Flat Nakagami Research Articles

Information Freshness in Uplink OFDM Based Multiple Access Networks in Flat Nakagami-$m$ Fading Channels

In flat Nakagami-<inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> fading channels, we study the total information freshness maximization problem for an uplink orthogonal frequency division multiplexing (OFDM) based multiple access network. Without channel state information, each user transmits the freshest version of the file to the base station for information updating using the OFDM scheme. Considering the actual transmission durations, we theoretically derive the analytical expression for average information freshness. Furthermore, we propose an alternating optimization algorithm to solve the total information freshness maximization problem. In the proposed algorithm, the bandwidth allocation problem is solved using the majorization-minimization based iterative algorithm and transmission rate optimization problem is solved by the bisection search. Numerical results illustrate that our proposed updating scheme is superior to the rate proportional and rate inverse proportional updating schemes.

On the Error and Outage Performance of Decode-and-Forward Cooperative Selection Diversity System With Correlated Links

A cooperative diversity system improves the communication reliability and throughput in a multipath fading environment with the help of relay nodes. We consider a cooperative diversity system with a source (S), a decode-and-forward relay (R), and a selection-combining-enabled destination (D). In this paper, we derive the exact end-to-end symbol error probability (SEP) for $M$ -ary phase-shift keying (MPSK) signaling using a paired error approach and differential binary phase-shift keying (DBPSK) signaling over correlated, nonidentical, slow, and flat Nakagami- $m$ fading channels by assuming the correlation between SD–RD, SR–SD, and SR–RD fading channels. In addition, we perform the exact outage probability analysis for the same scenario. Furthermore, we provide the asymptotic expressions for SEP and outage probability by removing the infinite-series terms to investigate the diversity order. In a nutshell, the numerical results reveal that the SR–RD correlated channel scenario outperforms the uncorrelated channel scenario in terms of SEP. In addition, SEP performance degradation is observed in the case of other correlated channel scenarios compared with the uncorrelated channel scenario. Moreover, marginal performance improvement in outage probability is observed in the low-signal-to-noise-ratio (SNR) regime of the SR–RD correlated channel scenario compared with the uncorrelated channel scenario. Finally, Monte Carlo simulations are performed to validate the theoretical results.

Bit error rate analysis of chaotic cognitive radio system over slow fading channels

In this paper, we analyze the bit error rate (BER) performance of a chaotic cognitive radio (CCR) system, which enjoys benefits of high security provided by a chaotic communication system and high flexibility in non-contiguous spectrum access offered by an overlay cognitive radio (CR) system. In the proposed CCR system, the chaotic sequence is generated in the frequency domain instead of in the time domain, hence enabling non-contiguous spectrum access. We hereby derive the bit error rate expressions of CCR systems over additive white Gaussian noise (AWGN) channel and slow flat Rayleigh, Rician, and Nakagami fading channels. Specifically, we use the probability distribution of the chaotic map to evaluate the energy distribution of the transmitted signals over the identified non-continuous subcarrier bands, and then apply the definite integral representation of Q-function to calculate the bit error rate. The results from theoretical analysis and numerical simulations are compared, demonstrating an excellent agreement between the two approaches.

Closed-Form Error Analysis of AF-CARQ with CSI-Assisted Relay over Nakagami- $$m$$ m Fading Channels

This paper presents a new Amplify-and-Forward Cooperative Automatic Repeat reQuest protocol with channel state information-assisted relay which is more suitable for the only-read access networks. The channels of any pair of terminations are quasi static flat Nakagami- $$m$$ m fading channels, which are mutually independent and non-identically distributed. Assuming that the coherent equal gain combining is adopted to combine the retransmitted signals from the same link at the destination and selective combining is adopted to the signals from different links. Based on the approximation of product of Nakagami- $$m$$ m variables, we obtain the end-to-end signal-to-noise rate of any link. The closed-form expression of the average bit error rate for several modulation schemes is obtained by analyzing cumulative distribution function (CDF) and Gaussian Q-function. Then we analyze the amount of fading of the fading channels by the $$n$$ n order moment which is obtained by CDF. Numerical simulation results show that the relay node can resist the fading of system effectively comparing with the system without relay node. And with the increasing of the number of transmission, the performance advantage of relay link is more and more obviously. It is better to let the maximum transmission time $$F=6$$ F = 6 , which is very useful for improving the transmission efficiency of the truncated ARQ system. The maximum reduction of amount of fading can be reached when $$t=3$$ t = 3 , if the total number of transmission is $$f=6$$ f = 6 . The number of bits in the frame should not have too big.

BER Performance of OFDM-BPSK Over Nakagami Fading Channels

paper, the Bit Error Rate (BER) performance of OFDM -BPSK system over flat Nakagami fading channels is analyzed. This model is versatile enough to represent fading. Here our approach is based on decomposition of Nakagami random variable into orthogonal random variables with Gaussian distribution envelopes. Finally simulations of OFDM signals are carried with Nakagami faded signal to understand the effect of channel fading and to obtain optimum value of m, n and q based on BER and SNR.

Performance analysis of PSK systems with phase error in fading channels: A survey

Communication system designers need to formulate an accurate and thoroughly reproducible error model for wireless mobile channels in order to assess the quality of communication with different modulation schemes. The task is relatively easy when an ideal situation is assumed, and is covered exhaustively in standard text books. However, the random time-varying nature of radio propagation renders estimation of different channel state information (CSI) very difficult and when these non-idealities (e.g. imperfect phase/frequency/timing information) are considered, the formulation complexity increases manifold. In this paper, we have set our attention on phase shift keying (PSK), which suffers mostly from phase synchronization error when proper CSI is not available at the receiver. The article surveys various error modelling methods for a PSK system operating over a slow flat Nakagami- m distributed wireless fading channel perturbed with additive white Gaussian noise (AWGN) in the presence of phase error. The phase distortions are considered to be random, unbiased, i.e. having zero mean, and may be represented by either Gaussian or Tikhonov distribution. We also provide a novel approach to classify these schemes that are surveyed, and summarize the major contributions of related works. Further, we identify the method that requires lesser mathematical operations and thus proves to be less complex, more stable and accurate than others. Apart from this, simple alternative approaches for calculating analytical bit error rate (BER) through Hermite’s method of integration for Gaussian distributed phase error and through moment generating function (MGF) for Tikhonov distributed phase error have been proposed. Both of these methods have wider applicability, are able to furnish reproducible results, and show significant improvement in accuracy regarding theoretical BER calculation as seen from the graphical comparisons. Extensive Monte Carlo simulations were performed to validate the theoretical results.

A Simple Exact Error Rate Analysis for DS-CDMA with Arbitrary Pulse Shape in Flat Nakagami Fading

A simple exact error rate analysis is presented for random binary direct sequence code division multiple access (DS-CDMA) considering a general pulse shape and flat Nakagami fading channel. First of all, a simple model is developed for the multiple access interference (MAI). Based on this, a simple exact expression of the characteristic function (CF) of MAI is developed in a straight forward manner. Finally, an exact expression of error rate is obtained following the CF method of error rate analysis. The exact error rate so obtained can be much easily evaluated as compared to the only reliable approximate error rate expression currently available, which is based on the Improved Gaussian Approximation (IGA).

Exact Error Rate Analysis for Pulsed DS- and Hybrid DS/TH-CDMA in Nakagami Fading

Exact bit error probabilities (BEP) are derived in closed-form for binary pulsed direct sequence (DS-) and hybrid direct sequence time hopping code division multiple access (DS/TH-CDMA) systems that have potential applications in ultra-wideband (UWB) communications. Flat Nakagami fading channel is considered and the characteristic function (CF) method is adopted. An exact expression of the CF is obtained through a straightforward method, which is simple and good for any arbitrary pulse shape. The CF is then used to obtain the exact BEP that requires less computational complexity than the method based on improved Gaussian approximation (IGA). It is shown under identical operating conditions that the shape of the CF, as well as, the BEP differs considerably for the two systems. While both the systems perform comparably in heavily faded channel, the hybrid system shows better BEP performance in lightly-faded channel. The CF and BEP also strongly depend on chip length and chip-duty that constitute the processing gain (PG). Different combinations of the parameters may result into the same PG and the BEP of a particular system for a constant PG, though remains nearly constant in a highly faded channel, may vary substantially in lightly-faded channel. A comparison of the results from the exact method with those from the standard Gaussian approximation (SGA) reveals that the SGA, though accurate for both the systems in highly-faded channel, becomes extremely optimistic for low-duty systems in lightly-faded channel. The SGA also fails to track several other system trade-offs.

Closed-Form Expressions for the Exact Symbol Error Probability of 32-Cross-QAM in AWGN and in Slow Nakagami Fading

Novel closed-form exact expressions for the average symbol error probability of 32-cross-QAM in an additive white Gaussian noise channel and in a slow, flat Nakagami fading channel with L-branch maximal ratio combining diversity are derived

An Exact Error Analysis for Low-Duty Pulsed DS-CDMA Systems in Flat Nakagami Fading

Based on the characteristic function method, an exact error analysis is presented for low-duty pulsed direct sequence code division multiple access (DS-CDMA) systems in flat Nakagami fading channel. The presented method is simple and good for any arbitrary pulse shape. The computational involvement of the method is simpler than the method based on improved Gaussian approximation (IGA), which is the only reliable method currently available for calculating error probabilities of such systems

Time-Hopping Multicarrier Code-Division Multiple Access

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A time-hopping multicarrier code-division multiple-access (TH/MC-CDMA) scheme is proposed and investigated. In the proposed TH/MC-CDMA, each information symbol is transmitted by a number of time-domain pulses with each time-domain pulse modulating a subcarrier. The transmitted information at the receiver is extracted from one of the, say, <formula formulatype="inline"><tex>$M$</tex></formula> possible time-slot positions, i.e., assuming that <formula formulatype="inline"><tex>$M$</tex></formula>-ary pulse-position modulation is employed. Specifically, in this paper, we concentrate on the scenarios such as system design, power spectral density (PSD) and single-user-based signal detection. The error performance of the TH/MC-CDMA system is investigated when each subcarrier signal experiences flat Nakagami-<formula formulatype="inline"><tex>$m$</tex></formula> fading in addition to additive white Gaussian noise. According to our analysis and results, it can be shown that the TH/MC-CDMA signal is capable of providing a near ideal PSD, which is flat over the system bandwidth available, while decreasing rapidly beyond that bandwidth. Explicitly, signals having this type of PSD are beneficial to both broadband and ultrawide-bandwidth communications. Furthermore, our results show that when optimum user address codes are employed, the single-user detector considered is near–far resistant, provided that the number of users supported by the system is lower than the number of subcarriers used for conveying an information symbol. </para>

Harmonic Mean and End-to-End Performance of Transmission Systems With Relays

Closed-form expressions for the statistics of the harmonic mean of two independent and identically distributed gamma variates are presented. The probability density function of the harmonic mean of two F variates is also derived. These statistical results are then applied to study the performance of wireless communication systems with nonregenerative relays over flat Nakagami fading channels. More specifically, outage probability formulas for noise-limited systems as well as systems affected by interference are obtained. Furthermore, general expressions for average bit-error rates are also derived. Finally, comparisons between regenerative and nonregenerative systems are presented. Numerical results show that the former systems clearly outperform the latter ones for low average signal-to-noise ratios (SNRs). They also show that the two systems have similar performance at high average SNRs.

Performance analysis of adaptive MMSE reception for DS-CDMA in flat Nakagami fading channels

An efficient method is derived in this paper to obviate the integral involved in the performance analysis of the minimum mean square error (MMSE) detector for direct-sequence code-division multiple-access (DS/CDMA) systems in fading environments. The new method is shown to significantly reduce the necessary computational load for the performance analysis of the MMSE detector. We then examine the behavior of the MMSE detector in flat Nakagami fading channels.