Quasi-static Fading Channels Research Articles

Performance analysis on LDPC-Coded systems over quasi-static (MIMO) fading channels

In this paper, we derive closed form upper bounds on the error probability of low-density parity-check (LDPC) coded modulation schemes operating on quasi-static fading channels. The bounds are obtained from the so-called Fano-Gallager's tight bounding techniques, and can be readily calculated when the distance spectrum of the code is available. In deriving the bounds for multiple-input multiple-output (MIMO) systems, we assume the LDPC code is concatenated with the orthogonal space-time block code as an inner code. We obtain an equivalent single-input single-output (SISO) channel model for this concatenated coded-modulation system. The upper bounds derived here indicate good matches with simulation results of a complete transceiver system over Rayleigh and Rician MIMO fading channels in which the iterative detection and decoding algorithm is employed at the receiver.

Vector similarity-based detection scheme for multi-antenna FH/MFSK systems in the presence of follower jamming

Follower partial band jamming has been recognised as an efficient strategy to degrade the performance of frequency hopping (FH) systems. To alleviate this detrimental effect, a novel detection scheme for slow FH/M-ary frequency shift keying systems, which use two receive antennas in a quasi-static flat fading channel, is proposed. Specifically, using the principle of vector similarity, an area-based vector similarity metric is formulated to give an estimate of the unknown spatial correlation of the received jamming components at the two receive antennas. The jamming signal can then be removed in the symbol detection process. The improved performance of the new scheme is verified by using an analysis under a jamming dominant environment as well as simulated bit error rate results.

Tree-Based Reparameterization with Distributional Approximations for Reduced-Complexity MIMO Symbol Detection

Detection of spatially multiplexed data transmissions subject to frequency flat fading is considered. Optimal decoders require knowledge of the marginal posterior distributions of the transmitted symbols, but their exact computation is not feasible for practical systems. Hence sub-optimal approaches are generally sought. By recasting this problem into the graphical model framework, we investigate here a recently proposed suboptimal approach which relies on a tree-based reparameterization principle. For quasi-static fading channels, the resulting decoder complexity has an order which is at most quadratic in the number of transmit antennas. However, in its standard form, the algorithm often fails to converge, severely restricting its practical usability. We here develop a novel methodology to ensure systematic convergence of the algorithm in this communication scenario at the expense of the introduction of a minimal bias on the computation of the symbol marginal posterior probabilities. This bias is quantified theoretically and its innocuity for the problem at hand is ultimately demonstrated through numerical simulations. For a system using 16-QAM modulation with four transmit and receive antennas, the proposed detector achieves a bit-error rate of 10-4 requiring only 3 dB greater SNR than the optimal method.

Full-rate full-diversity space–time block codes for any odd number of transmit antennas

The authors propose a new class of space-time block codes (STBCs) achieving full-rate and full spatial diversity for general quadrature amplitude modulation (QAM) when using any odd number of transmit antennas under quasi-static Rayleigh fading channels. These codes are the extended works of the conventional Alamouti-ST constellation-rotating (CR) codes which are designed by serially concatenating CR precoders with the Alamouti scheme for an even number of transmit antennas. From the computer simulation results, it is observed that the best code in this class outperforms the existing ST-CR code and also exhibits error performance within only about 1-dB of the maximal ratio combining receiver. The codes possessing quasi-orthogonal (QO) characteristic are also included in this class, allowing simple maximum likelihood (ML) decoding with almost the same error performance as the best code in this class and the conventional QO-STBCs with full diveristy. These codes have identical or much lowered ML decoding complexity compared with the conventional QO-STBCs.

Serially concatenated space time convolutional codes and continuous phase modulation

This paper addresses space time convolutional code design using continuous phase modulation (CPM). The possibility of constructing full diversity space time codes is investigated. A linear modulation approximation to CPM is done. Using the Gram-Schmidt orthogonalization transform the CPM signal is generated as a vector with finite energy in a different Euclidean space. A serially concatenated CPM construction is considered in searching channel codes which are able to exploit maximum diversity. Design criteria based on the encoding scheme are derived for an arbitrary number of transmit antennas. The investigations are done for a quasi-static Rayleigh fading channel.

Performance of Space–Time Codes: Gallager Bounds and Weight Enumeration

Since the standard union bound for space-time codes may diverge in quasi-static fading channels, the limit-before-average (LBA) technique has been exploited to derive tight performance bounds. However, it suffers from the computational burden arising from a multidimensional integral. In this paper, efficient bounding techniques for space-time codes are developed in the framework of Gallager bounds. Two closed-form upper bounds, the ellipsoidal bound and the spherical bound, are proposed that come close to simulation results within a few tenths of a decibel. In addition, two novel methods of weight enumeration operating on a further reduced state diagram are presented, which, in conjunction with the bounding techniques, give a thorough treatment of performance bounds for space-time codes.

Distributed Generalized Low-Density Codes for Multiple Relay Cooperative Communications

As a class of pseudorandom error correcting codes, generalized low-density (GLD) codes exhibit excellent performance over both additive white Gaussian noise (AWGN) and Rayleigh fading channels. In this paper, distributed GLD codes are proposed for multiple relay cooperative communications. Specifically, using the partial error detecting and error correcting capabilities of the GLD code, each relay node decodes and forwards some of the constituent codes of the GLD code to cooperatively form a distributed GLD code, which can work effectively and keep a fixed overall code rate when the number of relay nodes varies. Also, at relay nodes, a progressive processing procedure is proposed to reduce the complexity and adapt to the source-relay channel variations. At the destination, the soft information from different paths is combined for the GLD decoder thus diversity gain and coding gain are achieved simultaneously. Simulation results verify that distributed GLD codes with various number of relay nodes can obtain significant performance gains in quasistatic fading channels compared with the strategy without relays and the performance is further improved when more relays are employed.

Wireless Information-Theoretic Security

This paper considers the transmission of confidential data over wireless channels. Based on an information-theoretic formulation of the problem, in which two legitimates partners communicate over a quasi-static fading channel and an eavesdropper observes their transmissions through a second independent quasi-static fading channel, the important role of fading is characterized in terms of average secure communication rates and outage probability. Based on the insights from this analysis, a practical secure communication protocol is developed, which uses a four-step procedure to ensure wireless information-theoretic security: (i) common randomness via opportunistic transmission, (ii) message reconciliation, (iii) common key generation via privacy amplification, and (iv) message protection with a secret key. A reconciliation procedure based on multilevel coding and optimized low-density parity-check (LDPC) codes is introduced, which allows to achieve communication rates close to the fundamental security limits in several relevant instances. Finally, a set of metrics for assessing average secure key generation rates is established, and it is shown that the protocol is effective in secure key renewal-even in the presence of imperfect channel state information.

Performance of Transmit and Receive Antenna Selection in the Presence of Channel Estimation Errors

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.

Information outage probability and diversity order of symmetric coordinate interleaved orthogonal designs

Space-time block codes (STBCs) from coordinate interleaved orthogonal designs (CIODs) have attracted considerable attention lately due to their full-diversity and single-symbol decodability for multiple antenna systems. In this letter, we analyze the information outage probability of STBCs from symmetric structured CIODs in quasi-static frequency-nonselective Rayleigh fading channels. By using the probability density function (PDF) and the cumulative distribution function (CDF) of the product of two i.i.d. chi-square random variables and then exploiting a moment-matching approximation technique, we derive an accurate closed-form approximation for the information outage probability of symmetric CIODs and a corresponding asymptotic diversity order, the results of which can be used to theoretically predict the performance of symmetric CIODs with various antenna configurations in non-ergodic Rayleigh fading channels. Some simulations are performed to verify the accuracy of the derived formulas and illustrate the theoretical results.

Space-Time Continuous Phase Modulation for Non-Coherent Detection

The combination of space-time (ST) coding and continuous-phase modulation (CPM) is attractive for power- efficient transmission over fading channels. In this paper, we propose a diagonal block-based ST-CPM (DBST-CPM) scheme, which in addition to its high power efficiency facilitates noncoherent detection at the receiver. DBST-CPM can be regarded as a non-trivial extension of well-known differential ST modulation (DSTM) with diagonal signal matrices for linear modulation formats. For optimization of the code parameters of DBST-CPM we derive an upper bound on the frame-error rate of DBST-CPM in the quasi-static fading channel (QSFC) and we present an efficient optimization algorithm. Additionally, we derive decision rules for low-complexity non-coherent detection of DBST-CPM in various fading environments. Numerical and simulation results show that (a) the derived upper bound accurately predicts the performance of DBST-CPM in the QSFC, (b) the proposed code optimization yields highly power-efficient designs, and (c) the non-coherent detectors approach the performances of their coherent counterparts for various fading channel models.

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.

Performance analysis of turbo codes in quasi-static fading channels

The performance of turbo codes in quasi- static fading channels both with and without antenna diversity is investigated. In particular, simple analytic techniques that relate the frame error rate of a turbo code to both its average distance spectrum as well as the iterative decoder convergence characteristics are developed. Both by analysis and simulation, the impact of the constituent recursive systematic convolutional ( RSC) codes, the interleaver size and the number of decoding iterations on the performance of turbo codes are also investigated. In particular, it is shown that in systems with limited antenna diversity different constituent RSC codes or interleaver sizes do not affect the performance of turbo codes. In contrast, in systems with significant antenna diversity, particular constituent RSC codes and interleaver sizes have the potential to significantly enhance the performance of turbo codes. These results are attributed to the fact that in single transmit - single receive antenna systems, the performance primarily depends on the decoder convergence characteristics for E-b/N-o values of practical interest. However, in multiple transmit - multiple receive antenna systems, the performance depends on the code characteristics.

A Quasi-Random Approach to Space–Time Codes

This paper presents a quasi-random approach to space-time (ST) codes. The basic principle is to transmit randomly interleaved versions of forward error correction (FEC)-coded sequences simultaneously from all antennas in a multilayer structure. This is conceptually simple, yet still very effective. It is also flexible regarding the transmission rate, antenna numbers, and channel conditions (e.g., with intersymbol interference). It provides a unified solution to various applications where the traditional ST codes may encounter difficulties. We outline turbo-type iterative joint detection and equalization algorithms with complexity (per FEC-coded bit) growing linearly with the transmit antenna number and independently of the layer number. We develop a signal-to-noise-ratio (SNR) evolution technique and a bounding technique to assess the performance of the proposed code in fixed and quasi-static fading channels, respectively. These performance assessment techniques are very simple and reasonably accurate. Using these techniques as a searching tool, efficient power allocation strategies are examined, which can greatly enhance the system performance. Simulation results show that the proposed code can achieve near-capacity performance with both low and high rates at low decoding complexity.

Combining Beamforming and Space-Time Coding Using Quantized Feedback

We combine space-time coding and transmit beamforming over multiple-antenna quasi-static fading channels using limited-rate channel state information at the transmitter (CSIT). The combining is performed using a class of constellation sets inspired from orthogonal designs and directional beamforming or in general, unitary preceding with quantized feedback. This constellation class is called partly orthogonal designs (PODs). The conventional way of combining coding and quantized feedback beamforming is through precoded space-time block codes (PSTBCs) that provide full-diversity order with all system configurations in terms of the number of feedback regions and the number of transmit antennas. PODs maintain the same advantage. However, they require less decoding and quantization complexity compared to PSTBCs. We develop POD structures, analyze their performance, and optimize them based on pairwise error probability analysis. PODs create a larger combining space compared to PSTBCs. We can show that with certain system configurations, PODs outperform PSTBCs. Using PODs, we also propose a combined coding, beamforming, and spatial multiplexing scheme over multiple-antenna multi-user channels that enables a low-complexity joint interference cancellation scheme.

Fast simulation of space-time block codes concatenated with convolutional codes over quasi-static Rayleigh fading channels

The use of importance sampling for simulating concatenated space-time block codes with convolutional codes over quasi-static Rayleigh fading channels is illustrated. In particular, a method is provided to bias the probability density function of Rayleigh and additive white Gaussian noise processes using the variance scaling and mean translation methods, respectively, in order to maximise the computational efficiency gain. It is demonstrated that the proposed method requires much smaller sample sizes to achieve the same accuracy than required by a conventional Monte Carlo estimator.

Multirate Layered Space-Time Coding and Successive Interference Cancellation Receivers in Quasi-Static Fading Channels

We investigate the performance of multirate layered space-time coded MIMO systems with successive decoding and interference cancellation (SDIC) receivers in quasi-static Rayleigh fading channels. The proposed framework can be viewed as a class of diagonal layered space-time coded system with each of the layers is encoded independently with different rates subject to equal per-layer outage probabilities. We derive the probability density functions of the per-layer mutual informations, which can be used to estimate the per-layer rates. Using these densities we show that the proposed transceiver increases the outage capacity. We also present simulation results illustrating the outage capacity performance for a variety of transmit and receive antenna combinations and the associated near optimal per-layer rates of input signals. In particular we show that for sufficiently large numbers of transmit and receive antennas, the system can achieve near capacity in quasi-static fading environments. Based on these results, multirate codes are designed using punctured turbo codes and simulation results show significant gains in packet error-rate (PER) performances compared to that of V-BLAST architectures with lower receiver complexities.

Space–frequency coded cooperation in OFDM multiple-access wireless networks

A cooperative space–frequency (SF) coded orthogonal frequency division multiplexing system is considered and its performance over quasi-static frequency-selective Rayleigh fading channels is evaluated. An expression for exact outage error probability is derived and its tight closed-form lower bound is presented. The tightness of the lower bound is demonstrated through Monte Carlo simulation. Asymptotic analysis indicates that the proposed protocol achieves full spatial and frequency diversities available in the cooperative communication system. The theoretical analysis of the proposed SF coded cooperation protocol is further confirmed by computer simulation using a previously introduced SF block code that is capable of achieving full spatial and frequency diversities.

Rate and Power Allocation for Layered Transmission With Superposition Coding

We consider layered transmission of a Gaussian source over a quasi-static fading channel. A broadcast strategy is used in which multiple layers of source data are superimposed, and each layer is allocated a different power and transmission rate. For a multiple-antenna system where either the transmitter or the receiver has a single antenna, we propose a low-complexity algorithm for minimizing the expected end-to-end distortion of the received signal. Numerical results for a Rayleigh fading channel are presented, and the performance gain over a time-sharing strategy is quantified. It is numerically shown that for a wide range of operating conditions, equal rate allocation is as good as unequal rate allocation.

Serially Concatenated Space-Time Coded Continuous Phase Modulated Signals

We investigate the detection of space time codes (STC) modulated using continuous phase modulation (CPM), in quasi-static fading channels. A symbol-by-symbol iterative detector with an optimum front-end is derived, and its reduced-complexity implementation is considered. Also, we have introduced several full-rank STC-CPM systems, constructed by combining full-diversity STCs with simple, widely-used CPM schemes, and introducing a small frequency offset. According to the simulation results, the bit error rate (BER) performance of the detector for quasi-static fading is around 1 dB from the case without fading. Furthermore, a comparison of the performance of the proposed detector with results from previous work on STC-CPM showed an improvement in the range of 2-3 dB. Moreover, the detector is robust to the errors in estimating the channel state information (CSI), which is a desirable feature for practical implementation.