Simple Analysis for Average BER of Orthogonal Signals in Nonidentical Rician Channels with Improved-Gain Noncoherent Diversity Reception

This letter proposes a new noncoherent combiner, which we call the noncoherent weighted branches combiner (NC-WBC), to mitigate the disadvantages of the conventional noncoherent equal-gain combiner (NC-EGC) in nonidentically distributed Rician fading channels. It is shown that, unlike those of the NC-EGC, the NC-WBC results in simple closed-form expression for average bit error rate (BER) of the binary orthogonal signaling scheme. The results also show that the NC-WBC provides performance improvement, and alleviates the noncoherent combining loss of the NC-EGC. The theoretical development is verified by simulation results     

Improved-performance noncoherent weighted-coefficients diversity combiner for DPSK and NC-FSK signals in nonidentical Nakagami fading channels

It is well-known that noncoherent equal-gain combining (NC-EGC) is the simplest combining technique for noncoherent and differentially coherent communication systems. However, for nonidentical Nakagami-m channels (channels having nonuniform multipath intensity profile (MIP) and/or arbitrary non-integer fading parameters), the use of NC-EGC has three main disadvantages. First, its performance serves as a lossy upper bound to that of the optimum diversity combiner. Second, it results in complicated expressions for the system average error performance. Third, it incurs noncoherent combining loss (does not aid the use of diversity) at relatively low average signal-to-noise ratio (SNR). In this letter, we propose a modified version of the NC-EGC, which is a noncoherent combiner with weighting coefficients, to overcome the disadvantages of the conventional one. We show that this alternative combiner does provide improvements over the conventional N.C-EGC for all values of average SNRs, it does not incur any noncoherent combining loss, and it leads to a design of the receiver whose average error performance can be evaluated easily.     

Performance of Multiuser-Coded CDMA Systems With Transmit Diversity Over Nakagami- $m$ Fading Channels

The performance of a multiple-input–multiple-output (MIMO) code-division multiple-access (CDMA) system, using space–time spreading (STS), is analyzed over a frequency-flat Nakagami- $m$ fading channel. The convolutionally space–time coded system employs a decorrelator detector with $N = 2$ and $L$ antennas at the user side and base station (BS), respectively. Assuming independent Nakagami fading channels between transmit and receive antennas, we determine the probability density function (pdf) of the signal-to-interference-plus-noise ratio (SINR) at the output of the multiuser detector and after signal combining. Considering binary phase-shift keying (BPSK) transmission, we then evaluate the pairwise error probability and the corresponding bit-error-rate (BER) upper bounds over fast-fading channels. The derived error bounds, when compared to system simulations, are shown to be accurate at all signal-to-noise ratios (SNRs) of interest. Examining the asymptotic performance of the underlying space–time multiuser system, at high SNRs, we evaluate the overall diversity gain as a function of the number of transmit and receive antennas and the minimum free distance of the convolutional code.      

Performance Analysis of TDMA Relay Protocols Over Nakagami- $m$ Fading

Several time-division multiple-access (TDMA) cooperative wireless relay protocols and their performances have recently been developed by Nabar, Bolcskei, and Kneubuhler. Their work, however, is limited to an upper bound-based performance analysis for Rayleigh fading. We thus provide an exact analysis of two of their protocols in single-relay and multiple-relay networks over independent identically distributed (i.i.d.) Nakagami- $m$ fading channels. Our analysis is focused on an Alamouti-coded system with two-stage protocols, fixed-gain amplify-and-forward (AF) relays, and maximal ratio combiner (MRC) reception. The performance metrics are the capacity, the diversity order, and the symbol error rate (SER). The closed-form moment-generating function (MGF) of the total end-to-end signal-to-noise ratio (SNR) is derived. The MGF is then used to derive the diversity order and the SER of $M$-ary phase-shift keying ($M$-PSK) and $M$-ary quadrature amplitude modulation ($M$ -QAM). It is found that the end-to-end SNR for relaying with orthogonal channels is higher than that of nonorthogonal relay channels. The diversity order of a multiple-relay network ( $n$ relays) in a Nakagami-$m$ environment is shown to be $(n + 1)m$. The closed-form SER expressions for relay–destination links with high SNRs and static relay–destination links are derived. Numerical and simulation results are provided to verify the analysis.      

Two-Way Handshaking Circular Sequential $k$-Out-of- $n$ Congestion System

Many communication systems require a two-way, or three-way handshaking process to improve their dependability & authenticity in order to achieve a more successful operation. In this paper, we present a new two-way handshaking reliability model based upon threshold-based cryptography systems. Such systems require a two-way handshaking process to i) establish a group of participated servers in the first handshaking process, and ii) calculate a cipher with successfully connected servers collaboratively in the second handshaking process. When the servers are attempted, each server has three known connection probabilities in the following three states: i) successful, ii) breakdown, and iii) congested. These connection probabilities are unchanged in both handshaking processes. During the first handshaking process, we establish connections that more than servers are willing to participate. For the second handshaking process, the system becomes successful as soon as we can connect these servers successfully again. Because we need to connect servers successfully in the second handshaking process, we would rather connect additional servers besides the servers required to be connected successfully in the first handshaking process. This preference will minimize the chance that the system breaks down when fewer than servers can be reconnected successfully in the second handshaking process. We refer to this system as a Two-Way Handshaking Circular Sequential-out-of-Congestion (TWHCSknC) system. In this paper, we derived analytical formulas for the system's successful probability & average stop length, and we showed that the TWHCSknC system is a communication system with an efficient two-way handshaking process.     

Capacity Bounds for MIMO Nakagami- $m$ Fading Channels

This paper studies the ergodic capacity limits of multiple-input multiple-output (MIMO) antenna systems with arbitrary finite number of antennas operating on general fading environments. Through the use of majorization theory, we first investigate in detail the ergodic capacity of Nakagami- $m$ fading channels, for which we derive several ergodic capacity upper and lower bounds. We then show that a simple expression for the capacity upper bound is possible for high signal-to-noise ratio (SNR), which permits to analyze the impact of the channel fading parameter $m$ on the ergodic capacity. The asymptotic behavior of the capacity in the large-system limit in which the number of antennas at one or both side(s) goes to infinity, is also addressed. Results demonstrate that the capacity scaling laws for Nakagami-$m$ and Rayleigh-fading MIMO channels are identical. Finally, we employ the same technique to distributed MIMO (D-MIMO) systems undergoing composite log-normal and Nakagami fading, where we derive similar ergodic capacity upper and lower bounds. Monte Carlo simulation results are provided to verify the tightness of the proposed bounds.      

BER performance of DQPSK in Nakagami fading with selection diversity and maximal-ratio combining

A new expression for the average bit-error rate (BER) of differential quadrature phase-shift keying in slow frequency-nonselective Nakagami fading is derived for a space-diversity receiver having a cascade arrangement of L groups of M-branch selection combiners and an L-branch maximal-ratio combiner (MRC). This allows the use of a large number of antennas, for performance improvement, and a small number of M inputs to the combiners, for low complexity. The average BER performance of the cascade receiver is investigated for different fading severity conditions characterized by the Nakagami m factor, and compared with the conventional MRC receiver. As the fading gets less severe (m increases), performance improvement over the conventional MRC scheme is only noticeable for the larger range of average signal-to-noise ratio.     

Coherent detection of biorthogonal signals over Rayleigh fadingchannels

A practical coherent detection scheme for biorthogonal signals over Rayleigh fading channels is proposed. The proposed scheme improves the bit error rate (BER) performance compared to the noncoherent detection schemes for biorthogonal signals. It also outperforms the coherent and noncoherent detection schemes for orthogonal signals with comparable bandwidth efficiency. The BER performance for a Rayleigh fading channel with two path diversity combining is obtained by computer simulation. The results show that the required average signal-to-noise ratio per bit γ_b can be reduced by as much as 1.4 dB when we use this system in the CDMA cellular reverse link     

Microdiversity on Rician fading channels

The performance of an L-branch equal gain (EG) combiner on slow and nonselective Rician fading channels is analyzed. Two performance criteria are considered; the probability distribution of signal-to-noise power ratio (SNR) at the output of the EG combiner and the average bit error rate (BER). Matched filter receivers are considered for two binary modulation formats, coherent phase shift keying (CPSK) and noncoherent frequency shift keying (NCFSK). Results using both maximal ratio combining (MRC) and selection diversity combining (SC) are presented for comparison. Our results show that from a feasibility and practical tradeoffs point of view, the performance of an EG combiner may be as good as that of a MR combiner. The effects of gain unbalance between branches of the EG combiner on the probability distribution of SNR and on the bit error rates are also investigated. The Rician fading model may be used to model bath the microcellular environment and the mobile satellite fading channel. Hence, the results of this paper may be useful in both of these areas. Furthermore, in the development of the analysis, we present an efficient method for computing the distribution of sums of Rician random variables. This may be useful for other problems involving Rician fading. The suitability of modeling a Rician fading environment by a properly chosen Nakagami model is examined. A formula for determining the corresponding values of Rician parameter K and Nakagami parameter m is also assessed     

Post-detection diversity Nakagami fading channels with correlatedbranches

We derive a closed-form expression for the performance of the post-detection product detector combiner (PDC) operating on L correlated branches in Nakagami (1960) fading. We consider the 2-DPSK signaling scheme and nonselective slow fading. The average bit error rate (BER) obtained with this scheme is compared to the ideal predetection MRC, showing limited loss. Moreover, the post-detection PDC is shown to outperform the selection diversity combiner (SDC) under the considered case of Nakagami fading     

Performance Analysis and Design Criteria of BICM-ID With Signal Space Diversity for Keyhole Nakagami-$m$ Fading Channels

This paper generalizes the application bit-interleaved coded modulation with iterative decoding (BICM-ID) using signal space diversity (SSD) over keyhole Nakagami-$m$ fading channels. The tight union bound on the asymptotic error performance is first analytically derived. The near-optimal rotation matrix with respect to both the asymptotic performance and the convergence behavior is then determined. In particular, it is demonstrated that the suitable rotation matrix is the one that has 1) all entries equal in magnitude, 2) a high diversity order, and 3) a large minimum product of the ratios between squared distances to the power $m$ and log-squared distances to the power $m$ of the rotated constellation scaled by factors of signal-to-noise ratio (SNR) and the parameter $m$ . Various analytical and simulation results show that by employing SSD with a sufficiently large dimension, the error performance can closely approach that over an additive white Gaussian noise (AWGN) channel, even in the worst case of keyhole fading.      

Analysis of asynchronous FFH-MA systems with a hard-limited combining in Rayleigh fading

The bit error rate (BER) performance of the asynchronous fast frequency hopping multiple access (AFFH-MA) system with multiple hops per symbol is investigated considering the noncoherent M-ary frequency shift keying (MFSK) modulation and hard-limited linear combiner in Rayleigh fading. We present a method for the accurate evaluation of the BER of the AFFH-MA system, and verify the analytic works by Monte Carlo simulations.     

FFH/BFSK AGC接收机在部分带干扰Nakagami衰落信道下的性能分析

该文对基于自适应增益控制(AGC)的非相干快速跳频二进制正交移频键控(FFH/BFSK)扩频(SS)接收机在同时存在部分带干扰(PBJ)和加性高斯白噪声(AWGN)的频率非选择性慢衰落Nakagami信道下的比特误码率(BER)性能进行了分析,推导出一重积分形式的BER准确表达式,分析了衰落参数和分集数目取任意值时对系统性能的影响,数值分析结果比较了AGC接收机与乘积合并(PC)接收机在最坏情况下的BER性能。与以往误码率分析方法相比,本文所用方法的优点在于用统一的分析模式可以分析系统在不同衰落信道下的性能,简化了分析步骤。     

Switched diversity on microcellular Ricean channels

The performances of switched dual diversity systems operating on independent and correlated Ricean fading channels are analyzed using a discrete time model. The average bit error rate (BER) of the discrete time switched diversity system using binary noncoherent frequency shift keying (NCFSK) on slow, nonselective Ricean fading channels is derived. A closed form expression that gives the optimum switching threshold in a minimum error rate sense is derived for the case of independent branch signals. Results for the optimum switching threshold for the case of correlated branch signals, obtained numerically, are also presented. Results using selection diversity combining are obtained for comparison. The effects of fading severity on both the BER and on the optimum switching threshold are investigated. The Ricean fading model may be used to model both the microcellular radio environment and the mobile satellite fading channel. Hence, the results of the paper are useful for both of these areas     

Postdetection MRC diversity for pi /4-shift QDPSK mobile radio

Diversity reception using a postdetection maximal-ratio combiner (MRC) was experimentally investigated for pi /4-shift QDPSK signal transmission in Rayleigh fading environments. Two-branch postdetection MRC diversity reception provides a diversity gain, for a required E/sub b//N/sub 0/, of about 1.5 dB over selection diversity. It is also effective in reducing the impact of multipath channel delay spread. The average BER due to delay spread can be further reduced by a factor of about 1.5 times from selection diversity.<>     

Postdetection optimal diversity combiner for DPSK differentialdetection

Postdetection diversity reception weights and combines all the detector outputs before symbol decision to combat the effects of multipath fading. A theoretical analysis of a postdetection optimal diversity combiner that can minimize the symbol error probability for differential phase shift keying (DPSK) differential detection in the presence of multiplicative Rayleigh fading, and co-channel interference (CCI) is presented. The effect of unequal average powers among diversity branches is taken into account. It is shown that the postdetection maximal-ratio combiner (MRC) described previously by the author is not optimal unless all branches have the same average power. It is also found that the combiner optimized for the effect of CCI (fading induced random FM noise) should weight each branch detector output in inverse proportion to the average CCI power (desired signal power). Assuming two-branch diversity, calculated BER (bit-error-rate) performance of π/4-shift QDPSK due to AWGN, CCI, and random FM is presented. In addition, the BER due to multipath channel delay spread (which is not treated in the theoretical analysis) is also computed to find the optimal combiner     

Reliability Bounds for Multi-State $k$-out-of- $n$ Systems

Algorithms have been available for exact performance evaluation of multi-state k-out-of-n systems. However, especially for complex systems with a large number of components, and a large number of possible states, obtaining "reliability bounds" would be an interesting, significant issue. Reliability bounds will give us a range of the system reliability in a much shorter computation time, which allow us to make decisions more efficiently. The systems under consideration are multi-state k-out-of-n systems with i.i.d. components. We will focus on the probability of the system in states below a certain state d, denoted by Q_sd. Based on the recursive algorithm proposed by Zuo & Tian [14] for performance evaluation of multi-state k-out-of-n systems with i.i.d. components, a reliability bounding approach is developed in this paper. The upper, and lower bounds of Q_sd are calculated by reducing the length of the k vector when using the recursive algorithm. Using the bounding approach, we can obtain a good estimate of the exact Q_sd value while significantly reducing the computation time. This approach is attractive, especially to complex systems with a large number of components, and a large number of possible states. A numerical example is used to illustrate the significance of the proposed bounding approach.     

Mellin-Transform-Based Performance Analysis of FFH $M$ -ary FSK Using Product Combining for Combatting Partial-Band Noise Jamming

We employ the Mellin transform to facilitate the bit error ratio (BER) analysis of a fast frequency hopping (FFH)-assisted, $M$-ary frequency-shift keying (MFSK) using product combining (PC) when the transmitted signal is subjected to both Rayleigh fading and partial-band noise jamming. Exploiting the fact that the Mellin transform of the product of independent random variables is the product of their Mellin transforms, we derive the probability density function (PDF) of the PC's output. The derivation of the PDF then allows the computation of the system's BER. It is shown that the Mellin transform substantially simplifies the analysis of the PC receiver and hence facilitates, for the first time, the analysis of the FFH-MFSK PC receiver for modulation orders of $M ≫ 2$.      

Ricean $K$-Factors in Narrow-Band Fixed Wireless Channels: Theory, Experiments, and Statistical Models

Fixed wireless channels in suburban macrocells are subject to fading due to scattering by moving objects such as windblown trees and foliage in the environment. When, as is often the case, the fading follows a Ricean distribution, the first-order statistics of fading are completely described by the corresponding average path gain and Ricean K-factor. Because such fading has important implications for the design of both narrow-band and wideband multipoint communication systems that are deployed in such environments, it must be well characterized. We conducted a set of 1.9-GHz experiments in suburban macrocell environments to generate a collective database from which we could construct a simple model for the probability distribution of K as experienced by fixed wireless users. Specifically, we find K to be lognormal, with the median being a simple function of season, antenna height, antenna beamwidth, and distance and with a standard deviation of 8 dB. We also present plausible physical arguments to explain these observations, elaborate on the variability of K with time, frequency, and location, and show the strong influence of wind conditions on K.