Block Rayleigh Fading Channels Research Articles

Constellation Design for the Noncoherent MIMO Rayleigh-Fading Channel at General SNR

Constellation design for the noncoherent multiple-input-multiple-output (MIMO) block Rayleigh-fading channel is considered. For general signal-to-noise ratios (SNRs), starting from a given base unitary constellation of finite cardinality, and using the cutoff rate expression as the design criterion, input probabilities and per-antenna amplitudes for the constellation points are obtained via a difference of convex programming formulation. Using the mutual information as a performance metric, it is shown that the optimized constellations significantly outperform the base unitary designs from which they are obtained in the low-medium SNR regime, and indeed they also similarly outperform the mutual information achieved by isotropically distributed unitary inputs for the continuous input channel [i.e., the so-called unitary space-time capacity (USTC)]. At sufficiently high SNRs, the resulting mutual information coincides with that of the base unitary designs. Thus the optimum constellation design technique works over the entire range of SNRs. The bit energy/spectral efficiency tradeoff of the optimized constellations are also obtained, and these provide valuable insights on modulation and coding, which are especially useful for wideband channels where the SNR per degree of freedom is low

Analysis of Differential Orthogonal Space–Time Block Codes Over Semi-Identical MIMO Fading Channels

We study the performance of differential orthogonal space-time block codes (OSTBC) over independent and semi-identically distributed block Rayleigh fading channels. In this semiidentical fading model, the channel gains from different transmit antennas to a common receive antenna are identically distributed, but the gains associated with different receive antennas are nonidentically distributed. Arbitrary fluctuation rates of the fading processes from one transmission block to another are considered. We first derive the optimal symbol-by-symbol differential detector, and show that the conventional differential detector is suboptimal. We then derive expressions of exact bit-error probabilities (BEPs) for both the optimal and suboptimal detectors. The results are applicable for any number of receive antennas, and any number of transmit antennas for which OSTBCs exist. For two transmit antennas, explicit and closed-form BEP expressions are obtained. For an arbitrary number of transmit antennas, a Chernoff bound on the BEP for the optimal detector is also derived. Our results show that the semi-identical channel statistics degrade the error performance of differential OSTBC, compared with the identical case. Also, the proposed optimal detector substantially outperforms the conventional detector when the channel fluctuates rapidly. But in near-static fading channels, the two detectors have similar performances

A Comparison of Time-Sharing, DPC, and Beamforming for MIMO Broadcast Channels With Many Users

In this letter, we derive the scaling laws of the sum rate for fading multiple-input multiple-output Gaussian broadcast channels using time sharing to the strongest user, dirty-paper coding (DPC), and beamforming, when the number of users (receivers) n is large. Throughout the letter, we assume a fix average transmit power and consider a block-fading Rayleigh channel. First, we show that for a system with M transmit antennas and users equipped with N antennas, the sum rate scales like MloglognN for DPC, and beamforming when M is fixed and for any N (either growing to infinity or not). On the other hand, when both M and N are fixed, the sum rate of time sharing to the strongest user scales like min(M,N)loglogn. Therefore, the asymptotic gain of DPC over time sharing for the sum rate is (M/min(M,N)) when M and N are fixed. It is also shown that if M grows as logn, the sum rate of DPC and beamforming will grow linearly in M, but with different constant multiplicative factors. In this region, the sum-rate capacity of time -sharing scales like Nloglogn

An improved block equalization scheme for uncertain channel estimation

We consider the design of a block equalizer for an intersymbol interference channel, given that the channel impulse response is not perfectly known at the receiver. In contrast to other schemes, our receiver is designed for imperfect channel state information and incorporates the statistics of the channel estimation error. In particular, we suggest an error model for data transmission that takes the influence from the data symbols on the estimation noise into account. We derive the optimum detection rule for the considered error model according to the maximum likelihood criterion and verify that the covariance matrix of the estimation noise depends on the actual transmitted data symbols. Motivated by this result, we propose a realizable receiver structure adopting the turbo principle that exploits the data-dependency of the covariance matrix of the estimation noise. The proposed scheme outperforms conventional receivers that neglect the exact statistics of the estimation noise. The core of our receiver is a soft-input soft-output block equalizer based on constrained minimum variance filter design. We assess the performance of the proposed turbo equalization scheme for block Rayleigh fading channels, applying both one-shot training-based channel estimation and iterative data-aided channel estimation

EM‐based iterative receiver for coded MIMO systems in unknown spatially correlated noise

AbstractWe present iterative channel estimation and decoding schemes for multi‐input multi‐output (MIMO) Rayleigh block fading channels in spatially correlated noise. An expectation‐maximization (EM) algorithm is utilized to find the maximum likelihood (ML) estimates of the channel and spatial noise covariance matrices, and to compute soft information of coded symbols which is sent to an error‐control decoder. The extrinsic information produced by the decoder is then used to refine channel estimation. Several iterations are performed between the above channel estimation and decoding steps. We derive modified Cramer–Rao Bound (MCRB) for the unknown channel and noise parameters, and show that the proposed EM‐based channel estimation scheme achieves the MCRB at medium and high SNRs. For a bit error rate of 10−6 and long frame length, there is negligible performance difference between the proposed scheme and the ideal coherent detector that utilizes the true channel and noise covariance matrices. Copyright © 2006 John Wiley & Sons, Ltd.

Signal Mappings of 8-Ary Constellations for BICM-ID Systems over a Rayleigh Fading Channel

It is known that in a bit-interleaved coded-modulation with iterative decoding (BICM-ID), signal constellation and mapping strongly influence the system's error performance. This letter presents good mappings of various 8-ary constellations for BICM-ID systems operating over a frequency non-selective block Rayleigh fading channel. Simulation results for the error performance of different constellations/mappings are also provided and discussed.

Estimating statistical properties of MIMO fading channels

We propose maximum likelihood (ML) and restricted maximum likelihood (REML) methods for estimating the mean and covariance parameters of multi-input multi-output (MIMO) Ricean and Rayleigh block-fading channels using measurements from multiple coherent intervals containing both amplitudes and phases of the received signal. Correlated and independent fading scenarios with structured and unstructured line-of-sight (LOS) array response models are considered. Computationally efficient ML and approximate ML (AML) estimators are proposed for unitary space-time modulation schemes and orthogonal designs in correlated fading. We also derive Crame/spl acute/r-Rao bounds (CRBs) for the unknown parameters, discuss initialization of the proposed algorithms, and evaluate their performance via numerical simulations under the block- and continuous-fading scenarios.

Comparison of vector detection algorithms for MIMO-OFDM

The aim of this paper is to compare detection algorithms for MIMO-OFDM transmissions by simulation. For a coded transmission, it turns out that the list sphere detector, which has been considered a favorite for many applications, is far more complex than other methods yielding the same BER performance. Moreover, iterative equalization techniques based on soft interference cancellation connected with decoding via the well-known turbo principle can approach the matched filter bound for the 4 × 4 MIMO channels used in the simulation. Specifically, a block Rayleigh fading channel and a time-invariant frequency-selective channel with and without spreading in frequency and space are considered.

Improved 16-QAM constellation labeling for BI-STCM-ID with the Alamouti scheme

We design constellation labeling maps for bit-interleaved space-time coded modulation with iterative decoding (BI-STCM-ID) over Rayleigh block-fading channels using the Alamouti scheme and N/sub r/ receive antennas. To achieve the largest asymptotic coding gain from the constellation labeling, we propose a new design criterion that maximizes the (-2N/sub r/)-th power mean of the squared Euclidean distances associated with all error-free feedback events in the constellation. Based on this power mean criterion, we show that the labeling optimization problem falls into the category of quadratic assignment problems. We propose two novel 16-QAM labeling maps that are particularly designed for N/sub r/=1 and N/sub r/=2, respectively. Numerical results show that both labeling maps achieve about 1 dB coding gain over the conventional 16-QAM modified set partitioning labeling.

Capacity of Memoryless Channels and Block-Fading Channels With Designable Cardinality-Constrained Channel State Feedback

A coding theorem is proved for memoryless channels when the channel state feedback of finite cardinality can be designed. Channel state information is estimated at the receiver and a function of the estimated channel state is causally fed back to the transmitter. The feedback link is assumed to be noiseless with a finite feedback alphabet, or equivalently, finite feedback rate. It is shown that the capacity can be achieved with a memoryless deterministic feedback and with a memoryless device which select transmitted symbols from a codeword of expanded alphabet according to current feedback. To characterize the capacity, we investigate the optimization of transmission and channel state feedback strategies. The optimization is performed for both channel capacity and error exponents. We show that the design of the optimal feedback scheme is identical to the design of scalar quantizer with modified distortion measures. We illustrate the optimization using Rayleigh block-fading channels. It is shown that the optimal transmission strategy has a general form of temporal water-filling in important cases. Furthermore, while feedback enhances the forward channel capacity more effectively in low-signal-to noise ratio (SNR) region compared with that of high-SNR region, the enhancement in error exponent is significant in both high- and low-SNR regions. This indicates that significant gain due to finite-rate channel state feedback is expected in practical systems in both SNR regions.

Capacity Maximizing MMSE-Optimal Pilots for Wireless OFDM Over Frequency-Selective Block Rayleigh-Fading Channels

The location, number, and power of pilot symbols embedded in multicarrier block transmissions over rapidly fading channels, are important design parameters affecting not only channel estimation performance, but also channel capacity. Considering orthogonal frequency-division multiplexing (OFDM) systems with decoupled information-bearing symbols from pilot symbols transmitted over wireless frequency-selective Rayleigh-fading channels, we show that equispaced and equipowered pilot symbols are optimal in terms of minimizing the mean-square channel estimation error. We also design the number of pilots, and the power distributed between information bearing and pilot symbols, using as criterion a lower bound on the average capacity. Numerical results corroborate our theoretical findings.

On performance limits of space-time codes: a sphere-packing bound approach

A sphere-packing bound (SPB) on average word-error probability (WEP) is derived to determine the performance limits of space-time codes on Rayleigh block-fading channels under delay and maximum energy constraints. Two other explicit bounds, a looser bound and a tight approximate bound, are also derived to provide more intuition on how the system parameters affect the performance limits. Moreover, it is shown that as the block length grows to infinity, the SPB converges to the outage probability, and the asymptotic behavior of performance limits is determined by the outage probability.

BER analysis of MPSK space-time block codes with differential detection

Closed-form expressions of the bit error rate (BER) are derived for space-time block codes based on Alamouti's (1998) scheme and utilizing M-ary phase shift keying modulation with noncoherent differential encoding/decoding. The analysis is carried out for the flat block-fading Rayleigh channel, and the BER expression is an approximation for high signal to noise ratio. Theoretical results are validated by simulations for BPSK and QPSK modulations.

Serially concatenated space-time codes with iterative decoding and performance limits of block-fading channels

This work considers space-time channel coding for systems with multiple-transmit and a single-receive antenna, over space uncorrelated block-fading (quasi-static) channels. Analysis of the outage probability over such channels reveals the existence of a threshold phenomenon. The outage probability can be made arbitrary small by increasing the number of transmit antennas, only if the E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> /N/sub 0/ is above a threshold which depends on the coding rate. Furthermore, it is shown that when the number of transmit antennas is increased, the /spl epsi/-capacity of a block-fading Rayleigh channel tends to the Shannon capacity of an additive white Gaussian noise channel. This paper also presents space-time codes constructed as a serial concatenation of component convolutional codes separated by an interleaver. These schemes provide full transmit diversity and are suitable for iterative decoding. The rate of these schemes is less than 1 bit/s/Hz, but can be made arbitrary close to 1 bit/s/Hz by the use of Wyner-Ash codes as outer components. Comparison of these schemes with structures from literature shows that performance gains can be obtained at the expense of a small decrease in rate. Computer simulation results over block-fading Rayleigh channels show that the frame-error rate of several of these schemes is within 2-3 dB from the theoretical outage probability.

Non-full rank space-time trellis codes for serially concatenated system

The feasibility of the non-full rank space-time trellis codes (NFR-STTCs) for the serially concatenated system is described carefully in this letter and a QPSK-based NFR-STTC suitable for the system is proposed. As the simulation results show, over the flat block Rayleigh fading channels, a concatenated system with the proposed NFR-STTC inner code can achieve full diversity, and improve the coding gains compared with other concatenated systems adopting full-rank space-time trellis codes (FR-STTCs) of the same complexity. The introduction of the NFR-STTC to serial concatenation space-time (SCST) system provides a new research community of SCST.

Multiuser capacity in block fading with no channel state information

Consider M independent users, each user having his own transmit antenna, that transmit simultaneously to a receiver equipped with N antennas through a Rayleigh block-fading channel having a coherence interval of T symbols, with no channel state information (CSI) available to either the transmitters or to the receiver. The total transmitted power is independent of the number of users. For a given coherence time T, we wish to identify the best multiaccess strategy that maximizes the total throughput. If perfect CSI were available to the receiver, it is known that the total capacity would increase monotonically with the number of users. If the CSI is available to both the receiver and to all transmitters, the throughput maximizing strategy implies for N=1 that only the single user who enjoys the best channel condition transmits. In the absence of CSI one is forced to a radically different conclusion. In particular, we show that if the propagation coefficients take on new independent values for every symbol (e.g., T=1) then the total capacity for any M > 1 users is equal to the capacity for M=1 user, in which case time division multiple access (TDMA) is an optimal scheme for handling multiple users. This result follows directly from a recent treatment of the single-user multiple antenna block-fading channel. Again, motivated by the single-user results, one is lead to the following conjecture for the multiple-user case: for any T > 1, the maximum total capacity can be achieved by no more than M = T users. The conjecture is supported by establishing the asymptotic result that, for a fixed N and a constant M/T for large T, the total capacity is maximized when M/T/spl rarr/0, which yields a total capacity per symbol of N log(1 + /spl rho/), where /spl rho/ is the expected signal-to-noise ratio (SNR) at the receiver. We further support the conjecture by examining the asymptotic behavior with large to for fixed M, T, and N /spl les/ T.

Exact pairwise error probability of space-time codes

We describe a simple technique for the numerical calculation, within any desired degree of accuracy, of the pairwise error probability (PEP) of space-time codes over fading channels. This method applies also to the calculation of E[Q(/spl radic//spl xi/)] for any nonnegative random variable /spl xi/ whose moment-generating function /spl Phi//sub /spl xi//(s)=E[exp(-s/spl xi/)] is known. Its application to the multiple antenna independent Rayleigh-fading channel and to the Rayleigh block fading channel is discussed, and illustrated by two simple examples.

Advanced ICA-based receivers for block fading DS-CDMA channels

In this paper we propose two types of receivers, which perform blind interference suppression. The receivers are suitable for the third generation mobile communications systems, which are based on direct-sequence code division multiple access (DS-CDMA). We especially consider the statistical technique called independent component analysis (ICA) as a tuning element attached to an existing single-user or blind multiuser detector. By doing this, the statistical independence of the users’ signals can be exploited. In addition, it makes it possible to alleviate the performance drop due to the erroneous parameters estimation in the receiver. From the ICA point of view, the receiver observes a mixture of users’ original signals, determined by the user-specific spreading codes, the data symbols, and the state of the propagation channel. Since all of them might be complex valued by nature, complex ICA is needed. In the paper, a proof of global convergence is given for the kurtosis-based FastICA algorithm in the case of complex valued source signals with circular distribution, and considered as the ICA component of the advanced receivers. Two types of receivers, RAKE-ICA and MMSE-ICA, are proposed and studied in a Rayleigh block fading channel. Extensive numerical simulations indicate that the performance of RAKE and subspace MMSE detector, respectively, can be greatly improved. Quite significantly, their performance is close to the theoretical bound of an equal length MMSE detector.

Performance of parallel concatenated space-time codes

We study a channel turbo-coding scheme that consists of parallel concatenated systematic space-time codes and is referred to as turbo space-time coded modulation (turbo-STCM). The scheme features full rate and simulation results shows that it also provides full diversity. Performance with recursive versus nonrecursive space-time constituent codes is investigated. The advantage of recursive component codes is demonstrated by simulations for a four state 4-PSK turbo-STCM scheme operating over a Rayleigh block-fading channel. It is also shown that the turbo-STCM performs better than conventional space-time codes of similar complexity.

Turbo-coded modulation for systems with transmit and receive antenna diversity over block fading channels: system model, decoding approaches, and practical considerations

We study the use of turbo-coded modulation for wireless communication systems with multiple transmit and receive antennas over block Rayleigh fading channels. We describe an effective way of applying turbo-coded modulation as an alternative to the current space-time codes with appropriate interleaving. We study the performance with the standard iterative turbo decoding algorithm, as well as the iterative demodulation-decoding algorithm. In addition to the introduction of the turbo-coded modulation scheme, we consider a variety of practical issues including the case of large number of antennas, the effects of estimated channel state information, and correlation among subchannels between different transmit-receive antenna pairs. We present examples to illustrate the performance of the turbo-coded modulation scheme and observe significant performance gains over the appropriately interleaved space-time trellis codes.