of these STBCs when the channel state information (CSI) is perfectly known at the receiver. The CSI is not known to the transmitter in all of the studies in this dissertation. An analytical bound of the probability of bit error is developed and the Monte Carlo simulation is used when investigating these new STBC codes. In practical wireless communication system, the CSI is generally not available at the receiver and it is usually estimated by the receiver through the pilot signals or training signals known to the receiver. No matter what channel estimation method is used, the estimate of CSI will not match the CSI exactly and is noisy. The performance of these new STBCs using theTriple QPSK'' modulation when the estimate of the CSI is employed to detect the symbol is investigated in this dissertation. An upper bound of the bit error probability is developed when the noisy CSI is used to detect the symbols. The performance of the new STBCs using the Triple QPSK'' modulation is also evaluated using Monte Carlo simulation. When the CSI is not available to either the receiver or the transmitter, the differential encoding and decoding algorithm is applied to these new STBCs, which use theTriple QPSK'' modulation. The results showed that these orthogonal STBCs achieve full diversity full rate using ""Triple-QPSK"" modulation with differential detection. This provides a means of achieving space diversity and multiplexing gain without the CSI. A new differential encoding and decoding algorithm is proposed and analyzed for STBCs with 3 transmit antennas, whose transmission matrix is not square matrix, as part of this Ph.D. research. The STBCs using this algorithm achieve full diversity the MIMO system can possibly provide.

The authors consider a space–time coded (STC) orthogonal frequency-division multiplexing (OFDM) system with multiple transmitter and receiver antennas over correlated frequency- and time-selective fading channels. They propose first a maximum-likelihood (ML) receiver for space–time block code OFDM systems based on the expectation–maximisation (EM) algorithm. They then propose a low-density parity-check (LDPC)-code-based STC-OFDM system to interface with the EM algorithm. When comparing the proposed scheme with the conventional space–time trellis code, the LDPC-based STC significantly improves the system performance by exploiting both spatial and selective-fading diversity in wireless channels. Compared with the recently proposed turbo-code-based STC scheme, LDPC-based STC exhibits a lower complexity and more flexible scalability.

Multiple Input Multiple Output(MIMO) has been in much importance in recent past because of high capacity gain over a single antenna system. In this article, analysis over the capacity of the MIMO channel systems with spatial channel with modified precoder and decoder has been considered when the channel state information (CSI) is considered partial. Due to delay in acquiring transmitted information at the receiver end, the time selective fading wireless channel often induces incomplete or partial CSI. The dynamic CSI model has also been implemented consisting channel mean and covariance which leads to extracting of channel estimates and error covariance which then further applied with the modified precoder and decoder utilizing both the parameters indicating the CSI quality since these are the functions of temporal correlation factor, and based on this, the model covers data from perfect to statistical CSI, either partially or fully blind. It is found that in case of partial and imperfect CSI, the capacity depends on the statistical properties of the error in the CSI which has been manipulated according to the precoder and decoder conditions. Based on the knowledge of statistical distribution of the deviations in CSI knowledge, a new approach which maximizes the capacity of spatial channel model with modified precoder and decoder has been tried. The interference then interactively reduced by employing the iterative channel estimation and data detection approach, where by utilizing the detected symbols from the previous iteration, multiuser/MIMO channel estimation and symbol detection is improved.

Coordinate interleaved orthogonal designs (CIOD) (Khan and Rajan in IEEE Trans Inform Theory 52(5):2062---2091, 2006) can offer desirable properties, such as full rate, full diversity and single-symbol maximum likelihood decoding for two, three and four transmit antennas under quasi-static fading channels. When fading is time-selective, zero-forcing decoder can applied to achieve good performance while still maintain low decoding complexity. In this paper, theoretical analysis of symbol error rate performance for CIOD codes over time-selective fading channels with a zero-forcing linear receiver is derived. Firstly, a closed-form expression (i.e., not in integral form) is derived for the average symbol pair-wise error probability (SPEP) in time-selective frequency-nonselective independent identically distributed (i.i.d.) Rayleigh fading channels. Then, the SPEP is used to derive a tight upper bound (UB) for the symbol-error rate (SER) of CIOD codes. Simulation results indicate that our theoretical UB often coincides (within 0.05 dB) with the true SER obtained via Monte-Carlo simulation. The UB can thus be used to accurately predict and optimize the performance of CIOD codes over time-selective fading channels.

In time-selective fading channel, the Alamouti orthogonality principle is lost due to the variation of channel from symbol-to-symbol in space–time block-coded orthogonal frequency division multiplexing (STBC-OFDM) system and causes co-channel interference (CCI) effects. To combat the CCI effects, various signal detection schemes have been proposed earlier by assuming that a priori channel state information (CSI) is known to the receiver. However, in practice, the CSI is unknown and therefore accurate estimation of channel is required for efficient signal detection. In this paper, by exploiting circulant properties of the channel frequency response (CFR) autocorrelation matrix [Formula: see text], we propose an efficient low complexity linear-minimum-mean-square-error (LMMSE) estimator. This estimator applies an expectation–maximization (EM) iterative process to reduce the computational complexity significantly. Finally, we compare the proposed LMMSE-EM estimator with conventional least square (LS) and LMMSE estimator in terms of performance and computational complexity. The simulation results show that the proposed LMMSE-EM estimator achieves exactly the same performance as the optimal LMMSE estimator with much lower computational complexity.

Space-time coding has been proposed recently for MIMO wireless communication systems. Most of these space-time coding schemes use the assumption that either no channel state information, or the channel mean/covariance information, is available at the transmitter. We propose a new space-time coding scheme for a close-loop transmission system, where quantized channel phase information is available at the transmitter. A new performance criterion is derived for the quasi-static fading channel. This design criterion is then used to construct a new class of space-time trellis codes. The proposed code construction is based on the concatenation of a standard M-TCM outer code with an inner code. The inner code is selected from a series of inner codes using the channel phase feedback. The series of inner codes is constructed based on the systematic set partitioning of two classes of space-time signal designs. Simulation results show significant improvement over other space-time trellis codes. In addition, the proposed coding scheme enjoys low peak-to-average power ratio, simple decoding, and easy implementation without complicated eigenanalysis.

In this work we report the simulated performance of two digital wireless systems, designed for the transmission on a time selective Rayleigh flat fading channel. In the first system a four-dimensional trellis coded modulation with a non-coherent detection method, formed by a differential demodulator followed by a MLSE-type Viterbi decoder, has been adopted. The second system consists of a continuous phase modulation of GMSK type demodulated through a non-coherent detection method formed by a frequency discriminator followed by an estimator based on the Chung algorithm.

On the basis of analyzing the principle of multicarrier CDMA (MC-CDMA) technique and space–time coding technique, using the optimized complex wavelet packet as multicarrier modulation, a novel MC-CDMA system based on complex wavelet packet and space–time block codes is proposed. The bit error rate (BER) performance of the system is investigated in Rayleigh fading channel, and the corresponding BER expression is derived in detail. The system can overcome the decrease of spectrum efficiency of conventional MC-CDMA due to inserting cyclic prefix (CP). Moreover, the application of space–time coding technique strengthens the capability against fading channel significantly and perfects the system performance. Theoretical analysis shows that the proposed system with 2-transmitter antenna and 2-receiver antenna space–time block codes performs four times better than the single-antenna MC-CDMA system based on complex wavelet packet (CWP-MC-CDMA); the same conclusion is also reached by the simulation results in fading channel. As a result, the performance of the proposed CWP-MC-CDMA system outperforms a conventional MC-CDMA system based on DFT, it is close or superior to that of the conventional MC-CDMA with CP. Especially, the CWP-MC-CDMA system with space–time coding has superior ability to combat spatial fading and multi-access interference, and it slightly outperforms conventional MC-CDMA with CP and space–time coding.

The key assumption in all space-time block coded orthogonal frequency division multiplexing (OFDM) schemes is that the channel remains static within the whole codeword length. This will inevitably introduce an irreducible error floor, caused by the inter-transmit-antenna interference (ITAI), in the high signal-to-noise (SNR) region over the time selective fading channels. To mitigate the impact of ITAI, a novel signal detection scheme for four-transmit-antenna space-time-frequency coded OFDM system has been proposed in this paper. Through the theoretical analysis and computer simulations, it is proven that the proposed method can handle both slow and fast fading channels very effectively as well as efficiently, removing the error floor within the normal Doppler frequency range .

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.

Delay diversity is an effective transmit diversity technique to combat adverse effects of fading. Thus far, previous work in delay diversity assumed that perfect estimates of current channel fading conditions are available at the receiver and training symbols are required to estimate the channel from the transmitter to the receiver. However, increasing the number of the antennas increases the required training interval and reduces the available time within which data may be transmitted. Learning the channel coefficients becomes increasingly difficult for the frequency selective channels. In this paper, with the subspace method and the delay character of delay diversity, a channel estimation method is proposed, which does not use training symbols. It addresses the transmit diversity for a frequency selective channel from a single carrier perspective in the form of a simple equivalent flat fading model. Monte Carlo simulations give the performance of channel estimation and the performance comparison of our channel-estimation-based detector with decision feedback equalization, which uses the perfect channel information.

The accurate performance evaluation of differential amplitude and phase-shift keying (DAPSK) with postdetection equal gain combining (EGC) over generalized fading channels is of great theoretical interest and practical importance. In this paper, by using a decision variable-based moment generating function approach, exact error probability results for DAPSK over generalized Rician and Nakagami fading channels are derived, taking into account the effects of all the system and fading channel parameters. Several maximum likelihood (ML)-based detectors that do not require channel state information (CSI) are proposed for generalized Rician fading channels, and an exact bit error probability (BEP) union bound for the ML detection is derived. Assuming CSI, a performance upper bound for DAPSK with EGC is also presented. Simulation and numerical results show when both detectors have no CSI, the conventional DAPSK detector may perform closely to (though worse than) the ML detector. However, the EGC receiver with CSI performs substantially better than the ML detector without CSI, and very closely to the coherent APSK detector.