Bit error outage for diversity reception in shadowing environment

This letter addresses the problem of evaluating the bit error outage (BEO), i.e., the outage probability defined in terms of bit error probability, in a Rayleigh fading and shadowing environment. We consider coherent detection of binary phase-shift keying with maximal ratio combining (MRC). As an example application, the BEO in a log-normal shadowing environment is analyzed and the improvement in terms of BEO due to MRC is quantified in different shadowing environments.     

Invertible bounds for M-QAM in Rayleigh fading

In this letter, we derive tight invertible bounds on the bit-error probability (BEP) for the coherent detection of M-ary quadrature amplitude modulation with Gray code bit mapping in Rayleigh fading channels. These bounds enable us to easily obtain tight lower and upper bounds on the bit-error outage (BEO), i.e., BEP-based outage probability, in a log-normal shadowing environment. As examples of applications, these bounds are used to investigate the BEO and mean spectral efficiency for slow adaptive modulation.     

Digital transmission through a land mobile satellite channel

An analytical derivation of the probability of bit error noncoherent frequency-shift keying (FSK) and coherent phase-shift keying (PSK) signals transmitted through a land-mobile satellite channel is described. The channel characteristics used in the analysis are based on a recently developed model which includes the combined effects of fading and shadowing. Analytical expressions for the probability of bit error of FSK and coherent phase-shift keying (CPSK) signals are obtained. The results show that large amounts of signal-to-noise ratio (SNR) are required to compensate for the combined effect of fading and shadowing. An analytical expression for the irreducible probability of bit error of a CPSK signal due to phase variations caused by fading and shadowing is derived. The results described should be useful in the design of land mobile satellite communication systems     

Bit error probabilities MDPSK over the nonselective Rayleigh fadingchannel with diversity reception

Data transmission using M-ary differential phase shift keying (MDPSK) over the nonselective Rayleigh fading channel with diversity reception is considered. While previous studies on error probability mostly assume no fading fluctuation, the author considers, exclusively, the case in which the fading process fluctuates from one symbol interval to the next. Exact bit error probability results for 2, 4, and 8 DPSK as well as tight upper bounds are derived. Some applications of the results are discussed     

Performance of RS coded M-ary modulation with and without symbol overlapping

In this paper, we present analytical bit error probability results for M-ary modulation concatenated with Reed Solomon (RS) codes. The analysis of bit error probability is nontrivial as the number of bits per symbol for the RS codes may not be an integer multiple of the number of bits per symbol for a modulation symbol. We propose a Markov chain technique which allows analytical evaluation of the bit error probability for such cases. The performance of RS coding with coherent biorthogonal, coherent/non-coherent orthogonal modulation over an additive white Gaussian noise (AWGN) channel is evaluated. Simulation of the bit error probability of RS code concatenated with a Nordstrom Robinson (NR) code as an inner code is performed and compared with the case of biorthogonal modulation. From the results, we notice that a stronger inner code gives better bit error probability. In addition, the throughput of the coded system with biorthogonal modulation over an AWGN channel is discussed. For a Rayleigh flat fading and block fading channel, we analyze the bit error probability of RS codes concatenated with biorthogonal modulation. From the result, we notice that a stronger outer code gives a better bit error probability for the case of Rayleigh flat fading channel.     

Analysis of multidimensional trellis-coded MPSK in Rice-lognormalfading channels

The paper addresses the analysis of multidimensional trellis-coded M-ary phase shift keying (MPSK) modulation over a Rice-lognormal fading channel model, applicable to a variety of environments and to both terrestrial and satellite mobile communications. Bounds to the bit error probability are derived and applied to the analysis of a few selected trellis-coded modulation (TCM) schemes. The results, confirmed by simulation, show that on the Rice channel there exists a threshold in bit energy-to-noise density ratio above which the effective code length is the dominant parameter, while the free distance is dominating below. However, the influence of both parameters is mitigated when shadowing is present     

Performance evaluation of L-maximal ratio combining diversity with estimation error for Shadowed Beaulieu-Xie fading channels

To provide the increasing demand for wireless technologies, high capacity with lower latency is vital. New emerging technologies like 5G, millimeter wave, THz, and so forth are able to characterize such complex fading and shadowed environments. Spatial diversity is one of the techniques to minimize fading in the wireless communication channel. The performance of the wireless communication system can be further optimized by using estimators at the receivers. The influence of imperfect channel estimation on the performance over shadowed Beaulieu-Xie (SBX) fading channels with L-maximal ratio combining (MRC) diversity is studied. The probability density function (PDF) of the received output signal-to-noise ratio (SNR) with L-MRC over SBX fading channels is derived. Further PDF of the received output SNR, outage probability, and average bit error rate (ABER) using the derived PDF is evaluated for L-MRC diversity with channel estimation error over SBX fading channels. ABER expression for Gray-coded rectangular quadrature amplitude modulation over the SBX channel is also evaluated. The study also includes how the system performs under the effect of different shadowing and fading parameters.     

Performance analysis of multi‐input multi‐output systems with maximum likelihood detection over shadowed fading channels

Multiple‐input multiple‐output (MIMO) transmission techniques constitute an important technology in modern wireless communication. Hence, performance analysis methods for such systems are of considerable interest. This paper considers first the average pairwise error probability for uncoded MIMO systems employing maximum likelihood detection over a composite Rayleigh‐Lognormal fading channel with spatial correlation. It provides general results, applicable also to a wider class of shadowing models, concerning asymptotical diversity gains and shows that they are not changed by such shadowing. Then, analytical evaluation techniques for bit‐error‐rate (BER) over composite Rayleigh‐Lognormal fading channels, based on the truncated union bound and the transfer function, are considered. Furthermore, these techniques are modified for applications over spatially correlated channels. This paper shows that such performance evaluation techniques provide good approximations to BER of spatially uncorrelated MIMO systems and also in the presence of moderate spatial correlation, over Rayleigh‐Lognormal fading channels. Copyright © 2013 John Wiley & Sons, Ltd.     

Convolutionally interleaved PSK and DPSK trellis codes forshadowed, fast fading mobile satellite communication channels

Using a model from the literature, the performance of convolutionally interleaved phase-shift-keying (PSK) and differential phase-shift-keying (DPSK) trellis codes for digital speech transmission over shadowed mobile satellite communication channels is determined by computer simulation. First the characteristics of fading channels are examined and analyzed in terms of the probability distributions of amplitude, phase, and burst errors. A statistical method, using a histogram approach, is utilized along with the simulations of fading channels to generate these probability distributions. A test for channel burst error behavior is presented. A periodic convolutional interleaver/deinterleaver to be used with trellis coding to combat slow fading in digital, shadowed mobile satellite channels is designed. This interleaver ha less than half the time delay for the same bit error performance than a block interleaver. The results show that the periodic convolutional interleaver provides considerable improvement in the error and time delay performance of mobile satellite communication channels for up to average shadowing conditions as compared to other techniques     

Diversity reception over generalized-K (KG) fading channels

A detailed performance analysis for the most important diversity receivers operating over a composite fading channel modeled by the generalized-K (Kg) distribution is presented. The Kg distribution has been recently considered as a generic and versatile distribution for the accurate modeling of a great variety of short term fading in conjunction with long term fading (shadowing) channel conditions. For this relatively new composite fading model, expressions for important statistical metrics of maximal ratio combining (MRC), equal gain combining (EGC), selection combining (SC) and switch and stay combining (SSC) diversity receivers are derived. Using these expressions and by considering independent but not necessarily identical distributed fading channel conditions, performance criteria, such as average output signal-to-noise ratio, amount of fading and outage probability are obtained in closed form. Moreover, following the moments generating function (MGF) based approach for MRC and SSC receivers, and the Pade approximants method for SC and EGC receivers, the average bit error probability is studied. The proposed mathematical analysis is complemented by various performance evaluation results which demonstrate the accuracy of the theoretical approach.     

Effect of Microdiversity and Macrodiversity on Average Bit Error Probability in Gamma‐Shadowed Rician Fading Channels

In this letter, we analyze the error performance of a mobile communication system with microdiversity and macrodiversity reception in gamma‐shadowed Rician fading channels for a binary differential phase‐shift keying modulation scheme. Analytical expressions for the probability density function (PDF) and moment‐generating function (MGF) are derived. The average bit error probability can be calculated by averaging the conditional bit error probability over the PDF or using the MGF‐based approach. Numerical results are graphically presented to show the effects of macrodiversity, correlation, number of diversity branches, and severity of both fading and shadowing.     

M-ary symbol error outage over Nakagami-m fading channels in shadowing environments

This letter addresses the problem of finding a tractable expression for the symbol error outage (SEO) in flat Nakagami-m fading and shadowing channels. We deal with M-ary phase shift keying (M-PSK) and quadrature amplitude modulation (M-QAM) which extends our previous results on BPSK signaling. We propose a new tight approximation of the symbol error probability (SEP) holding for M-PSK and M-QAM signals which is accurate over all signal to noise ratios (SNRs) of interest. We derive a new generic expression for the inverse SEP which facilitates the derivation of a tight approximation of the SEO in a lognormal shadowing environment.     

Performance comparison of different decoding strategies for abandwidth-efficient block-coded scheme on mobile radio channels

The performance of bandwidth-efficient Reed-Solomon (RS)-coded MPSK schemes is evaluated on a shadowed Rician fading channel using different decoding strategies, namely, errors-only, errors-and-erasures, and soft-decision decoding. The lower bounds of the bit error probability are found for errors-only and for errors-and-erasures decoding. For the soft-decision decoding the upper bound of the bit error rate is derived. The error bounds are calculated and examined by simulation for some RS-coded MPSK schemes on a shadowed Rician channel. It is shown that their performance is significantly improved compared to uncoded QPSK. The amount of improvement depends on the signal-to-noise ratio (SNR), the decoding strategy, and the degree of shadowing. A comparison between different decoding techniques, for one of the RS-coded schemes, for different degrees of shadowing shows that the use of channel measurement information in the decoding process is more effective for heavy shadowed channels     

Performance analysis of mobile radio systems over composite fading/shadowing channels with co-located interference

This paper presents an analytical framework for performance evaluation of mobile radio systems operating in composite fading/shadowing channels in the presence of colocated co-channel interference. The desired user and the interferers are subject to Nakagami fading superimposed on gamma shadowing. The paper starts by presenting generic closed-form expressions for the signal-to-interference ratio (SIR) probability density function (pdf). From this pdf, closed-form expressions for the outage probability, the average bit error rate and the channel capacity are obtained in both cases of statistically identical interferers and multiple interferers with different parameters. The newly derived closed-form expressions of the aforementioned metrics allow us to easily assess the effects of the different channel and interference parameters. It turns out that the system performance metrics are predominantly affected by the fading parameters of the desired user, rather than by the fading parameters of the interferers.     

Probability of bit error for MPSK modulation with diversityreception in Rayleigh fading and log-normal shadowing channel

In an additive white Gaussian noise channel subject to Rayleigh fading and log-normal shadowing, consideration is given to diversity reception with K-port macroscopic selection and L-branch microscopic maximal-ratio combining, and analytical expressions are derived for upper and lower bounds on the bit error probabilities for BPSK, QPSK, 8-PSK, and 16-PSK modulations. The derived expressions can be evaluated at any location in the serving cell. Error-probability can be calculated by averaging over all possible locations within the serving cell. By evaluating these bounds, numerical results for the following cases are presented: without diversity reception, microdiversity combining, macrodiversity selection, and simultaneous use of macrodiversity selection and microdiversity combining. For symmetrical arrangement of macrodiversity ports against the lognormal shadowing, error probability at the equidistant point gives upper bounds on the error probabilities for most of the area in the serving cell. Error probability at the equidistant point is a good estimate of the error probability obtained by averaging over all possible locations in the cell     

On the energy utilization for WSN based on BPSK over the Generalized-K shadowed fading channel

Energy is a scarce resource in the battery-powered nodes of wireless sensor networks (WSNs). In this paper the energy utilization for WSN based on BPSK communications has been investigated over the Generalized-K shadowed fading channel. A comprehensive analysis is reported based on the various important performance metrics like: amount of fading, average bit error probability, outage probability and energy utilized per bit (EUB). Simulation results reveal that composite use of shadowing and fading degrade energy levels to a considerable extent and hence contribute in downsizing the network life-span. We have derived the EUB metric and performed its evaluation with respect to optimal transmit energy levels by varying fading and shadowing severity parameters. We also considered the impact of varying transmit energy levels on the outage probability and hence on transmit and EUB levels. Although, embedding of training sequences and re-transmissions do help in enhancing effective synchronization and improved reliability, but this is done at a cost of higher energy utilization. Under the given set of assumptions, it is observed that an decrease in fading by about 11 %, improves the EUB by about 7 %. With increase in outage probability by about 10 %, EUB improves by about 3 %. An increase in SNR by 6 % improves the EUB levels by about 7 %. The investigations reported in this paper may enable designers to optionally choose suitable parameters to make WSN communications energy-efficient.     

Detection performance of cooperative spectrum sensing with hard decision fusion in fading channels

In this paper, we investigate the detection performance of cooperative spectrum sensing (CSS) using energy detector in several fading scenarios. The fading environments comprise relatively less-studied Hoyt and Weibull channels in addition to the conventional Rayleigh, Rician, Nakagami-m and log-normal shadowing channels. We have presented an analytical framework for evaluating different probabilities related to spectrum sensing, i.e. missed detection, false alarm and total error due to both of them, for all the fading/shadowing models mentioned. The major theoretical contribution is, however, the derivation of closed-form expressions for probability of detection. Based on our developed framework, we present performance results of CSS under various hard decision fusion strategies such as OR rule, AND rule and Majority rule. Effects of sensing channel signal-to-noise ratio, detection threshold, fusion rules, number of cooperating cognitive radios (CRs) and fading/shadowing parameters on the sensing performance have been illustrated. The performance improvement achieved with CSS over a single CR-based sensing is depicted in terms of total error probability. Further, an optimal threshold that minimises total error probability has been indicated for all the fading/shadowing channels.     

On the performance analysis of wireless receiver using generalized-gamma fading model

In this paper, we provide a unified analysis for wireless system over generalized fading channels that is modeled by the two parameter generalized gamma model. This model is versatile enough to represent short-term fading such as Weibull, Nakagami-m, or Rayleigh as well as shadowing. The performance measures such as the amount of fading, average bit error rate, and signal outage are considered for analysis. With the aid of moment generating function (MGF) approach and Padé approximation (PA) technique, outage probability and average bit error rate have been evaluated for a variety of modulation formats. We first use the PA technique to find a simple way to evaluate compact rational expressions for the MGF of output signal-to-noise ratio, unlike previously derived intricate expressions in terms of Fox’s H and MeijerG functions. Using these rational expressions, we evaluate the performance of wireless receivers under a range of representative channel fading conditions. Our results are validated through computer simulations, which shows perfect match.     

Effect of shadowing on the performance of space-time trellis-coded systems

We analyze the performance of space-time trellis codes over shadowed Rician fading channels. The shadowed Rician channel is a generalization of the Rician model, where the line-of-sight path is subjected to a lognormal transformation due to foliage attenuation, also referred to as shadowing. Using the moment generating function method, we derive an exact expression for the pairwise error probability (PEP) of space-time trellis coded systems operating over this channel. The asymptotic analysis of PEP shows that the design criteria of space-time trellis codes proposed for Rayleigh fading still hold when used over shadowed Rician channels. We also present simulation results for bit-error rate performance under various degrees of shadowing.     

Performance Analysis of System with Micro- and Macrodiversity Reception in Correlated Gamma Shadowed Rician Fading Channels

In this paper, the performance of wireless system employing microdiversity to mitigate the effects of short-term fading and macrodiversity to reduce long-term fading (shadowing) effects is studied. The system model assumes implementation of maximal-ratio combining (MRC) at the microlevel and selection combining (SC) at the macrolevel. The received signal envelope follows a Rician distribution and it also suffers gamma shadowing. Novel expressions for the probability density function (PDF), cumulative distribution function (CDF), and moment-generating function (MGF) of the output signal-to-noise ratio (SNR) are obtained. Several useful performance criteria, such as the moments of the output SNR and outage probability are analytically derived. Moreover, the average bit error probability (ABEP) for noncoherent binary differential phase-shift keying (BDPSK) is calculated using the MGF based approach while the ABEP for coherent binary phase-shift keying (BPSK) is studied by averaging the conditional bit error probability over the PDF. Numerical results are graphically presented to show the effects of various system parameters to the system performance, as well as the enhancement due to use of the combination of micro- and macrodiversity. Some of numerical results are complemented by equivalent computer simulated results which validate the accuracy of the proposed analysis. The agreement between the Rician-gamma and Rician-lognormal fading model is also established.