Time-correlated Rayleigh Fading Channels Research Articles

On the Impact of Time-Correlated Fading for Downlink NOMA

This paper investigates the performance of non-orthogonal multiple access (NOMA) systems over time-correlated Rayleigh fading channels, where the users have heterogeneous quality of service requirements, e.g., a latency-critical user with a low target rate and a delay-tolerant user with a large target rate. In order to meet the different requirements of the users, two partial hybrid automatic repeat request (HARQ) schemes, including partial HARQ with chase combining (HARQ-CC) and HARQ with incremental redundancy (HARQ-IR), are proposed. The closed-form expressions of outage probabilities for NOMA with and without re-transmission are derived. With the developed outage probabilities, a condition on the superiority of NOMA to orthogonal multiple access (OMA) is obtained. In particular, the condition is characterized by the transmit powers for NOMA without re-transmission and is obtained by using the bisection method in the case with re-transmission. To further improve the performance of the HARQ enabled NOMA schemes, we consider an average transmit power minimization problem by optimizing the transmit power among different transmission rounds with outage constraints. However, due to the complexity of the developed outage probabilities, the formulated problem is non-convex and challenging to solve. Then we approximate the original problem by deriving the upper-bound approximations of the outage probabilities and solve it by using the geometric programming method. Simulation results demonstrate the accuracy of the developed analytical results. It is shown that the performance of NOMA is superior to OMA, only when the obtained condition is satisfied. HARQ-CC and HARQ-IR can enhance the outage performance of NOMA over time-correlated fading channels and the HARQ-IR has excellent performance in terms of energy efficiency.

Analysis of HARQ-IR Over Time-Correlated Rayleigh Fading Channels

In this paper, performance of hybrid automatic repeat request with incremental redundancy (HARQ-IR) over Rayleigh fading channels is investigated. Different from prior analysis, time correlation in the channels is considered. Under time-correlated fading channels, the mutual information in multiple HARQ transmissions is correlated, making the analysis challenging. By using polynomial fitting technique, probability distribution function of the accumulated mutual information is derived. Three meaningful performance metrics including outage probability, average number of transmissions, and long term average throughput (LTAT) are then derived in closed-forms. Moreover, diversity order of HARQ-IR is also investigated. It is proved that full diversity can be achieved by HARQ-IR, i.e., the diversity order is equal to the number of transmissions, even under time-correlated fading channels. These analytical results are verified by simulations and enable the evaluation of the impact of various system parameters on the performance. Particularly, the results unveil the negative impact of time correlation on the outage and throughput performance. The results also show that although more transmissions would improve the outage performance, they may not be beneficial to the LTAT when time correlation is high. Optimal rate design to maximize the LTAT is finally discussed and significant LTAT improvement is demonstrated.

Effects of Heterogenous Mobility on Rate Adaptation and User Scheduling in Cellular Networks With HARQ

In this paper, we investigate the effects of heterogeneous mobility on rate adaptation and user scheduling in cellular networks with hybrid automatic repeat request (HARQ). To this end, we first show the performance tradeoff between two extreme scheduling criteria: retransmission-oriented scheduling (ROS) and mixed scheduling (MS) criteria over time-correlated Rayleigh fading channels. Then, we propose an ROS-based joint rate adaptation and user scheduling (JRAUS) policy for cellular networks and compare it with the conventional and reference JRAUS policies. We also evaluate the system-level performance of the proposed ROS-based JRAUS policy in various user distribution and mobility scenarios. In particular, in an asymmetric user distribution and heterogeneous mobility scenario, which is the most general one in practice, the proposed JRUAS policy yields a throughput gain of 49% and a fairness gain of 155% over the conventional JRAUS policies. In this paper, we find that the rate adaptation is significant not only in a single point-to-point link but in multiuser systems with heterogeneous mobility as well.

The LLR Metric for q-ary LDPC Codes with MPSK Modulation over Rayleigh Channels with Imperfect CSI

We consider the iterative decoding of low-density parity-check codes with M-ary phase-shift keying transmission and pilot-symbol-assisted channel estimation over time correlated Rayleigh fading channels. We present the correct conceptual approach for deriving the log-likelihood ratio (LLR) expression for a general q-ary code. Its bit-error probability (BEP) performance is compared with that of the conventional metric which does not take into account the information concerning the channel estimation accuracy. Simulation results show that this LLR metric outperforms the conventional metric in both BEP performances and average number of decoding iterations required for convergence. The work here demonstrates the importance of incorporating the knowledge of the channel estimation accuracy in the iterative decoding process.

Optimal Rate Adaptation for Hybrid ARQ in Time-Correlated Rayleigh Fading Channels

Most analytical studies on hybrid automatic repeat request (HARQ) have been carried out in either slow fading or fast fading assumptions. However, since practical wireless channels typically exhibit a time-correlated property, we need to take into account the effects of time correlation in the design of HARQ. In this paper, we analyze the outage probability and delay-limited throughput of HARQ with rate adaptation in a time-correlated channel model. Then, we propose a rate adaptation scheme to maximize the delay-limited throughput and evaluate the performance of the proposed scheme under a delay constraint. Our analytical and numerical results show that the proposed rate adaptation scheme outperforms the conventional rate adaptation schemes. The proposed rate adaptation scheme is further simplified by using a Gaussian approximation on the effective channel power gain. The rate adaptation based on the proposed Gaussian approximation reduces the complexity and achieves a throughput gain comparable to that with the exact channel distributions.

Performance analysis of single source and single relay cooperative ARQ protocols under time correlated Rayleigh fading channel

In this paper, we analyze the performance of a cooperative Automatic Repeat reQuest (ARQ) protocol under Poisson arrivals and time correlated Rayleigh fading. The conventional non-cooperative ARQ protocol under the same channel environment is also analyzed to compare its performance with that of the cooperative ARQ protocol. A two-dimensional discrete time Markov chain is constructed for the analysis. Using the steady state analysis of the Markov chain, the average frame latency and the probability generating function of the frame service time are derived. We validate our analytical results by comparing them with simulation results. From our analysis, we show that the cooperative ARQ protocol outperforms the non-cooperative ARQ protocol and the effect of the time correlation in the fading channel is not negligible. We also see that the performance metrics which we consider in this paper are almost constant as long as d S R 2 + d R D 2 remains constant, where d S R is the distance between the source node and the relay node and d R D is the distance between the relay node and the destination node.

Compact Rayleigh and Rician fading simulator based on random walk processes

This article describes a significantly improved sum-of-sinusoids-based model for the accurate simulation of time-correlated Rayleigh and Rician fading channels. The proposed model utilises random walk processes instead of random variables for some of the sinusoid parameters to more accurately reproduce the behaviour of wireless radio propagation. Every fading block generated using our model has accurate statistical properties on its own and hence, unlike previously proposed models, there is no need for time-consuming ensemble-averaging over multiple blocks. Using numerical simulation it is shown that the important statistical properties of the generated fading samples have excellent agreement with the theoretical reference functions. A fixed-point hardware implementation of the corresponding Rayleigh and Rician fading channel simulator on a field-programmable gate array (FPGA) is presented. By efficiently scheduling the operations, the reconfigurable fading channel simulator is compact enough that it can be efficiently used to simulate multipath scenarios and multiple-antenna systems (e.g. a 4×4 MIMO channel) using a single FPGA.

Performance Analysis of Linear Modulation Schemes With Generalized Diversity Combining on Rayleigh Fading Channels With Noisy Channel Estimates

Generalized diversity combining (GDC), also known as hybrid selection/maximal ratio combining or generalized selection combining, is a low-complexity diversity combining technique by which a fixed subset of a large number of available diversity channels is chosen and then combined using the rules of maximal ratio combining. In this paper, we analyze the performance of GDC on time-correlated Rayleigh fading channels with noisy channel estimates. We derive expressions for the probability of error for various linear modulation schemes with coherent detection, and discuss the conditions under which the analysis can be extended to noncoherent and differentially coherent receiver structures. Throughout the paper, using a fundamental approach to obtain the decision statistic at the combiner output, a number of new expressions for the error probabilities are obtained in a rigorous way, along with a presentation of their performance with channel estimation errors. The final expressions have roughly the same complexity of evaluation as that for the channel with only additive Gaussian noise. Our results correct various inaccuracies in the literature, and show that coherent receivers based on imperfectly estimated channel knowledge incur a significant performance loss.

Diversity analysis of space-time modulation over time-correlated Rayleigh-fading channels

Most space-time codes in the literature were proposed based on two ideal channel conditions: either quasistatic or rapid fading. However, these codes may suffer performance degradation due to temporal correlation caused by the movement of the mobile terminal or imperfect interleaving. In this correspondence, we provide a novel analytical framework for the diversity analysis of space-time modulation in time-correlated fading environment. We show that the space-time signals of square size achieving full diversity in quasistatic fading channels also achieve full diversity in time-correlated fading channels, independently of the time correlation matrix. Consequently, various classes of space-time signals designed for quasistatic fading channels can also be used for full-diversity transmission over time-correlated fading channels. Moreover, we show that if the time correlation matrix is of full rank, the design criteria for time-correlated fading channels are the same as those for rapid fading channels. To illustrate the theoretical results, some simulations were also performed under various temporal fading conditions.