Frequency-nonselective Rayleigh Fading Channel Research Articles

Low-Density Spreading Design Based on an Algebraic Scheme for NOMA Systems

In this letter, a code-domain nonorthogonal multiple access (NOMA) technique based on an algebraic design is studied. We propose an improved low-density spreading (LDS) sequence design based on projective geometry. In terms of its bit error rate (BER) performance, our proposed improved LDS code set outperforms the existing LDS designs over the frequency-nonselective Rayleigh fading and additive white Gaussian noise (AWGN) channels. We demonstrated that achieving the best BER depends on the minimum distance.

Tight Upper Bound Performance of Full-Duplex MIMO-BICM-IDD Systems in the Presence of Residual Self-Interference

In this paper, we derive a tight upper bound on the performance of a coded full-duplex multiple-input multiple-output (MIMO)-based bidirectional transceiver. Iterative detection and decoding (IDD) are proposed to suppress the residual self-interference (SI) remaining after applying different stages of SI cancellation. IDD comprises an adaptive minimum mean-squared error filter with log-likelihood ratio demapping, while the soft decoder by using soft-in soft-out decoding utilizes the maximum a posteriori algorithm. Furthermore, bit-interleaved coded modulation is considered in the presence of additive white Gaussian noise over MIMO frequency non-selective Rayleigh fading channels. Simulation results are presented to demonstrate the bit-error rate (BER) performance as a function of the signal-to-noise ratio showing a close match to the SI-free case for the proposed system. Furthermore, we validate our results by deriving a tight upper bound on the performance of the proposed system using rate-1/2 convolutional codes together with $M$ -ary quadrature amplitude modulation, which asymptotically exhibits a close agreement with the simulated BER performance. Moreover, extrinsic information transfer chart analysis is used to investigate the convergence behavior of the proposed IDD receiver and to determine the number of iterations required for this convergence.

Modelling, analysis and performance comparison of two direct sampling DCSK receivers under frequency non‐selective fading channels

Two direct sampling correlator-type receivers for differential chaos shift keying (DCSK) communication systems under frequency non-selective fading channels are proposed. These receivers operate based on the same hardware platform with different architectures. In the first scheme, namely sum-delay-sum (SDS) receiver, the sum of all samples in a chip period is correlated with its delayed version. The correlation value obtained in each bit period is then compared with a fixed threshold to decide the binary value of recovered bit at the output. On the other hand, the second scheme, namely delay-sum-sum (DSS) receiver, calculates the correlation value of all samples with its delayed version in a chip period. The sum of correlation values in each bit period is then compared with the threshold to recover the data. The conventional DCSK transmitter, frequency non-selective Rayleigh fading channel, and two proposed receivers are mathematically modelled in discrete-time domain. The authors evaluated the bit error rate performance of the receivers by means of both theoretical analysis and numerical simulation. The performance comparison shows that the two proposed receivers can perform well under the studied channel, where the performances get better when the number of paths increases and the DSS receiver outperforms the SDS one.

Performance of a Double Uniform Circular Array in a Three-Dimensional Environment

ABSTRACTIn this paper, an array configuration with double uniform circular arrays (DUCAs) is provided in a three-dimensional environment with the goal of optimizing compact multiantenna user terminals. The DUCA extends the general two-dimensional multiantenna model to three-dimensional space. To accurately consider the spatial fading correlation (SFC) between antennas and the capacity of multiple input multiple output (MIMO) multipath channels, this paper uses the equivalent network model under mutual coupling (MC). Furthermore, the methods for calculating SFC with and without MC and capacity for a frequency non-selective Rayleigh fading channel are given. For simplicity, the azimuth and elevation angle distributions are assumed to be uniform. Simulation results show that the DUCA provided by this paper can decrease SFC between antennas, hence increasing capacity compared with UCAs of the same size. Taking MC into consideration, capacity will increase when the radius of the circle is smaller than . The parameters of arrival signals have a significant impact on the system performance as well. This investigation expands the application of a statistical channel model and optimizes the study of the terminal antenna array.

Non-orthogonal Amplify and Forward Relay Selection Systems with Distributed Space–Time Trellis Coded Continuous Phase Modulation

Most of the works on cooperative systems with or without relay selection have focused on linear modulations such as phase shift keying and quadrature amplitude modulation. Whereas, continuous phase modulation (CPM) is a good alternative to these modulations due to its constant envelope property which enables us to use inexpensive and energy-efficient non-linear power amplifiers. In the literature, a few works are based on relaying systems with CPM. To the best of our knowledge, none exists with relay selection. In this paper, we propose single and multiple relay selection CPM schemes based on a new generalized relay selection criterion for non-orthogonal amplify and forward (AF) systems operating with various time sharing protocols. In particular, using the proposed criterion, the best relay or the best two relays over a set of four available relays is/are selected. Error performances of the non-orthogonal AF relay selection systems and their counterparts are compared over frequency non-selective quasi-static Rayleigh fading channels using Viterbi algorithm at the destination terminal. Our numerical results present superiority of the proposed non-orthogonal relay selection systems.

Classes of sum-of-cisoids processes and their statistics for the modeling and simulation of mobile fading channels

In this paper, we present a fundamental study on the stationarity and ergodicity of eight classes of sum-of-cisoids (SOC) processes for the modeling and simulation of frequency-nonselective mobile Rayleigh fading channels. The purpose of this study is to determine which classes of SOC models enable the design of channel simulators that accurately reproduce the channel’s statistical properties without demanding information on the time origin or the time-consuming computation of an ensemble average. We investigate the wide-sense stationarity, first-order stationarity of the envelope, mean ergodicity, and autocorrelation ergodicity of the underlying random processes characterizing the different classes of stochastic SOC simulators. The obtained results demonstrate that only the class of SOC models comprising cisoids with constant gains, constant frequencies, and random phases is defined by a set of stationary and ergodic random processes. The analysis presented here can easily be extended with respect to the modeling and simulation of frequency-selective single-input single-output (SISO) and multiple-input multiple-output channels. For the case of frequency-selective SISO channels, we investigate the stationarity and ergodicity in both time and frequency of 16 different classes of SOC simulation models. The findings presented in this paper can be used in the laboratory as guidelines to design efficient simulation platforms for the performance evaluation of modern mobile communication systems.

Exact symbol and bit error probabilities of linearly modulated signals with maximum ratio combining diversity in frequency non-selective Rician and Rayleigh fading channels

The exact symbol and bit error probabilities of linearly modulated signals in frequency non-selective Rician fading channels with Lth diversity branches are derived, where coherent detection with maximum ratio combining (MRC) is used at the receiver. For performance evaluation, the multiplicative distortion is combined with the additive Gaussian noise and form an additive noise is formed. This method allows computing the exact symbol and bit error probabilities of M-ary phase shift keying (M-PSK), M-ary quadrature amplitude modulation (M-QAM), M-ary amplitude modulation (M-AM) and M-ary amplitude modulation phase modulation (M-AMPM) for any arbitrary bit mappings. The results contain several versions of one simple integral. The error probabilities are also obtained for Rayleigh channel, which is a special case of Rice channel. Further, the results for Nakagami-m channel with the integer parameter are found. The results quite match with the previous ones while having simple forms. Also, for some unsolved cases, the exact error probabilities are presented. Simulations are carried out to verify the analytical evaluations.

Repeat-punctured superorthogonal convolutional turbo codes on AWGN and flat Rayleigh fading channels

Repeat-punctured turbo codes, an extension of the conventional turbo-coding scheme, has shown a significant increase in bit-error rate performance at moderate to high signal-to-noise ratios for short frame lengths. Superorthogonal convolutional turbo codes (SCTC) makes use of superorthogonal signals to improve the performance of the conventional turbo codes and a coding scheme that applies the repeat-punctured technique into SCTC has shown to perform better. We investigated two new low-rate coding schemes, repeat-punctured superorthogonal convolutional turbo codes (RPSCTC) and dual-repeat-punctured superorthogonal convolutional turbo codes (DRPSCTC), that make use of superorthogonal signaling, together with repetition and puncturing, to improve the performance of SCTC for reliable and effective communications. Simulation results in the additive white Gaussian noise (AWGN) channel and the frequency non-selective Rayleigh fading channel are presented together with analytical bounds of bit error probabilities, derived from transfer function bounding techniques. From the simulation results and the analytical bounds presented, it is evident that RPSCTC and DRPSCTC offer a more superior performance than SCTC in the AWGN channel, as well as in flat Rayleigh non-line-of-sight fading channels. The distance spectrum is also presented for the new schemes and accounts for the performance improvement rendered in simulations. It is important to note that the improved performance that SCTC, and consequently RPSCTC and DRPSCTC, exhibit is achieved at the expense of bandwidth expansion and complexity and would be ideal for power-limited satellite communication links or interference-limited systems.

Repeat-punctured superorthogonal convolutional turbo codes on AWGN and flat Rayleigh fading channels

Repeat-punctured turbo codes, an extension of the conventional turbo-coding scheme, has shown a significant increase in bit-error rate performance at moderate to high signal-to-noise ratios for short frame lengths. Superorthogonal convolutional turbo codes (SCTC) makes use of superorthogonal signals to improve the performance of the conventional turbo codes and a coding scheme that applies the repeat-punctured technique into SCTC has shown to perform better. We investigated two new low-rate coding schemes, repeat-punctured superorthogonal convolutional turbo codes (RPSCTC) and dual-repeat-punctured superorthogonal convolutional turbo codes (DRPSCTC), that make use of superorthogonal signaling, together with repetition and puncturing, to improve the performance of SCTC for reliable and effective communications. Simulation results in the additive white Gaussian noise (AWGN) channel and the frequency non-selective Rayleigh fading channel are presented together with analytical bounds of bit error probabilities, derived from transfer function bounding techniques. From the simulation results and the analytical bounds presented, it is evident that RPSCTC and DRPSCTC offer a more superior performance than SCTC in the AWGN channel, as well as in flat Rayleigh non-line-of-sight fading channels. The distance spectrum is also presented for the new schemes and accounts for the performance improvement rendered in simulations. It is important to note that the improved performance that SCTC, and consequently RPSCTC and DRPSCTC, exhibit is achieved at the expense of bandwidth expansion and complexity and would be ideal for power-limited satellite communication links or interference-limited systems.

Performance analysis of a noise-normalized FFH/MFSK receiver over Rayleigh fading channels with partial-band noise jamming

Fast frequency hopping can reduce the degradation caused by interference. The performance of noise-normalized fast frequency-hopped M-ary orthogonal frequency-shift-keying (FFH/MFSK) receivers over frequency nonselective Rayleigh fading channels with partial-band noise jamming is analyzed. Instead of numerical evaluation, a closed-form error probability expression is given based on the theory of complex variables. The simulation results validate the analytical results. It is shown that there is an optimum diversity order and the system performance gets better with an increase in the modulation order.

QPSK DS-CDMA System over Rayleigh Channel with a Randomly-Varying Frequency Narrow-Band Interference: Frequency Tracking Analysis

This paper analyses frequency tracking characteristics of a complex-coefficient adaptive infinite-impulse response (IIR) notch filter used for suppression of narrow-band interference (NBI) with a randomly-varying frequency in a quadriphase shift keying (QPSK) modulated direct-sequence code-division multiple-access (DS-CDMA) communication system. The QPSK DS-CDMA signals are transmitted over a frequency non-selective Rayleigh fading channel. The analysis is based on a first-order real-coefficient difference equation with respect to steady-state instantaneous frequency tracking error from which a closed-form expression that relates frequency tracking mean square error (MSE) with number of DS-CDMA active users and NBI power is obtained. Closed-form expressions for optimum notch bandwidth coefficient and step size constant that minimize the frequency tracking MSE are also derived. Computer simulations are included to substantiate the accuracy of the analyses.

Performance of Binary Phase Shift Keying (BPSK) and Quartenary Phase Shift Keying (QPSK) Signalling Schemes in Fast and Frequency Non-Selective Rayleigh Fading Channel with a Decision Feedback Equalizer (DFE) at the Receiver

In this paper, we study the performance of Binary phase shift keying (BPSK) and Quartenary phase shift keying (QPSK) modulation signalling over fast and frequency non-selective Rayleigh fading channel with mobile digital communication and usually a decision feedback equalizer (DFE) at the receiver. Mobile communication is generally a complex process in which the input modulated signals propagate to the receiver over many different paths resulting in what is known as multipath propagation. Its main effects are delay spread and Doppler spread. These effects result in the channel being classified as fast and frequency non selective. Performances in terms of Bit Error Rate (BER) with respect to the Signal-to-Noise Ratio (SNR) at different selected velocities of 10, 40, 70 and 100km/hr are investigated with Adaptive Equalizer. Simulation results are obtained using MATLAB 7.0 programming language. The results indicate that at all the velocities considered; there is an excessive degradation in the BER performance due to fading with both the BPSK and QPSK modulation schemes. However, the BER improves for BPSK modulation signalling scheme when a decision feedback equalizer is used at the receiver

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.

Coordinate Interleaved Orthogonal Design with Two Transmit Antennas in Spatially Correlated Rayleigh Fading Channels: Symbol-Error Rate and Diversity Order

Full-diversity transmission for space-time block codes (STBCs) with multiple transmit antennas can be achieved by using coordinate interleaved orthogonal designs (CIODs). To effectively evaluate the performance of CIODs, we derive union upper and lower bounds on the symbol-error rate (SER) and a corresponding asymptotic diversity order of symmetric structured CIOD, in particular, with two transmit antennas over quasi-static spatially uncorrelated/correlated frequency-nonselective Rayleigh fading channels. Some numerical results are provided to verify our analysis.

Adaptive IIR Filters for Single Interference Suppression in a BPSK DS CDMA System In Rayleigh Fading Channel

In this paper, effect of a single narrow-band interference (NBI) on bit error rate (BER) performance for a binary phase shift keying (BPSK) synchronous direct-sequence code-division multiple access (DS CDMA) communication system operating in a frequency nonselective Rayleigh fading channel is analyzed. Second-order adaptive infinite impulseresponse (IIR) notch filters with plain gradient algorithm (GA) for suppression of NBI in the DS CDMA system are proposed. A general closed-form BER expression for the DS CDMA system with NBI suppression second order adaptive IIR notch filters is derived based on the standard Gaussian approximation (SGA) method. BER expressions are then derived for the allpass filter-based adaptive IIR notch filter and adaptive IIR notch filter with constrained poles and zeros, the two structures that are commonly found in literature. It is observed that both adaptive IIR notch filter structures exhibit comparable BER performance. Extensive computer simulation results are presented to verify the accuracy and limitations of the analysis.

Low-complexity iterative channel estimation for serially concatenated systems over frequency-nonselective Rayleigh fading channels

A low-complexity iterative maximum a posteriori (MAP) channel estimator is proposed whose complexity increases linearly with the symbol alphabet size 'M. Prediction-based MAP channel estimation is not appropriate with a high-order prediction filter or a large modulation alphabet size, since the computational complexity increases with ML , where L is the predictor order. In contrast, the proposed channel estimator has a constant number of trellis states regardless of the prediction filter order, and is shown to provide comparable error performance to the prediction-based MAP estimator

How Good Is PSK for Peak-Limited Fading Channels in the Low-SNR Regime?

This paper investigates the achievable information rate of phase-shift keying (PSK) over frequency nonselective Rayleigh and Rician fading channels without channel state information (CSI). The fading process exhibits general temporal correlation characterized by its spectral density function. We consider both discrete-time and continuous-time channels, and find their asymptotics at low signal-to-noise ratio (SNR). Compared to known capacity upper bounds under peak constraints, these asymptotics lead to negligible rate loss in the low-SNR regime for slowly time-varying fading channels. We further specialize to case studies of Gauss-Markov and Clarke's fading models

Space-Time Block Coded Joint Transmit/Receive Diversity in a Frequency-Nonselective Rayleigh Fading Channel

Antenna diversity is an effective technique for improving the transmission performance in a multi-path fading channel. Recently, transmit diversity has been attracting much attention since it can alleviate the complexity problem of the mobile terminals. Joint transmit diversity/receive diversity achieves a much improved transmission performance. In this paper, we propose a new space-time block coding algorithm for joint transmit/receive diversity, which requires the channel state information (CSI) only at the transmitter side. Unlike the conventional space-time transmit diversity (STTD), the space-time block coded joint transmit/receive diversity (STBC-JTRD) can use arbitrary number of transmit ; antennas, while the number of receive antennas is limited to 4. STBC-JTRD achieves a larger diversity gain than joint STTD/receive antenna diversity. The bit error rate (BER) analysis in a frequency-nonselective Rayleigh fading channel is presented. The BER performance is evaluated and is confirmed by the computer simulation.

Linear receivers for the multiple-input multiple-output multiple-access channel

We consider a multiuser multiple-input multiple-output (MIMO) communication system using code-division multiple access (CDMA) and multiuser detection to discriminate the different users. Our focus is on the CDMA uplink of a frequency-nonselective Rayleigh fading channel. We study two types of receivers: joint receivers, which address simultaneously both spatial and multiple-access interference; and separate receivers, addressing the two types of interference individually. This approach allows assessing the benefits of adding MIMO processing capabilities to existing multiuser single-input single-output systems. For both receiver types, we analyze solutions based on linear (matched filter, decorrelator, minimum mean-square error) and maximum-likelihood receivers. For all the receivers considered, we provide closed-form expressions (as expectations of given functions) of the resulting pairwise error probabilities. Performance results are obtained in terms of frame-error rate versus E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> , following two different approaches. An analytic approach using large-system asymptotic methods, whereby the system parameters (number of users and antennas, spreading gain) are assumed to grow to infinity with finite limiting ratios. A computer-simulation approach is used to illustrate the differences between asymptotic and simulation results

The impact of fading correlation on the error performance of MIMO systems over Rayleigh fading channels

This paper analyzes the impact of receive fading correlation on the error performance of a multiple-input multiple-output (MIMO) system that employs a zero-forcing detection scheme over frequency-nonselective Rayleigh fading channels. Error rate expressions as a function of the eigenvalues of the fading correlation matrix and the number of transmit and receive antennas are derived. Numerical results indicate that MIMO systems are resistant to receive fading correlation.