Block Fading Channels Research Articles

Oversampling Increases the Pre-Log of Noncoherent Rayleigh Fading Channels

We analyze the capacity of a continuous-time, time-selective, Rayleigh block-fading channel in the high signal-to-noise ratio (SNR) regime. The fading process is assumed stationary within each block and to change independently from block to block; furthermore, its realizations are not known a priori to the transmitter and the receiver (noncoherent setting). A common approach to analyzing the capacity of this channel is to assume that the receiver performs matched filtering followed by sampling at symbol rate (symbol matched filtering). This yields a discrete-time channel in which each transmitted symbol corresponds to one output sample. Liang & Veeravalli (2004) showed that the capacity of this discrete-time channel grows logarithmically with the SNR, with a capacity pre-log equal to 1-Q/N. Here, N is the number of symbols transmitted within one fading block, and Q is the rank of the covariance matrix of the discrete-time channel gains within each fading block. In this paper, we show that symbol matched filtering is not a capacity-achieving strategy for the underlying continuous-time channel. Specifically, we analyze the capacity pre-log of the discrete-time channel obtained by oversampling the continuous-time channel output, i.e., by sampling it faster than at symbol rate. We prove that by oversampling by a factor two one gets a capacity pre-log that is at least as large as 1-1/N. Since the capacity pre-log corresponding to symbol-rate sampling is 1-Q/N, our result implies indeed that symbol matched filtering is not capacity achieving at high SNR.

Closed-Loop Beam Alignment for Massive MIMO Channel Estimation

Training sequences are designed to probe wireless channels to obtain channel state information for block-fading channels. Optimal training sounds the channel using orthogonal beamforming vectors to find an estimate that optimizes some cost function, such as mean square error. As the number of transmit antennas increases, however, the training overhead becomes significant. This creates a need for alternative channel estimation schemes for increasingly large transmit arrays. In this work, we relax the orthogonal restriction on sounding vectors. The use of a feedback channel after each forward channel use during training enables closed-loop sounding vector design. A misalignment cost function is introduced, which provides a metric to sequentially design sounding vectors. In turn, the structure of the sounding vectors aligns the transmit beamformer with the true channel direction, thereby increasing beamforming gain. This beam alignment scheme for massive MIMO is shown to improve beamforming gain over conventional orthogonal training for a MISO channel.

Low‐complexity ad‐hoc non‐linearities for blind multiuser detection of long‐code code‐division multiple access signals and asymptotic performance evaluation

In this study, monomials with odd integer powers are proposed for blind multiuser detection of code-division multiple access signals with long spreading codes, in the near-far situation. The performance of the new non-linear detectors are substantiated asymptotically and confirmed via simulations. It is demonstrated that the proposed non-linear detectors significantly outperform the matched filter detector in the block fading and Ricean fading channels, at the cost of a small increase in computational complexity. The optimum integer power value for the block fading channel with a limited interferer level, the Ricean channel with a given K factor and asynchronous channel is determined. The proposed multiuser detectors are blind in the sense that they require neither training nor the spreading code of the interferers. The detectors also do not require long convergence time for decision making in contrast to conventional blind multiuser detectors.

Modulation Discovery Over Arbitrary Additive Noise Channels Based on the Richardson-Lucy Algorithm

We address the problem of discovering unknown digital amplitude-phase modulations over block-fading additive noise channels. The proposed method uses the iterative Richardson-Lucy algorithm to determine the distribution of the transmitted symbols, which completely characterizes the underlying signal constellation. The decoding of the received signals can then be carried out based on the estimate of the signal constellation. An important application of the proposed method is to construct a modulation dictionary in an offline manner prior to performing any type of real time classification, thereby improving the performance of the automatic modulation classification algorithms proposed in the literature.

Soft Decoding Assisted SNR Estimation Under Block Fading Channels for Orthogonal Modulations

The performance of the coded orthogonal modulation (OM) system under slow fading channels heavily depends on the estimation of the signal-to-noise ratio (SNR), including the fading amplitude and the noise spectral density. However, a relatively long packet of pilot symbols is often required to guarantee the accuracy of the SNR estimation, which makes it impractical in some situations. To address this problem, this paper proposes an iterative SNR estimation algorithm using the soft decoding information based on the expectation-maximization algorithm. In the proposed method, a joint iterative loop between the SNR estimator and decoder is performed, where the extrinsic information generated by the soft decoder is employed to enhance the estimation accuracy and the SNR estimated by the estimator is used to generate the soft information to the decoder. Also, no pilot symbols are needed to estimate the SNR in the proposed estimator. The Cramer---Rao lower bound (CRLB) of fully data-aided (FDA) estimation is derived to works as the final benchmark. The performance of the proposed algorithm is evaluated in terms of the normalized mean square errors (NMSEs) and the bit error rates (BERs) under block fading channels. Simulation results indicate that the NMSE of the proposed estimator reaches the CRLB of the FDA estimator and outperforms that of the approximate ML (ML-A) estimator proposed by Hassan et al. by 4.1 dB. The BER performance of coded OM system with the proposed estimation algorithm is close to the ideal case where the channel fading and the noise spectral density are known at the receiver.

Spectrum sensing and resource allocation for multicarrier cognitive radio systems under interference and power constraints

Multicarrier waveforms have been commonly recognized as strong candidates for cognitive radio. In this paper, we study the dynamics of spectrum sensing and spectrum allocation functions in cognitive radio context using very practical signal models for the primary users (PUs), including the effects of power amplifier nonlinearities. We start by sensing the spectrum with energy detection-based wideband multichannel spectrum sensing algorithm and continue by investigating optimal resource allocation methods. Along the way, we examine the effects of spectral regrowth due to the inevitable power amplifier nonlinearities of the PU transmitters. The signal model includes frequency selective block-fading channel models for both secondary and primary transmissions. Filter bank-based wideband spectrum sensing techniques are applied for detecting spectral holes and filter bank-based multicarrier (FBMC) modulation is selected for transmission as an alternative multicarrier waveform to avoid the disadvantage of limited spectral containment of orthogonal frequency-division multiplexing (OFDM)-based multicarrier systems. The optimization technique used for the resource allocation approach considered in this study utilizes the information obtained through spectrum sensing and knowledge of spectrum leakage effects of the underlying waveforms, including a practical power amplifier model for the PU transmitter. This study utilizes a computationally efficient algorithm to maximize the SU link capacity with power and interference constraints. It is seen that the SU transmission capacity depends critically on the spectral containment of the PU waveform, and these effects are quantified in a case study using an 802.11-g WLAN scenario.

Rate Adaptation for Cooperative HARQ

We analyze the average throughput and the outage probability for relay-based incremental redundancy HARQ transmission over block fading channel. We focus on the effects of having an error-free multi-bit feedback channel instead of the single-bit ACK/NACK feedback used in conventional HARQ. This multi-bit feedback message provides the cooperating nodes with outdated channel state information (CSI) so that they can adapt their transmission rate. We discuss a network with M relay nodes and assume adaptive transmission rate for all the cooperating nodes. We describe the adaptation problem as a Markov Decision Process (MDP) and employ the Dynamic Programming (DP) for optimization. The numerical results obtained in the case of one relay transmission, indicate that significant throughput gains can be obtained when compared to non-adaptive, i.e, fixed-rate HARQ. Moreover, we study the performance limits of the system model by finding an upper bound of the throughput for the cooperative HARQ channel which is applicable to both adaptive and non-adaptive models. Finally, we analyze the discretization issues and conclude that only a small number of feedback bits is required by the adaptive system to outperform the conventional single-bit HARQ.

Resource Allocation for Two Source-Destination Pairs Sharing a Single Relay with a Buffer

In this paper, we obtain the optimal resource allocation scheme in order to maximize the achievable rate region in a dual-hop system that consists of two independent source-destination pairs sharing a single half-duplex relay. The relay decodes the received information and possesses buffers to enable storing the information temporarily before forwarding it to the respective destination. We consider both non-orthogonal transmission with successive interference cancellation at the receivers and orthogonal transmission. Also, we consider Gaussian block-fading channels and we assume that the channel state information is known and that no delay constraints are required. We show that, with the aid of buffering at the relay, joint user-and-hop scheduling is optimal and can enhance the achievable rate significantly. This is due to the joint exploitation of multiuser diversity and multihop diversity in the system. We provide closed-form expressions to characterize the average achievable rates in a generic form as functions of the statistical model of the channels. Furthermore, we consider sub-optimal schemes that exploit the diversity in the system partially and we provide numerical results to compare the different schemes and demonstrate the gains of the optimal one.

Directional Estimation of Block-Fading MIMO Channels Using Spherical Harmonics Expansion and Tensor Analysis

The well-known benefits of multiple input multiple output (MIMO) wireless communication systems suppose an efficient use of spatial diversity at both the transmitter and receiver. An important and ...

Delay Outage Probability in Block Fading Channel and Relay-Assisted Hybrid-ARQ Network

In this letter, we focus on the delay outage probability in block fading channels and relay-assisted decode-and-forward hybrid-automatic retransmission request (HARQ-I) based systems. The delay outage is defined as the probability that the requirement on the average delay in additive white Gaussian noise (AWGN), could not be sustained in block fading channels. In other words, the system is said to be in outage if the mean delay exceeds a certain threshold θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> due to the retransmission mechanism of erroneous packets. Our contribution lies in two folds: A closed form expression of the end-to-end delay in relay-assisted HARQ scheme is derived. Using the derived delay expression, an analytical form of the delay outage probability is proposed which might be very useful to avoid lengthy simulations.

Rate Adaptation and Power Allocation for Cognitive Radio Networks with HARQ-Based Primary System

In this paper, we propose a protocol for the coexistence of primary and secondary systems over block-fading channels. In the protocol, the primary system employs a hybrid automatic repeat request (HARQ). When the primary system retransmits the data signal, the secondary system serves as a relay for the retransmission of the primary system and simultaneously transmits its data signal. To efficiently accomplish the protocol, we analyze the average throughput of the primary and secondary systems by using the long-term average throughput (LAT). We formulate an optimization problem to maximize the LAT of the secondary system. The constraint of the optimization problem is that the LAT of the primary system with secondary system is not less than that of the primary system alone. Through the optimization problem, we obtain the closed-form solutions of the transmission rate of the secondary system and the fraction of the transmit power for relaying the primary system's data signal and transmitting the secondary system's data signal. Numerical results show that the primary system does not lose the average throughput, and rather achieves an additional throughput gain by adjusting the fraction of the transmit power of the secondary system.

Packet error rate‐based adaptive rate optimisation with selective‐repeat automatic repeat request for convolutionally‐coded M‐ary quadrature amplitude modulation systems

Link adaptation using adaptive modulation and coding (AMC) is a popular physical layer technique for efficient use of time-varying fading channels. Using a cross-layer approach, AMC and truncated automatic repeat request scheme at data link layer are jointly considered. For a convolutionally-coded M-ary quadrature amplitude modulation system under block fading channel condition, a variable rate transmission scheme that uses imperfect channel state information is derived. First, a closed-form expression for approximating packet error rate (PER) is found as a function of coded information rate. It is then shown that by solving an optimisation problem using this expression, optimum transmission rate can be determined in a way that maximises the spectral efficiency while satisfying an average PER constraint. Hence, the parameters in physical and medium access control layers are incorporated in the analysis.

Low‐complexity iterative channel estimation with lattice reduction‐based detection for multiple‐input multiple‐output systems

Iterative channel estimation and detection (ICED) can provide a better performance as the channel estimation can be improved through iterations. For a multiple-input multiple-output channel, owing to a large size of the signal alphabet, ICED becomes less practical unless a low-complexity detector such as a lattice reduction-based detector is employed. However, since the lattice basis reduction has to be carried out for each iteration, the resulting complexity can be still high. In this study, a computationally efficient technique was proposed to perform the lattice basis reduction within ICED over both static and slowly time-varying block-fading channels, where orthogonal defect of basis, as well as error probability are considered to decide whether or not basis reduction is needed for each iteration.

Achieving Delay Diversity in Asynchronous Underwater Acoustic (UWA) Cooperative Communication Systems

In cooperative UWA systems, due to the low speed of sound, a node can experience significant time delays among the signals received from geographically separated nodes. One way to combat the asynchronism issues is to employ orthogonal frequency division multiplexing (OFDM)-based transmissions at the source node by preceding every OFDM block with an extremely long cyclic prefix (CP) which reduces the transmission rates dramatically. One may increase the OFDM block length accordingly to compensate for the rate loss which also degrades the performance due to the significantly time-varying nature of UWA channels. In this paper, we develop a new OFDM-based scheme to combat the asynchronism problem in cooperative UWA systems without adding a long CP (in the order of the long relative delays) at the transmitter. By adding a much more manageable (short) CP at the source, we obtain a delay diversity structure at the destination for effective processing and exploitation of spatial diversity by utilizing a low complexity Viterbi decoder at the destination, e.g., for a binary phase shift keying (BPSK) modulated system, we need a two-state Viterbi decoder. We provide pairwise error probability (PEP) analysis of the system for both time-invariant and block fading channels showing that the system achieves full spatial diversity. We find through extensive simulations that the proposed scheme offers a significantly improved error rate performance for time-varying channels (typical in UWA communications) compared to the existing approaches.

Information Networks With In-Block Memory

A class of channels is introduced for which there is memory inside blocks of a specified length and no memory across the blocks. The multi-user model is called an information network with in-block memory (NiBM). It is shown that block-fading channels, channels with state known causally at the encoder, and relay networks with delays are NiBMs. A cut-set bound is developed for NiBMs that unifies, strengthens, and generalizes existing cut bounds for discrete memoryless networks. The bound gives new finite-letter capacity expressions for several classes of networks including point-to-point channels, and certain multiaccess, broadcast, and relay channels. Cardinality bounds on the random coding alphabets are developed that improve on existing bounds for channels with action-dependent state available causally at the encoder and for relays without delay. Finally, quantize-forward network coding is shown to achieve rates within an additive gap of the new cut-set bound for linear, additive, Gaussian noise channels, symmetric power constraints, and a multicast session.

Cooperative Key Agreement for Wireless Networking: Key Rates and Practical Protocol Design

In this paper, we investigate the design of a practical information-theoretically secure secret key agreement protocol for a cooperative wireless network employing standard modulation. Assuming relay selection has been completed, the key agreement problem is studied in a three-node cooperative wireless communication system over block-fading channels. Passive attacks from an eavesdropper collocated with the relay are considered. We derive upper and lower bounds on the secret key rate of this cooperative wireless system. The difference between the bounds is shown to be small for practical communication scenarios, which indicates they are tight. We then propose a practical secret key agreement protocol for this system with both the communicants and the honest relay participating in the public discussion. The tradeoff between security and protocol efficiency is considered in the joint design of advantage distillation, information reconciliation, and privacy amplification. The protocol parameters are optimized to achieve the tight bound on the secret key rate.

On Noisy ARQ in Block-Fading Channels

Assuming noisy feedback channels, this paper investigates the data transmission efficiency and robustness of different automatic repeat request (ARQ) schemes using adaptive power allocation. Considering different block-fading channel assumptions, the long-term throughput, the delay-limited throughput, the outage probability and the feedback load of different ARQ protocols are studied. A closed-form expression for the power-limited throughput optimization problem is obtained which is valid for different ARQ protocols and feedback channel conditions. Furthermore, the paper presents numerical investigations on the robustness of different ARQ protocols to feedback errors. It is shown that many analytical assertions about the ARQ protocols are valid both when the channel remains fixed during all retransmission rounds and when it changes in each round (in)dependently. As demonstrated, optimal power allocation is crucial for the performance of noisy ARQ schemes when the goal is to minimize the outage probability.

Low-Complexity LDPC-Coded USTM Noncohereny MIMO Receivers

This paper proposes a scheme of combining low-density parity check (LDPC) code with unitary space time modulation (USTM) for noncoherent multiple-input-multiple-output (MIMO) transmitter and receiver over Rayleigh block fading and additive white Gaussian noise (AWGN) channel. The main aim is to design the low complexity coded noncoherent MIMO receiver which is completely dependent on the structural feature of unitary space-time matrix without sending the pilot symbol at the transmitter and estimating the channel state information at the receiver. Considering soft information required by belief-propagation (BP) iterative decoder of LDPC code, we deduce a maximum a posteriori probability (MAP) demodulating algorithm using a special USTM based on the sine-cosine function. A novel dual-demodulator is conceived for decreasing the computational complexity of this MAP demodulator. Furthermore, the iterative feedback scheme between MAP demodulator and BP decoder is introduced and its modified parameter scheme is considered for further improving performance of the dual-demodulator. Comparing with uncoded USTM, our LDPC-coded USTM MIMO receiver can obtain about 17 dB coding gain at 10-6 BER.

Cross-Layer Framework for Multiuser Real Time H.264/AVC Video Encoding and Transmission over Block Fading MIMO Channels Using Outage Probability

We present a framework for cross-layer optimized real time multiuser encoding of video using a single layer H.264/AVC and transmission over MIMO wireless channels. In the proposed cross-layer adaptation, the channel of every user is characterized by the probability density function of its channel mutual information and the performance of the H.264/AVC encoder is modeled by a rate distortion model that takes into account the channel errors. These models are used during the resource allocation of the available slots in a TDMA MIMO communication system with capacity achieving channel codes. This framework allows for adaptation to the statistics of the wireless channel and to the available resources in the system and utilization of the multiuser diversity of the transmitted video sequences. We show the effectiveness of the proposed framework for video transmission over Rayleigh MIMO block fading channels, when channel distribution information is available at the transmitter.

Throughput Analysis of ARQ Schemes in Gaussian Block Fading Channels

This paper examines throughput performance, and its optimization, for lossless and truncated automatic repeat request (ARQ) schemes in Gaussian block fading channels. Specifically, ARQ, repetition redundancy, and in part also incremental redundancy-hybrid ARQ, are considered with various diversity schemes. We propose a parameterization-based method that allows (semi-)closed-form expressions, linking optimized throughput, optimal rate, and mean SNR, to be derived for any ARQ and repetition redundancy-HARQ method even when a non-parameterized closed-form does not exist. We derive numerous throughput and optimal throughput expressions for various ARQ schemes and diversity scenarios, potentially useful for benchmarking purposes or as design guidelines.