Time-varying Rayleigh Fading Channels Research Articles

MU-MIMO Receiver Design and Performance Analysis in Time-Varying Rayleigh Fading

Minimizing the symbol error in the uplink of multi-user multiple input multiple output systems is important, because the symbol error affects the achieved signal-to-interference-plus-noise ratio (SINR) and thereby the spectral efficiency of the system. Despite the vast literature available on minimum mean squared error (MMSE) receivers, previously proposed receivers for block fading channels do not minimize the symbol error in time-varying Rayleigh fading channels. Specifically, we show that the true MMSE receiver structure does not only depend on the statistics of the CSI error, but also on the autocorrelation coefficient of the time-variant channel. It turns out that calculating the average SINR when using the proposed receiver is highly non-trivial. In this paper, we employ a random matrix theoretical approach, which allows us to derive a quasi-closed form for the average SINR, which allows to obtain analytical exact results that give valuable insights into how the SINR depends on the number of antennas, employed pilot and data power and the covariance of the time-varying channel. We benchmark the performance of the proposed receiver against recently proposed receivers and find that the proposed MMSE receiver achieves higher SINR than the previously proposed ones, and this benefit increases with increasing autoregressive coefficient.

Trade-off between spectral efficiency and normalized energy in Ad-hoc wireless networks

With the ever-increasing deployment of wireless communication technologies, effective management of scarce power and radio spectrum resources is of primary concern. The available bandwidth spectrum should be utilized in the most efficient and controlled way for practical economic growth of industries in conformity with the evolving demand of energy for powering wireless devices. In the proposed optimization scheme, energy management and limited spectrum sharing are distributively implemented for handling quality of service provisioning and potential resource allocation across multiple nodes with inherent operational capability deficiencies. We employ cross-layer information exchange and convex optimization techniques to simultaneously achieve more efficient radio spectrum usage and optimal energy consumption in ad-hoc wireless networks with distributed scenarios. We consider the time-invariant additive white Gaussian noise channel and the time-varying Rayleigh fading channel to study the trade-off between the two network design objectives of achieving improved spectrum efficiency and minimizing the energy overhead in data routing paradigm. The original problem is transformed into an equivalent convex optimization problem through logarithmic processing to obtain the approximate global optimal solution. Moreover, the robustness and efficiency of the proposed framework is evaluated in large-scale set ups to provide the scalability analysis on both the employed performance objectives. The developed optimization scheme is compared with the machine learning models previously proposed in literature by employing the computational and/or time complexity metrics. Finally, the effectiveness of the proposed optimization model is substantiated through the simulation comparison results with the existing schemes in terms of various key performance parameters such as throughput, energy efficiency, and average bit errors.

Performance Analysis of a Linear MMSE Receiver in Time-Variant Rayleigh Fading Channels

The performance of the uplink of single and multiuser multiple input multiple output (MIMO) systems depends crucially on the receiver architecture and the quality of channel state information at the receiver. Therefore, several previous works have developed minimum mean squared error (MMSE) receivers and proposed balancing the resources spent on acquiring channel state information and transmitting the payload of data packets. Somewhat surprisingly, the most popular MIMO linear MMSE receivers do not exploit the correlation structure that is present in autoregressive Rayleigh fading environments. Therefore, in this article we first develop a new linear receiver that not only takes channel state information errors into account in minimizing the MSE of the received data symbols, but it also utilizes that the subsequent noisy channel coefficients are correlated. For this new linear MMSE receiver, we derive the achieved MSE as a function of the number of receive antennas and the pilot-to-data power ratio. Interestingly, we find that the pilot power that minimizes the MSE of the data symbols does not depend on the number of antennas and that the new linear MMSE receiver outperforms previously proposed MIMO receivers when the autocorrelation coefficient of the channel is high.

Performance analysis of bit error rate of data link system under pulse LFM interference in time-varying rayleigh channel

In such mobile platforms as ships and aircraft, the detection and reconnaissance devices are near to the communication facilities. When working at the same time, they will create interference or jamming themselves. Especially, the high-power radar equipment tend to cause a high bit error rate (BER) in the data link system (DLS), with the result that the DLS cannot operate normally. For this reason, this paper makes a study of the BER performance of the DLS under the pulse linear frequency modulation (LFM) interference in the time-varying Rayleigh channel. In view of the the time-varying characteristics of channel in the practical conditions, the interference channel is modeled as a time-varying Rayleigh fading channel and the formula of BER is derived. Through simulation, the theoretical deduction is proved to be correct. This is of much importance to analyzing the variation of BER performance with the pulse width, power and doppler frequency shift under the pulse LFM interference.

Deep Learning-Based Channel Estimation Algorithm Over Time Selective Fading Channels

The research about deep learning application for physical layer has been received much attention in recent years. In this paper, we propose a Deep Learning (DL) based channel estimator under time varying Rayleigh fading channel. We build up, train and test the channel estimator using Neural Network (NN). The proposed DL-based estimator can dynamically track the channel status without any prior knowledge about the channel model and statistic characteristics. The simulation results show the proposed NN estimator has better Mean Square Error (MSE) performance compared with the traditional algorithms and some other DL-based architectures. Furthermore, the proposed DL-based estimator also shows its robustness with the different pilot densities.

BER Performance Investigation of WPM with Unknown CSI Using Time-Domain MMSE Equalization

Wavelet Packet Modulation (WPM) is an emerging Multi-Carrier Modulation (MCM) technique regarded as a potential alternative to widely used Orthogonal Frequency Division multiplexing (OFDM). OFDM uses Cyclic Prex (CP) and can rely on one-tap equalization. Since WPM has overlapping symbols in the time domain, equalization cannot depend on the use of CP. This paper considers time-domain Minimum Mean-Square Error (MMSE) equalization for WPM with unknown Channel State Information (CSI), where equalizer filter coefficients are computed using known training sequences. The infuence of the transmission overhead due to training sequences on the Bit Error Rate (BER) performance is investigated considering quasistatic time-varying Rayleigh fading channels. Numerical results from computer simulations show that, with moderate overhead due to training sequences, BER performances are comparable with the case of known CSI. Furthermore, WPM is compared to OFDM with one-tap equalization, and is shown to provide better BER performances as compared to OFDM. Finally, this paper demonstrates improvement in Peak-to-Average Power Ratio (PAPR) of the transmitted signal using subcarrier combining for WPM in heterogeneous communication environments, where low-rate and high-rate devices share the same transmission resources.

Performance Analysis of Spatial Modulation Under Rapidly Time-Varying Rayleigh Fading Channels

Due to the problem of inter-channel interference, the average bit error probability (ABEP) performance of the traditional multiple transmit and multiple receive antenna systems obviously deteriorates. A promising scheme to address this issue is the spatial modulation (SM) which activates only one transmit antenna at each signaling period. In addition, the demand to provide data services for high mobility users is ever increasing, where fading channels are more likely to be rapidly time-varying. Therefore, in this paper, we investigate the ABEP performance of SM under the assumption that system’s fading channels are Rayleigh and varying from one signaling period to another within the same transmitted data block. Further, to simplify the decoding complexity at the receiver, the channel is assumed to be estimated at the first location of each data block and then used to detect the received symbols at the remaining locations of the block. For such a system, and unlike other literature works, we derive novel, exact and closed-form reduced enough expressions for the average pairwise error probabilities (average-PEPs), which are then used to compute the system’s overall per-block ABEP efficiently. The derived expressions are generic and valid for both time-varying and slow fading environments. Furthermore, the obtained analytical results are exploited to quantitatively show that the time-varying fading environment degrades the SM system’s performance through irreducible error floors. Numerical and simulation results of various examples are provided to validate the theoretical analyses and also to get some insights into the effect of the different system parameters (such as the speed of the mobile, the carrier frequency, and the block size of the channel variations) on the overall SM error performance.

On Optimal Power Allocation over Time-Varying Rayleigh Fading Channels for Maximum-Ratio Combining in Diversity Systems with Partial CSI

This paper studies the problem of optimal power allocation (OPA) over independent but not necessarily identically distributed time-varying Rayleigh fading channels with maximum-ratio combining to exploit transmit and/or receive diversity. Specifically, the optimal average rate-maximizing and M-ary phase shift keying symbol-error-rate (SER)-minimizing power allocation problems subject to a total transmit power constraint are formulated as stochastic optimization problems. After that, the stochastic problems are reformulated into deterministic ones in terms of the average rate and SER, respectively, which require only partial channel state information (CSI) in the form of channel gains. Novel closed-form expressions are derived for the deterministic OPA for average rate-maximization and SER-minimization, and a linear-complexity water-filling algorithm is then proposed to efficiently determine the OPA based on derived closed-form solutions. Moreover, dynamic OPA (with full CSI knowledge) is analyzed and closed-form solutions for the optimal average rate and SER are obtained. Simulation results are presented to validate the theoretical analysis, and demonstrate that the deterministic OPA algorithm outperforms equal power allocation and yields comparable average rate and SER performances to the dynamic OPA.

A Real-Valued Weighted Covariance-Based Detection Method for Cognitive Radio Networks With Correlated Multiple Antennas

The weighted covariance-based detection (WCD) method for spectrum sensing (SS) can offer a reliable detection performance in the spatially correlated time-varying Rayleigh fading channel. However, it involves huge complex computations. As is well known, one complex multiplication requires two real additions and four real multiplications. To this end, we transfer the complex-valued SS problem into the real-valued SS problem and present a novel-reduced complexity WCD method in this letter, which is referred to as a real-valued WCD (RWCD) method. In particular, an asymptotic closed-form expression of the probability of detection is derived for the proposed RWCD method, which is intractable in the WCD method. Through the complexity analysis, the RWCD method can save nearly half of the computational complexity compared to the WCD method. Meanwhile, simulation results show that the proposed method achieves almost the same performance as that of the WCD method, and both outperform their competitors.

Timing and Integer Frequency Offset Estimation for DLMT System over Time-Varying Rayleigh Fading Channel

In this paper, we study the timing and integer carrier frequency offset (ICFO) estimation problem for dynamic lattice multicarrier transmission (DLMT) system over time-varying Rayleigh fading channel. Firstly, a novel preamble structure based on two constant amplitude zero auto-correlation (CAZAC) sequences is designed for DLMT system. Then, by using the designed dual-CAZAC preamble, a discrete cross ambiguity function (DCAF) based timing and ICFO estimation algorithm is proposed. Simulation results show that the proposed DCAF based timing and ICFO estimation algorithm can mitigate the impact of time-varying multipath Rayleigh fading channel and outperforms traditional estimators on the correct estimation probability performance.

A Robust Blind Detection Algorithm for Cognitive Radio Networks With Correlated Multiple Antennas

This letter concentrates on the spectrum sensing problem for secondary user equipped with a large number of low-correlated antennas, and a robust blind detection method based on Ljung-Box (LB) test is proposed, which leverages the autocorrelation function of the received time series to evaluate the signal existence. In the scenarios where the correlation between receive antennas is low, simulation results illustrate that the proposed LB-test method attains a significant detection performance improvement compared with the existing covariance-based methods in the time-varying Rayleigh fading channel.

LMMSE channel estimation for wireless energy harvesting AF relaying

Wireless energy harvesting can be adopted in relaying systems to solve the energy issue at the relay node. Channel estimation is an important aspect of its system design. Thus, in this paper, we study channel estimation for wireless energy harvesting relaying. In the study, we use the linear minimum mean squared error (LMMSE) estimators to estimate the source-to-relay link and the relay-to-destination link separately in an amplify-and-forward relaying system. Time-varying Rayleigh fading channels using the Jakes model are considered. Both time-switching (TS) and power-splitting (PS) energy harvesting strategies are examined. Fixed-gain relaying is compared with variable-gain relaying. The signal-to-noise ratios and the bit error rates are calculated. Numerical results are used to show that the system suffers from an error floor due to the use of LMMSE estimators and that its performance depends on several important system parameters. In particular, it is found that PS outperforms TS, variable-gain relaying is better than fixed-gain relaying, and a stationary relay can lead to better performance than a mobile relay. For PS, the choice of the PS factor is important. On the other hand, the symbol position has little effect on the BER.

Relay selection Algorithm for wireless cooperative networks: a learning‐based approach

Relay selection in cooperative communication is a crucial task for achieving the spatial diversity since the improper relay selection can decrease the overall capacity of the network. In this study, the authors use a reinforcement learning technique, called as Q-learning (QL), to solve the relay selection problem. They propose a ‘QL-based relay selection algorithm’ (QL-RSA) for wireless cooperative networks that maximises the total capacity of the network. QL-RSA receives the reward (feedback) in terms of the capacity by learning a multi-node amplify-and-forward cooperative environment with time-varying Rayleigh fading channels. The advantages of QL-RSA are that it is less complex, requires less channel feedback information and it is distributed in a multiple-sources environment as it provides each source a self-learning capability to find the optimal relay without exchanging information with other source nodes.

Robust signal recognition algorithm based on machine learning in heterogeneous networks

There are various heterogeneous networks for terminals to deliver a better quality of service. Signal system recognition and classification contribute a lot to the process. However, in low signal to noise ratio (SNR) circumstances or under time-varying multipath channels, the majority of the existing algorithms for signal recognition are already facing limitations. In this series, we present a robust signal recognition method based upon the original and latest updated version of the extreme learning machine (ELM) to help users to switch between networks. The ELM utilizes signal characteristics to distinguish systems. The superiority of this algorithm lies in the random choices of hidden nodes and in the fact that it determines the output weights analytically, which result in lower complexity. Theoretically, the algorithm tends to offer a good generalization performance at an extremely fast speed of learning. Moreover, we implement the GSM/WCDMA/LTE models in the Matlab environment by using the Simulink tools. The simulations reveal that the signals can be recognized successfully to achieve a 95% accuracy in a low SNR (0 dB) environment in the time-varying multipath Rayleigh fading channel.

A Receiver Structure for Frequency-Flat Time-Varying Rayleigh Channels and Performance Analysis

This paper proposes a wavelet based receiver structure for frequency-flat time-varying Rayleigh channels, consisting of a receiver front-end followed by a Maximum A-Posteriori (MAP) detector. Discretization of the received continuous time signal using filter banks is an essential stage in the front-end part, where the Fast Haar Transform (FHT) is used to reduce complexity. Analysis of our receiver over slow-fading channels shows that it is optimal for certain modulation schemes. By comparison with literature, it is shown that over such channels our receiver can achieve optimal performance for Time-Orthogonal modulation. Computed and Monte-Carlo simulated performance results over fast time-varying Rayleigh fading channels show that with Minimum Shift Keying (MSK), our receiver using four basis functions (filters) lowers the error floor by more than one order of magnitude with respect to other techniques of comparable complexity. Orthogonal Frequency Shift Keying (FSK) can achieve the same performance as Time-Orthogonal modulation for the slow-fading case, but suffers some degradation over fast-fading channels where it exhibits an error floor. Compared to MSK, however, Orthogonal FSK provides better performance.

Multiantenna Spectrum Sensing in the Presence of Multiple Primary Users over Fading and Nonfading Channels

The basis of this paper is Wei and Tirkkonen, 2012, in which expressions for the key performance metrics of the sphericity test applied to the multiantenna cooperative spectrum sensing of multiple primary transmitters in cognitive radio networks over nonfading channels are provided. The false alarm and the detection probabilities were derived in Wei and Tirkkonen, 2012, based on approximations obtained by matching the moments of the test statistics to the Beta distribution. In this paper we show that the model adopted in Wei and Tirkkonen, 2012, does not apply directly to fading channels, yet being considerably inaccurate for some system parameters and channel conditions. Nevertheless, we show that the original expressions from Wei and Tirkkonen, 2012, can be simply and accurately applied to a modified model that considers fixed or time-varying channels with any fading statistic. We also analyze the performance of the sphericity test and other competing detectors with a varying number of primary transmitters, considering different situations in terms of the channel gains and channel dynamics. Based on our results, we correct several interpretations from Wei and Tirkkonen, 2012, in what concerns the performance of the detectors, both over a fixed-gain additive white Gaussian noise channel and over a time-varying Rayleigh fading channel.

Differential dual‐hop relaying under user mobility

This study studies dual-hop amplify-and-forward relaying system employing differential encoding and decoding over time-varying Rayleigh-fading channels. First, the convectional ‘two-symbol’ differential detection (CDD) is theoretically analysed in terms of the bit error rate. The obtained analysis clearly shows that performance of two-symbol differential detection severely degrades in fast-fading channels and reaches an irreducible error floor at high signal-to-noise ratio region. To overcome the error floor experienced with fast-fading, a practical suboptimal ‘multiple-symbol’ detection (MSD) is designed and its performance is theoretically analysed. The analyses of CDD and MSD are verified and illustrated with simulation results under different fading scenarios. Specifically, the obtained results show that the proposed MSD can significantly improve the system performance in fast-fading channels.

Performance of Selection Combining for Differential Amplify-and-Forward Relaying Over Time-Varying Channels

Selection combining (SC) at the destination for differential amplify-and-forward (AF) relaying is attractive as it does not require channel state information as compared to the semi maximum-ratio-combining (semi-MRC) while delivering close performance. Performance analysis of the SC scheme was recently reported but only for the case of slow-fading channels. This paper provides an exact average bit-error-rate (BER) of the SC scheme over a general case of time-varying Rayleigh fading channels and when the DBPSK modulation is used together with the non-coherent detection at the destination. The presented analysis is thoroughly verified with simulation results in various fading scenarios. It is shown that the performance of the system is related to the auto-correlation values of the channels. It is also shown that the performance of the SC method is very close to that of the semi-MRC method and the existence of an error floor at high signal-to-noise ratio region is inevitable in both methods. The obtained BER analysis for the SC method can also be used to approximate the BER performance of the MRC method, whose exact analytical evaluation in time-varying channels appears to be difficult.

SER performance of enhanced spatial multiplexing codes with ZF/MRC receiver in time-varying Rayleigh fading channels.

We propose enhanced spatial multiplexing codes (E-SMCs) to enable various encoding rates. The symbol error rate (SER) performance of the E-SMC is investigated when zero-forcing (ZF) and maximal-ratio combining (MRC) techniques are used at a receiver. The proposed E-SMC allows a transmitted symbol to be repeated over time to achieve further diversity gain at the cost of the encoding rate. With the spatial correlation between transmit antennas, SER equations for M-ary QAM and PSK constellations are derived by using a moment generating function (MGF) approximation of a signal-to-noise ratio (SNR), based on the assumption of independent zero-forced SNRs. Analytic and simulated results are compared for time-varying and spatially correlated Rayleigh fading channels that are modelled as first-order Markovian channels. Furthermore, we can find an optimal block length for the E-SMC that meets a required SER.

Precoded Spatial Multiplexing MIMO Systems in Time- Varying Fading Channel

Conventional precoded spatial multiplexing multiple-input multiple-output (MIMO) systems using limited feedback are mainly based on the notion of time invariant channels throughout transmission. Consequ-encely, the precoding matrix can be found during the training symbols and used over the subsequent data symbols. In this paper, a more practical system where the channel varies from one block of symbols to another is considered. In such scenario, the precoding matrix designed at the receiver based on the previous training symbols becomes outdated, which results in significant system performance degradation. In order to avoid this problem, and reduce performance degradation, we propose the use of a Kalman filter linear predictor at the receiver to provide the transmitter with the precoding matrix for the next block of symbols. The performance of this method is assessed using computer simulation, and the obtained results for the proposed channel prediction demonstrate improved bit error rate performance for time-varying Rayleigh fading channels. 