Spread-response precoding for communication over fading channels

Interleaving is an important technique for improving the effectiveness of traditional error-correcting codes in data transmission systems that exhibit multipath fading. Such channels often arise in mobile wireless communications. We present an alternative to interleaving for such systems, which we term “spread-response precoding”. From the perspective of the coded symbol stream, spread-response precoding effectively transforms an arbitrary Rayleigh fading channel into a nonfading, simple white marginally Gaussian noise channel. Furthermore, spread-response precoding requires no additional power or bandwidth, and is attractive in terms of computational complexity, robustness, and delay considerations     

Transmit antennae space-time block coding for generalized OFDM inthe presence of unknown multipath

Transmit antenna diversity has been exploited to develop high-performance space-time coders and simple maximum-likelihood decoders for transmissions over flat fading channels. Relying on block precoding, this paper develops generalized space-time coded multicarrier transceivers appropriate for wireless propagation over frequency-selective multipath channels. Multicarrier precoding maps the frequency-selective channel into a set of flat fading subchannels, whereas space-time encoding/decoding facilitates equalization and achieves performance gains by exploiting the diversity available with multiple transmit antennas. When channel state information is unknown at the receiver, it is acquired blindly based on a deterministic variant of the constant-modulus algorithm that exploits the structure of space-time block codes. To benchmark performance, the Cramer-Rao bound of the channel estimates is also derived. System performance is evaluated both analytically and with simulations     

Limited feedback unitary precoding for orthogonal space-time block codes

Orthogonal space-time block codes (OSTBCs) are a class of easily decoded space-time codes that achieve full diversity order in Rayleigh fading channels. OSTBCs exist only for certain numbers of transmit antennas and do not provide array gain like diversity techniques that exploit transmit channel information. When channel state information is available at the transmitter, though, precoding the space-time codeword can be used to support different numbers of transmit antennas and to improve array gain. Unfortunately, transmitters in many wireless systems have no knowledge about current channel conditions. This motivates limited feedback precoding methods such as channel quantization or antenna subset selection. This paper investigates a limited feedback approach that uses a codebook of precoding matrices known a priori to both the transmitter and receiver. The receiver chooses a matrix from the codebook based on current channel conditions and conveys the optimal codebook matrix to the transmitter over an error-free, zero-delay feedback channel. A criterion for choosing the optimal precoding matrix in the codebook is proposed that relates directly to minimizing the probability of symbol error of the precoded system. Low average distortion codebooks are derived based on the optimal codeword selection criterion. The resulting design is found to relate to the famous applied mathematics problem of subspace packing in the Grassmann manifold. Codebooks designed by this method are proven to provide full diversity order in Rayleigh fading channels. Monte Carlo simulations show that limited feedback precoding performs better than antenna subset selection.     

Spatial multiplexing in correlated fading via the virtual channel representation

Spatial multiplexing techniques send independent data streams on different transmit antennas to maximally exploit the capacity of multiple-input multiple-output (MIMO) fading channels. Most existing multiplexing techniques are based on an idealized MIMO channel model representing a rich scattering environment. Realistic channels corresponding to scattering clusters exhibit correlated fading and can significantly compromise the performance of such techniques. In this paper, we study the design and performance of spatial multiplexing techniques based on a virtual representation of realistic MIMO fading channels. Since the nonvanishing elements of the virtual channel matrix are uncorrelated, they capture the essential degrees of freedom in the channel and provide a simple characterization of channel statistics. In particular, the pairwise-error probability (PEP) analysis for correlated channels is greatly simplified in the virtual representation. Using the PEP analysis, various precoding schemes are introduced to improve performance in virtual channels. Unitary precoding is proposed to provide robustness to unknown channel statistics. Nonunitary precoding techniques are proposed to exploit channel structure when channel statistics are known at the transmitter. Numerical results are presented to illustrate the attractive performance of the precoding techniques.     

Space-time codes for high data rate wireless communication:performance criterion and code construction

We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into n streams that are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. We derive performance criteria for designing such codes under the assumption that the fading is slow and frequency nonselective. Performance is shown to be determined by matrices constructed from pairs of distinct code sequences. The minimum rank among these matrices quantifies the diversity gain, while the minimum determinant of these matrices quantifies the coding gain. The results are then extended to fast fading channels. The design criteria are used to design trellis codes for high data rate wireless communication. The encoding/decoding complexity of these codes is comparable to trellis codes employed in practice over Gaussian channels. The codes constructed here provide the best tradeoff between data rate, diversity advantage, and trellis complexity. Simulation results are provided for 4 and 8 PSK signal sets with data rates of 2 and 3 bits/symbol, demonstrating excellent performance that is within 2-3 dB of the outage capacity for these channels using only 64 state encoders     

Performance analysis of space-time transmitter diversity techniques for WCDMA using long range prediction

Transmitter diversity in the downlink of code-division multiple-access (CDMA) systems achieves similar performance gains to the mobile-station receiver diversity without the complexity of a mobile-station receiver antenna array. Pre-RAKE precoding at the transmitter can be employed to achieve the multipath diversity without the need of the RAKE receiver at the mobile station. We examine feasibility of several transmitter diversity techniques and precoding for the third-generation wideband CDMA (WCDMA) systems. In particular, selective transmit diversity, transmit adaptive array and space-time pre-RAKE (STPR) techniques are compared. It is demonstrated that the STPR method is the optimal method to combine antenna diversity and temporal precoding. This method achieves the gain of maximum ratio combining of all space and frequency diversity branches when perfect channel state information is available at the transmitter. We employ the long range fading prediction algorithm to enable transmitter diversity techniques for rapidly time varying multipath fading channels.     

MIMO Precoder Designs for Frequency-Selective Fading Channels Using Spatial and Path Correlation

Multiple-input–multiple-output (MIMO) precoder design for frequency-selective fading channels using partial channel information based on the spatial and path correlation matrices is presented. By representing a frequency-selective fading channel as a multipath model with $L$ effective paths, a general precoding structure is proposed and used to derive optimum precoding designs that maximize Jensen's upper bound on the channel ergodic capacity under the transmitted power constraint for two cases, i.e., uncorrelated and correlated channel paths. Analytical results show that, in the uncorrelated case, the precoder structure consists of a number of parallel precoders for frequency-flat fading channels. The power assignment to each precoder and the power allocation over the eigenmodes of each precoder are calculated based on the power of channel paths and the eigenvalues of the transmit correlation matrix. In the correlated case, the precoder structure is an eigenbeamformer with the beams referred to a function of eigenvectors of the Kronecker product of path and transmit correlation matrices. Furthermore, the power allocated to each eigenmode can be obtained from a statistical water-pouring policy that is specified by the product of eigenvalues of the transmit antenna and path correlation matrices. Simulation results for different scenarios indicate that the proposed precoder can increase the ergodic capacity of MIMO systems in a frequency-selective fading environment with spatial and path correlations, and its offered capacity gain is increased with the level of correlation and numbers of antennas and channel paths.      

A Unified Framework for Layered Transmission Over Fading and Packet Erasure Channels

We consider layered transmission of a successively refinable source over a quasi-static fading channel. We establish a duality relationship between this problem and that of packet transmission over erasure channels and use it to share solution techniques in both domains. For a Gaussian source and the fading channel, a low-complexity, optimal algorithm is proposed, and it is shown that the corresponding dual for packet erasure channels has a linear complexity as opposed to the quadratic complexity of the best known optimal algorithms in the literature. For non-Gaussian sources, the optimal rate allocation problem for fading channels is solved using the dual solution for erasure channels. It is also shown that a single-layer system is optimal for fading channels if the goal is to maximize the rate. Numerical results for multiple antenna Rayleigh fading channels are presented for Gaussian sources and practical image coders. It is shown that a few number of layers significantly improves the performance. Finally, we numerically show that for practical operating conditions, optimizing the asymptotic measure of distortion exponent is not enough when there are more than one transmit or receive antennas.     

Sum capacity of Gaussian vector broadcast channels

This paper characterizes the sum capacity of a class of potentially nondegraded Gaussian vector broadcast channels where a single transmitter with multiple transmit terminals sends independent information to multiple receivers. Coordination is allowed among the transmit terminals, but not among the receive terminals. The sum capacity is shown to be a saddle-point of a Gaussian mutual information game, where a signal player chooses a transmit covariance matrix to maximize the mutual information and a fictitious noise player chooses a noise correlation to minimize the mutual information. The sum capacity is achieved using a precoding strategy for Gaussian channels with additive side information noncausally known at the transmitter. The optimal precoding structure is shown to correspond to a decision-feedback equalizer that decomposes the broadcast channel into a series of single-user channels with interference pre-subtracted at the transmitter.     

Performance of antenna diversity multiuser receivers in CDMA channels with imperfect fading estimation

The performance of antenna diversity coherent and differentially coherent linear multiuser receivers is analyzed in frequency-nonselective Rayleigh fading CDMA channels with memory. The estimates of the complex fading processes are utilized for maximal-ratio combining and carrier recovery of the coherent multiuser receiver. To analyze the impact of channel estimation errors on the receiver performance, error probability is assessed directly in terms of the fading rate and the number of active users, showing the penalty imposed by imperfect channel estimation as well as the fading-induced error probability floor. The impact of fading dynamics on the differentially coherent decorrelating receiver with equal-gain combining is quantified. While performance of multiuser receivers at lower SNR is determined by both the fading dynamics and the number of active CDMA users, performance at higher SNR is given by an error probability floor which is due to fading only and has the same value as in a single-user case. The comparison of the two receiver structures indicates that the coherent decorrelating receiver with diversity reception may be preferable to the differentially coherent one in nonselective fading CDMA channels with memory.     

Optimal designs for space-time linear precoders and decoders

We introduce a new paradigm for the design of transmitter space-time coding that we refer to as linear precoding. It leads to simple closed-form solutions for transmission over frequency-selective multiple-input multiple-output (MIMO) channels, which are scalable with respect to the number of antennas, size of the coding block, and transmit average/peak power. The scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension. The specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses, under average and peak power constraints. The solutions are shown to convert the MIMO channel with memory into a set of parallel flat fading subchannels, regardless of the design criterion, while appropriate power/bits loading on the subchannels is the specific signature of the different designs. The proposed designs are compared in terms of various performance measures such as information rate, BER, and symbol mean square error     

A space-time trellis coding scheme for vector Gaussian broadcast channels

In this letter, a multiuser space-time trellis coding (MU-STTC) scheme is proposed for MIMO vector Gaussian broadcast channels (VGBC). For the system with two transmit antennas and two users with one receive antenna each, the proposed scheme decomposes the system into two subsystems, each of which is equivalent to a system with two transmit and one receive antenna with known interference. A novel precoding scheme is developed to eliminate such interference. The proposed scheme enables to incorporate space time trellis coding and adaptive weighting into the system to provide a significant coding and weighting gain. Simulation results confirm its good performance.     

Low-density parity-check codes for space-time wireless transmission

Irregular low-density parity-check (LDPC) codes have shown exceptionally good performance for single antenna systems over a wide class of channels. In this paper, we investigate their application to multiple antenna systems in flat Rayleigh fading channels. For small transmit arrays, we focus mainly on space-time coding with 2/sup p/-ary LDPC codes, where p equals the number of encoded bits transmitted by the transmit antenna array during each signaling interval. For large transmit arrays, we study a layered space-time architecture using binary LDPC codes as component codes of each layer: We show through simulation that, when applied to multiple antenna systems with high diversity order, LDPC codes of quasi-regular construction are able to achieve higher coding gain and/or diversity gain than previously proposed space-time trellis codes, space-time turbo codes, and convolutional codes in a number of fading conditions. Extending the work of density evolution with Gaussian approximation, we study 2/sup p/-ary LDPC codes on multiple antenna fading channels, and search for the optimum 2/sup p/-ary quasi-regular codes in quasi-static fading. We also show that on fast fading channels, 2/sup p/-ary irregular LDPC codes, though designed for static channels, have superior performance to nonbinary quasiregular codes and binary irregular codes specifically designed for fast fading channels.     

Clustered linear precoding for downlink network MIMO systems with partial CSI

We propose two novel clustered linear precoding schemes applicable to network multi‐input multi‐output systems using only partial channel state information to enhance the sum‐rate of the system. Using a channel model that decomposes a multi‐input multi‐output channel matrix into transmit and receive steering vectors and assuming that only transmit steering vectors are available at the base transmit stations, we, first, propose a regularized channel inversion precoding scheme to enhance the sum‐rate assuming only single‐antenna users are available in the system. Next, because of the limitation of regularized channel inversion to handle users with multiple receive antennas, a novel block diagonalization method is proposed. We construct the precoding matrices that jointly eliminate inter‐cell interference and maximize the sum‐rate for a given input covariance matrix. Assuming total power constraint and per‐base‐station power constraints, optimal power allocation schemes are further developed to optimize the sum‐rate. We analytically show that the sum‐rate increases linearly with the number of users when only single‐antenna users are present in the system. Numerical results show that at low signal‐to‐noise ratios, the block diagonalization precoding outperforms the regularized channel inversion in terms of the bit error rate; while at high signal‐to‐noise ratios, the regularized channel inversion provides a better performance. Copyright © 2016 John Wiley & Sons, Ltd.     

Progressive linear precoder optimization for MIMO packet retransmissions

This paper investigates the optimal linear precoder design for packet retransmissions in multi-input-multi-output (MIMO) systems. To fully utilize the time diversity provided by automatic repeat request (ARQ), we derive a sequence of successive optimal linear ARQ precoders for flat fading MIMO channels, which minimize the mean-square error between the transmitted data and the joint receiver output. The optimization is subject to an overall transmit power constraint. This progressive linear ARQ precoder combines the appropriate power loading and the optimal pairing of channel matrix singular values in the current retransmission with previous transmissions. This optimal pairing is a special feature unique to our sequential ARQ precoding approach. Simulation results demonstrate the effectiveness of this optimized ARQ precoding in reducing symbol MSE and detection bit-error rate.     

Optimized Transmission for Fading Multiple-Access and Broadcast Channels With Multiple Antennas

In mobile wireless networks, dynamic allocation of resources such as transmit powers, bit-rates, and antenna beams based on the channel state information of mobile users is known to be the general strategy to explore the time-varying nature of the mobile environment. This paper looks at the problem of optimal resource allocation in wireless networks from different information-theoretic points of view and under the assumption that the channel state is completely known at the transmitter and the receiver. In particular, the fading multiple-access channel (MAC) and the fading broadcast channel (BC) with additive Gaussian noise and multiple transmit and receive antennas are focused. The fading MAC is considered first and a complete characterization of its capacity region and power region are provided under various power and rate constraints. The derived results can be considered as nontrivial extensions of the work done by Tse and Hanly from the case of single transmit and receive antenna to the more general scenario with multiple transmit and receive antennas. Efficient numerical algorithms are proposed, which demonstrate the usefulness of the convex optimization techniques in characterizing the capacity and power regions. Analogous results are also obtained for the fading BC thanks to the duality theory between the Gaussian MAC and the Gaussian BC.     

Blind multiuser detection for V-BLAST coded multicarrier CDMA system

Focusing on the space-time coded multiuser mobile communication systems in the frequencyselective fading environment, this paper proposes a Vertical Bell labs LAyered Space-Time （V-BLAST） coded Multicarrier Code-Division Multiple-Access （MC-CDMA） scheme and its blind channel identification algorithm. This algorithm employs an ESPRIT-like method and the singular value decomposition, and the channels between every transmit antenna of every user and every receive antenna of the base station are blindly estimated with a closed-form solution. Based on it, an equivalent Minimum Mean-Squared Error （MMSE） time-domain multiuser detector is derived. Moreover, the proposed scheme exploits the precoding in the transmitter in order to eliminate the constraint of more receive antennas than transmit ones, required by most conventional V-BLAST codec schemes. Computer simulation results demonstrate the validity of this proposed scheme.     

Robust Transmit Antenna Selection with Phase Feedback Over Correlated Fading Channels

A new transmit antenna selection (TAS) scheme with phase feedback for multiple-input multiple-output systems is proposed in this paper. This scheme allows two or more transmit antennas to simultaneously use one radio frequency chain. By grouping the transmit antennas according to their similarities in instantaneous channel coefficients into two subsets and treating each subset as a single antenna, both hardware complexity reduction and antenna array gain can be achieved. Compared with the transmit antenna selection combined with space-time block code (TAS/STBC) scheme, the proposed TAS scheme provides excellent robustness, in terms of symbol error rate performance, against spatially correlated fading channels. Moreover, the proposed TAS scheme need not use STBC encoder and decoder which used in the TAS/STBC schemes. Therefore, the proposed TAS scheme is simpler than the TAS/STBC schemes in practical hardware implementation.     

Performance analysis of orthogonal space-time block codes in spatially correlated MIMO Nakagami fading channels

Orthogonal space-time block coding (STBC) is an open-loop transmit diversity scheme that decouples the multiple-input multiple-output (MIMO) channel, thereby reducing the space-time decoding into a scalar detection process. This characteristic of STBC makes it a powerful tool, achieving full diversity over MIMO fading channels, and requiring little computational cost for both the encoding and decoding processes. In this paper, we exploit the single-input single-output equivalency of STBC in order to analyze its performance over nonselective Nakagami fading channels in the presence of spatial fading correlation. More specifically, we derive exact closed-form expressions for the outage probability and ergodic capacity of STBC, when the latter is employed over spatially correlated MIMO Nakagami fading channels. Moreover, we derive the exact symbol error probability of coherent M-PSK and M-QAM, when these modulation schemes are used along with STBC over such fading channels. The derived formulae are then used to assess the robustness of STBC to spatial correlation by considering general MIMO correlation models and analyzing their effects on the outage probability, ergodic capacity, and symbol error probability achieved by STBC.     

Analysis of Transmit Antenna Selection/Maximal-Ratio Combining in Rayleigh Fading Channels

In this paper, we investigate a multiple-input-multiple-output (MIMO) scheme combining transmit antenna selection and receiver maximal-ratio combining (the TAS/MRC scheme). In this scheme, a single transmit antenna, which maximizes the total received signal power at the receiver, is selected for uncoded transmission. The closed-form outage probability of the system with transmit antenna selection is presented. The bit error rate (BER) of the TAS/MRC scheme is derived for binary phase-shift keying (BPSK) in flat Rayleigh fading channels. The BER analysis demonstrates that the TAS/MRC scheme can achieve a full diversity order at high signal-to-noise ratios (SNRs), as if all the transmit antennas were used. The average SNR gain of the TAS/MRC is quantified and compared with those of uncoded receiver MRC and space-time block codes (STBCs). The analytical results are verified by simulation. It is shown that the TAS/MRC scheme outperforms some more complex space-time codes of the same spectral efficiency. The cost of the improved performance is a low-rate feedback channel. We also show that channel estimation errors based on pilot symbols have no impact on the diversity order over quasi-static fading channels.