Block Rayleigh Fading Channels Research Articles

Low-Complexity Rate Selection of HARQ With Chase Combining in Rayleigh Block-Fading Channels

We consider hybrid automatic repeat request with Chase combining (HARQ-CC) in a Rayleigh block-fading channel, where rate adaptation is based on long-term channel statistics instead of instantaneous channel information because the latter may be outdated. In the HARQ-CC with long-term rate adaptation, optimal selection of the transmission rate for each HARQ round requires a two-step numerical search procedure with heavy computational burden. In this paper, we propose two suboptimal rate-selection algorithms that substantially reduce the computational burden: In the first scheme, the solution of the second-step numerical search is approximated by using a closed-form Lambert W function, and in the second scheme, additionally, the solution of the first-step numerical search is approximated by a closed-form lower bound. Analytical and numerical results are presented to show that the proposed algorithms yield the performance of the long-term average transmission rate tightly approaching that of the optimal numerical search algorithm.

Physical layer network coding with channel and delay estimation

Decode-and-forward physical layer network coding (PLNC) is one of the promising high-performance techniques for wireless relay networks. This study presents a channel and delay estimation algorithm along with a detection scheme for time-domain two-way relay network in Rayleigh block fading channels. Preambles are attached for frame-based synchronisation and channel estimation. Moreover, to achieve low-complexity estimation, the preambles are designed in Alamouti code structure. The Cramer-Rao bound (CRB) of the channel estimation is given, and simulations show that the mean-square error of channel estimation of the proposed scheme could reach the CRB. Compared with the traditional approach, the newly proposed combined scheme can achieve almost the same performance, but with significant improvement in computational complexity. At last, bit-error-rate performances analysis is given. Simulation validates the authors' analysis, and shows the upper bound and lower bound are tight.

Joint Network-Channel Coding with Rateless Code in Two-Way Relay Systems

In this paper, we propose a three-stage rateless coded protocol for a half-duplex time-division two-way relay system, where two terminals send messages to each other through a relay between them. In the protocol, each terminal takes one of the first two stages respectively to encode its message using rateless code and broadcast the result until the relay acknowledges successful decoding. During the third stage, the relay combines and re-encodes both messages with a joint network-channel coding scheme based on rateless coding which provides incremental redundancy. Together with the packets received directly in previous stages, each terminal then retrieves the desired message using an iterative decoder. The degree profiles of the specific rateless codes, i.e., Raptor codes, implemented at both terminals and the relay, are jointly optimized for both the AWGN channel and the Rayleigh block fading channel through solving a set of linear programming problems. Simulation results show that, the system throughput as well as the error rate achieved by the optimized degree profiles always outperforms those achieved by the conventional degree profile optimized for Binary Erasure Channel (BEC) and the previous network coding scheme with rateless codes.

LDPC-Coded Cooperation with Receive Multi-Antenna and Unknown CSI in the Destination

This paper studies a coded cooperation scheme with receive multi-antenna in the destination. A kind of simple-encoding irregular systematic low-density-parity-check (LDPC) codes is applied to the scheme. For Rayleigh block fading channels, in the unknown channel state information scenario, space-based adaptive least-mean square (LMS) transversal filters are adopted in the destination to realize receive diversity gain. The filtered signals from the source and relay are decoded by a joint "Min-Sum" iterative decoding algorithm. This algorithm agrees with the bilayer Tanner graph that can be used to fully characterize two distinct irregular systematic LDPC codes employed by the source and relay. Simulation results verify the effectiveness of the space-based adaptive LMS transversal filters in the coded cooperation scheme. Meanwhile, theoretical analysis and numerical simulation show that the proposed coded cooperation scheme can well combine cooperation diversity, multi-receive diversity and channel coding gains, and clearly outperforms the coded non-cooperation one under the same conditions.

Noncoherent Amplitude/Phase Modulated Transmission Schemes for Rayleigh Block Fading Channels

In this paper, we investigate noncoherent transmission schemes using amplitude/phase modulation. For uncoded transmission schemes, we derive the pairwise error probability (PEP) and its high-SNR approximation for signal vectors with unequal power values using a noncoherent maximum-likelihood detector under Rayleigh block fading channels. For coded transmission schemes, we consider differential amplitude/phase modulated signals and introduce a codeword-interleaving strategy to improve the error performance. The design criteria for the signal labelling and bit interleaving are also derived via the high-SNR approximation of the PEP. At the receiver, we devise an iterative channel amplitude estimator to enhance the detection reliability. With the help of a specially-designed iterative receiving algorithm, the designed noncoherent coded scheme can provide a significant improvement, either in the error-floor or the waterfall region.

Performance analysis for buffer‐aided communication over block Rayleigh fading channels: queue length distribution, overflow probability, and ε‐overflow rate

ABSTRACTIn this paper, we consider information transmission over a block Rayleigh fading channel, where a finite size buffer is employed to match the source traffic with the channel service capability. Given the buffer size, the transmission capability of a block fading Rayleigh channel is characterized from two aspects: (i) the buffer behavior when the input traffic rate is constant; and (ii) the traffic rate that can be supported by the channel for a given overflow probability constraint. For the first problem, the stationary distribution of the queue length in the buffer is derived by discretizing the queue length using a uniform quantization strategy. It is also shown that the overflow probability of the finite size buffer decreases exponentially with buffer size. An explicit upper bound on the overflow probability is also given. For the second one, a new concept of ε‐overflow rate is proposed to measure the transmission capability of a block fading channel under overflow probability constraints. It will be shown that the ε‐overflow rate is larger than the ε‐outage capacity under the same outage constraint and will meet the great gap between outage capacity and ergodic capacity as the overflow probability constraint varies. Copyright © 2012 John Wiley & Sons, Ltd.

Exact outage probability of cognitive two-way relaying scheme with opportunistic relay selection under interference constraint

In this study, the authors analyse the outage performance of a cognitive two-way relaying system under an interference constraint. In the proposed protocol, the best relay which is chosen by an opportunistic relay selection strategy, combines the received packets using XOR operation and then forwards the combined packet to two secondary sources. The authors derive an exact closed-form expression of outage probability over flat and block Rayleigh fading channels. Various Monte-Carlo simulations are presented to verify the theoretical analyses and to compare the performance of the proposed protocol with that of the two-way relaying protocol without network coding.

Array Gain in the DMT Framework for MIMO Channels

Following the seminal work by Zheng and Tse on the diversity and multiplexing tradeoff (DMT) of multiple-input multiple-output (MIMO) channels, in this paper, we introduce the array gain to investigate the fundamental relation between transmission rate and reliability in MIMO systems. The array gain gives information on the power offset that results from exploiting channel state information at the transmitter or as a consequence of the channel model. Hence, the diversity, multiplexing, and array gain (DMA) analysis is able to cope with the limitations of the original DMT and provide an operational meaning in the sense that the DMA gains of a particular system can be directly translated into a parameterized characterization of its associated outage probability performance. In this paper, we derive the best DMA gains achievable by any scheme employing isotropic signaling in uncorrelated Rayleigh, semicorrelated Rayleigh, and uncorrelated Rician block-fading MIMO channels. We use these results to analyze the effect of important channel parameters on the outage performance at different points of the DMT curve.

Outage Probability Analysis and Power Allocation for Two-Way Relay Networks with User Selection and Outdated Channel State Information

This paper considers a multiuser two-way relay network (TWRN) consisting of one base station (BS), one amplify-and-forward (AF) relay and K mobile stations (MSs) among which the Nth-best MS is selected to exchange information with the BS. Specifically, we study the impact of outdated channel state information (CSI) on the system over time-varying Rayleigh block-fading channels by deriving a tight closed-form lower bound for the outage probability. We also obtain an asymptotic outage probability expression for high signal-to-noise ratio (SNR). Moreover, by minimizing the asymptotic outage probability, we optimize the power allocation (PA) among the network nodes. Numerical and simulation results collaborate the proposed studies.

Using Channel Output Feedback to Increase Throughput in Hybrid-ARQ

Hybrid automatic repeat request (ARQ) protocols have become common in many packet transmission systems due to their incorporation in various standards. Hybrid-ARQ combines the normal ARQ method with forward error correction (FEC) codes to increase reliability and throughput. In this paper, we look at improving upon this performance using feedback information from the destination, in particular, using a powerful FEC code in conjunction with a proposed linear feedback code for the Rayleigh block fading channels. The new hybrid-ARQ scheme is initially developed for full received packet feedback in a point-to-point link. It is then extended to various multiple-antenna scenarios [e.g., multiple-input single-output (MISO), multiple-input multiple-output (MIMO), etc.] with varying amounts of packet feedback information. Simulations illustrate gains in throughput.

Quantize-and-Forward Schemes for the Orthogonal Multiple-Access Relay Channel

The multiple-access relay channel with two sources, a single relay, and one destination is considered. Under the assumption of noisy source-relay links causing the relay to be unable to decode without error, we propose a framework for designing one- and two-dimensional quantizers for quantizing the soft information at the relay. These quantizers are mutual-information preserving. Simulation results show a) that mutual-information preserving quantization schemes outperform techniques in which the soft information is forwarded in an analog fashion to the destination, b) that two-dimensional quantization outperforms one-dimensional quantization for source-relay links of different quality, and c) that diversity order of two can be gained in block Rayleigh fading channels by having the relay adaptively select a two-dimensional quantizer from a fixed set of quantizers shared with the destination, depending on the channel state on the source-relay links.

Low Complexity Time-Concatenated Turbo Equalization for Block Transmission Without Guard Interval: Part 1—The Concept

This paper proposes a novel time-concatenated turbo equalization technique, chained turbo equalization (CHATUE), that allows block transmission systems to eliminate the guard interval (GI), while achieving excellent performance. The proposed CHATUE algo- rithm connects turbo equalizers neighboring in time, so that they exchange information about their inter-block-interference components in the form of a posteriori log-likelihood ratio. The latest version of the low complexity sub-optimal turbo equalization technique for block-wise single carrier transmission, frequency domain soft cancellation and minimum mean squared error, is fully exploited in developing the CHATUE algorithm. Results of extrinsic informa- tion transfer chart analysis as well as a series of bit-error rate (BER) simulations show that excellent performances can be achieved without imposing heavy computational burden in multipath-rich (quasi-static) block Rayleigh fading channels. It is shown that, if the informa- tion bit-rate is kept identical (because it may be unpreferable for the industry to change the frame structure), the CHATUE algorithm achieves lower BER than that with block transmis- sion with GI, because lower rate (strong) code for error protection can be used by utilizing the time-duration made available by eliminating the GI. In addition, by combining the proposed structure with a simple rate-1 doped accumulator, further BER improvement exhibiting clear turbo cliff can be achieved. A sister paper (a Part-2 paper) applies the proposed CHATUE algorithm to single carrier frequency division multiple access systems Hui et al. (Wirel Pers Commun, 2011).

Rate-Distortion Optimized Cross-Layer Rate Control in Wireless Video Communication

A wireless video communication system can be designed based on the rate-distortion (R-D) criterion, i.e., minimizing the end-to-end distortion (which includes quantization distortion and transmission distortion) subject to the transmission bit-rate constraint. The minimization can be achieved by adjusting the source encoding parameters and channel encoding parameters. This rate-distortion optimization (RDO) is usually done for each video frame individually in a real-time video communication system, e.g., video calls or videoconferencing. To achieve this, an accurate bit-rate model and distortion model for each frame can be used to reduce the RDO complexity. In this paper, we derive a source bit-rate model and quantization distortion model; we also improve the performance bound for channel coding under a convolutional code and a Viterbi decoder, and derive its performance bound under a Rayleigh block fading channel. Given the instantaneous channel condition, e.g., signal-to-noise ratio and transmission bit-rate constraint, we design an R-D optimized cross-layer rate control (CLRC) algorithm by jointly choosing quantization step size in source coding and code rate in channel coding. Experimental results show that our proposed R-D models are more accurate than the existing R-D models. Experimental results also showed that the rate control under our models has more stable R-D performance than the existing rate control algorithms; using the channel estimation, CLRC can further achieve remarkable R-D performance gain over that without channel estimation. Another important result is that the subjective quality of our CLRC algorithm is much better than the existing algorithms due to its intelligent reference frame selection.

On the Minimum Differential Feedback for Time-Correlated MIMO Rayleigh Block-Fading Channels

In this paper, we consider a general multiple input multiple output (MIMO) system with channel state information (CSI) feedback over time-correlated Rayleigh block-fading channels. Specifically, we first derive the closed-form expression of the minimum differential feedback rate to achieve the maximum erdodic capacity in the presence of channel estimation errors and quantization distortion at the receiver. With the feedback-channel transmission rate constraint, in the periodic feedback system, we further investigate the relationship of the ergodic capacity and the differential feedback interval, and we find by theoretical analysis that there exists an optimal differential feedback interval to maximize ergodic capacity. Finally, analytical results are verified through simulations in a practical periodic differential feedback system using Lloyd's quantization algorithm.

Coding versus ARQ in Fading Channels: How Reliable Should the PHY Be?

This paper studies the tradeoff between channel coding and ARQ (automatic repeat request) in Rayleigh block-fading channels. A heavily coded system corresponds to a low transmission rate with few ARQ re-transmissions, whereas lighter coding corresponds to a higher transmitted rate but more retransmissions. The optimum packet error probability, where optimum refers to the maximization of the average successful throughput, is derived and is shown to be a decreasing function of the average signal-to-noise ratio and of the channel diversity order. A general conclusion of the work is that the optimum error probability is quite large (e.g., 10% or larger) for reasonable channel parameters, and that operating at a very small error probability can lead to a significantly reduced throughput. This conclusion holds even when a number of practical ARQ considerations, such as delay constraints and acknowledgement feedback errors, are taken into account.

Delay performance of cognitive radio networks for point-to-point and point-to-multipoint communications

In this article, we analyze the packet transmission time in spectrum sharing systems where a secondary user (SU) simultaneously accesses the spectrum licensed to primary users (PUs). In particular, under the assumption of an independent identical distributed Rayleigh block fading channel, we investigate the effect of the peak interference power constraint imposed by multiple PUs on the packet transmission time of the SU. Utilizing the concept of timeout, exact closed-form expressions of outage probability and average packet transmission time of the SU are derived. In addition, employing the characteristics of the M/G/1 queuing model, the impact of the number of PUs and their peak interference power constraint on the stable transmission condition and the average waiting time of packets at the SU are examined. Moreover, we then extend the analysis for point-to-point to point-to-multipoint communications allowing for multiple SUs and derive the related closed-form expressions for outage probability and successful transmission probability for the best channel condition. Numerical results are provided to corroborate our theoretical results and to illustrate applications of the derived closed-form expressions for performance evaluation of cognitive radio networks.

Rate-Adaptation-Based Cooperative Hybrid-ARQ Relaying Scheme in Rayleigh Block-Fading Channels

We propose to optimize a decode-and-forward (DF) cooperative relaying scheme with Hybrid Automatic-Repeat-reQuest (HARQ) protocol for maximizing long-term average transmission rate (LATR) while satisfying the required maximum number of HARQ rounds and the required outage probability in Rayleigh block-fading channels. We analyze the outage probability and the LATR of the cooperative HARQ relaying scheme for varying placements of a source, a relay, and a destination. We formulate and numerically solve an optimization problem of the cooperative HARQ relaying scheme, which is called the CO-LATR, to maximize the LATR by finding optimal values of parameters: the round transmission rate, transmit power allocation ratio between source and relay, and allowable maximum number of HARQ rounds on the link between source and relay. The CO-LATR outperforms the direct-link HARQ scheme, which does not include a relay and outperforms the cooperative HARQ relaying scheme with the conventional method in terms of the LATR.

Noncoherent Physical-Layer Network Coding with FSK Modulation: Relay Receiver Design Issues

A channel-coded physical-layer network coding strategy is refined for practical operation. The system uses frequency-shift keying (FSK) modulation and operates noncoherently, providing advantages over coherent operation: there are no requirements for perfect power control, phase synchronism, or estimates of carrier-phase offset. In contrast with analog network coding, which relays received analog signals plus noise, the system relays digital network codewords, obtained by digital demodulation and channel decoding at the relay. The emphasis of this paper is on the relay receiver formulation. Closed-form expressions are derived that provide bitwise log-likelihood ratios, which may be passed through a standard error-correction decoder. The role of fading-amplitude estimates is investigated, and an effective fading-amplitude estimator is developed. Simulation results are presented for a Rayleigh block-fading channel, and the influence of block length is explored. An example realization of the proposed system demonstrates a 32.4% throughput improvement compared to a similar system that performs network coding at the link layer. By properly selecting the rates of the channel codes, this benefit may be achieved without requiring an increase in transmit power.

Wideband Fading Channels With Feedback

The Rayleigh flat fading channel at low SNR is considered. With full channel state information (CSI) at the transmitter and receiver, its capacity is shown to be essentially SNR log(1SNR) nats/symbol, as SNR goes to zero. In fact, this rate can be achieved with a just one bit of CSI at the transmitter (per fading realization) and with no receiver CSI. The capacity for the case of noisy transmitter CSI is also found. Then a Rayleigh block fading channel of coherence interval T ≤ 1/ SNR is considered which has causal feedback and no a priori CSI. A training based scheme is proposed for such channels, which achieves a rate of SNR logT nats/symbol in the limit of small SNR and large T. Thus, when coherence interval T is of the order 1/SNR, without any a priori CSI at either end, the capacity with full CSI at both ends is achievable. For smaller values of T, a rate of SNR logT nats/symbol is shown to be achievable.

Iterative Multisymbol Noncoherent Reception of Coded CPFSK

A system involving the multisymbol noncoherent reception of coded continuous-phase frequency-shift keying is developed, optimized, and analyzed. Unlike coherent systems, the modulation index of the waveform does not need to be rational with a small denominator, and the oscillator only needs to be stable for the duration of a small block of symbols. The achievable performance over AWGN and Rayleigh block-fading channels is determined by computing the average mutual information, which is the capacity of a channel using the given modulation format and receiver architecture under the constraint of uniformly distributed input symbols. The code rate and modulation index are jointly optimized with respect to average mutual information under a bandwidth constraint. For binary and quaternary signaling, the information-theoretic results are corroborated by bit-error-rate curves generated using a standardized turbo code in conjunction with iterative demodulation and decoding. It is shown that, while more robust than a system with coherent reception, the proposed system offers superior energy efficiency compared with conventional single-symbol noncoherent reception.