Number Of Diversity Branches Research Articles

Diversity analysis for energy detection-based spectrum sensing

In this study the authors perform a diversity analysis for an energy detection-based non-coherent spectrum sensing scheme and benchmark it against a genie aided coherent spectrum sensing scheme, which has full knowledge of the fading channel. In both cases the sensor has access to multiple independent channel observations. Results show that both schemes achieve full diversity. However, the authors find that the coherent scheme approaches this asymptotic limit faster than the non-coherent scheme. Through analysis the authors determine the penalty of the non-coherent scheme over the coherent scheme in converging to the asymptotic limit as a function of the SNR and the number of diversity branches. With these results the authors substantiate analysis, previously made, and thus provide further insights into the trade-off between complexity and performance for spectrum sensing schemes.

Simple Detection Based on Soft-Limiting for Binary Transmission in a Mixture of Generalized Normal-Laplace Distributed Noise and Gaussian Noise

In this letter, a simplified suboptimum receiver based on soft-limiting for the detection of binary antipodal signals in non-Gaussian noise modeled as a generalized normal-Laplace (GNL) distribution combined with Gaussian noise is presented. The suboptimum receiver has low computational complexity. Furthermore, when the number of diversity branches is small, its performance is very close to that of the Neyman-Pearson optimum receiver based on the probability density function obtained by the Fourier inversion of the characteristic function of the GNL-plus-Gaussian distribution.

Performance of SC Receiver over Generalized K Fading Channel in the Presence of Imperfect Reference Signal Recovery

This paper considers a partially coherent detection of quadrature phase-shift keying (QPSK) signals in a composite generalized K (KG) fading channel. At the reception the selection combining is applied, while the branches of the combiner are not identically distributed. The extraction of the reference carrier from non-modulated pilot signal is performed in a phase-locked loop (PLL) circuit. The difference between received signal phase and extracted reference signal phase is a stochastic variable with Tikhonov probability density function. The influence of the fading parameters, the standard deviation of phase error and the number of diversity branches on the system performance is examined. The bit-error rate is used as a measure of the reception quality. Ill. 6, bibl. 17 (in English; abstracts in English and Lithuanian).http://dx.doi.org/10.5755/j01.eee.115.9.746

The impact of spatial correlation on the statistical properties of the capacity of nakagami-m channels with MRC and EGC

In this article, we have studied the statistical properties of the instantaneous channel capacitya of spatially correlated Nakagami-m channels for two different diversity combining methods, namely maximal ratio combining (MRC) and equal gain combining (EGC). Specifically, using the statistical properties of the instantaneous signal-to-noise ratio, we have derived the analytical expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the instantaneous channel capacity. The obtained results are studied for different values of the number of diversity branches and for different values of the receiver antennas separation controlling the spatial correlation in the diversity branches. It is observed that an increase in the spatial correlation in the diversity branches of an MRC system increases the variance as well as the LCR of the instantaneous channel capacity, while the ADF of the channel capacity decreases. On the other hand, when EGC is employed, an increase in the spatial correlation decreases the mean channel capacity, while the ADF of the instantaneous channel capacity increases. The presented results are very helpful to optimize the design of the receiver of wireless communication systems that employ spatial diversity combining techniques. Moreover, provided that the feedback channel is available, the transmitter can make use of the information regarding the statistics of the instantaneous channel capacity by choosing the right modulation, coding, transmission rate, and power to achieve the capacity of the wireless channelb.

Second-order statistics of a maximum ratio combiner with unbalanced and unequally distributed Nakagami branches

In this study, exact closed-form expressions for the second-order statistics of the signal-to-noise ratio at a maximum ratio combiner (MRC) output for a Nakagami fading channel are derived. Using the joint characteristic function for the MRC output and its time derivative, the level crossing rate, average fading duration and autocorrelation function expressions are derived for the case of independent but unbalanced diversity branches, with unequal fading parameters and an arbitrary number of diversity branches. The analytical results are validated by simulations.

Energy Detection of Unknown Signals in Fading and Diversity Reception

A comprehensive performance analysis of the energy detector over fading channels with single antenna reception or with antenna diversity reception is developed. For the no-diversity case and for the maximal ratio combining (MRC) diversity case, with either Nakagami-m or Rician fading, expressions for the probability of detection are derived by using the moment generating function (MGF) method and probability density function (PDF) method. The former, which avoids some difficulties of the latter, uses a contour integral representation of the Marcum-Q function. For the equal gain combining (EGC) diversity case, with Nakagami-m fading, expressions for the probability of detection are derived for the cases L =2,3,4 and L >; 4, where L is the number of diversity branches. For the selection combining (SC) diversity, with Nakagami-m fading, expressions for the probability of detection are derived for the cases L =2 and L >; 2. A discussion on the comparison between MGF and PDF methods is presented. We also derive several series truncation error bounds that allow series termination with a finite number of terms for a given figure of accuracy. These results help quantify and understand the achievable improvement in the energy detector's performance with diversity reception. Numerical and simulation results are also provided.

Performance Analysis of LDPC Codes with Maximum-Ratio Combining Cascaded with Selection Combining over Nakagami-m Fading

Low-density parity-check (LDPC) codes combined with cascade combining are able to achieve excellent bit-error rate (BER) performance over multipath fading channels. Cascade combining, which involves two stages of diversity combining, is very useful for situations where site diversity exists and it can reduce the complexity of the combiner when the number of diversity branches increases. The average output signal-to-noise ratio and the uncoded BER expressions of cascade combining over independent and identically distributed (i.i.d.) Nakagami-m fading channels are derived. The BER expressions of cascade combining with LDPC codes over i.i.d. Nakagami-m fading channels are derived based on the Gaussian approximation (GA) approach. These expressions include selection combining and maximum-ratio combining as special cases. The signal-to-noise ratio (SNR) thresholds for error-free decoding are obtained using density evolution (DE). Comparisons among GA analysis, DE analysis, and simulations show that they are in good agreement. The expressions obtained from the GA analysis provide better theoretical understanding of the system performance and allow us to compute the BER and SNR threshold more efficiently as compared to DE and simulations. Lastly, the stability conditions for GA and DE analyses, which are found to be exactly the same, are also presented.

Performance analysis of signal-to-interference-plus-noise ratio-based selection diversity over correlated Rayleigh fading channels

In wireless communications systems, desired signal can be exposed to fading, cochannel interference (CCI) and noise. Diversity combining, such as space diversity, is a well-known method that can be used to alleviate the effects of these degradations. L-branch selection combining (SC) receiver which uses signal-to-interference-plus-noise ratio (SINR) power algorithm over correlated Rayleigh fading channels in the presence of Rayleigh distributed CCI and Gaussian noise is considered. The outage probability as significant performance criteria is analytically derived. The main contribution of this paper is that the analysis is carried out including the noise as a stochastic process, not only its average power value. The proposed mathematical analysis is complemented by various evaluation results showing the effects of the fading correlation as well as the number of diversity branches on the system's performance. In addition, SC performance in interference-plus-noise environment is compared with performance in noise- and interference-limited environments.

Performance of Equal Gain Combining with Quantized Phases in Rayleigh Fading Channels

In this paper, we analyze the error probability of equal gain combining with quantized channel phase compensation for binary phase shift keying signalling over Rayleigh fading channels. The probability density and characteristic functions of the combined signal amplitude are derived and used to compute the analytic expressions for the bit error probability in dependance of the number of quantization levels L, the number of diversity branches N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> and the average received signal-to-noise ratio. The analysis is utilized to outline the trade-off between N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> and L and to compare the performance with non-coherent binary frequency shift keying and differential binary phase shift keying schemes under diversity reception.

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.

Outage probability of SC receiver over exponentially correlated K fading channels

A mathematical expression for the outage probability of a selection combining diversity receiver with an arbitrary number of input branches is presented for exponentially correlated K fading channels. Numerical and simulation results are plotted and the effect of correlation, number of diversity branches and fading parameter on the outage performance of the receiver is studied. Results suggest that a correlation coefficient less than 0.5 may be used in practice.

Optimization of multi-branch switched diversity systems

A performance optimization based on the optimal switching threshold(s) for a multi-branch switched diversity system is discussed in this paper. For the conventional multi-branch switched diversity system with a single switching threshold, the optimal switching threshold is a function of both the average channel SNR and the number of diversity branches, where computing the optimal switching threshold is not a simple task when the number of diversity branches is high. The newly proposed multi-branch switched diversity system is based on a sequence of switching thresholds, instead of a single switching threshold, where a different diversity branch uses a different switching threshold for signal comparison. Thanks to the fact that each switching threshold in the sequence can be optimized only based on the number of the remaining diversity branches, the proposed system makes it easy to find these switching thresholds. Furthermore, some selected numerical and simulation results show that the proposed switched diversity system with the sequence of optimal switching thresholds outperforms the conventional system with the single optimal switching threshold.

Performance of M-PSK in mobile satellite communication over combined ionospheric scintillation and flat fading channels with MRC diversity

Combined scintillation and terrestrial fadings occur in mobile satellite communication channels as the signal passes through the ionosphere and the lower atmosphere. This results in a product fading channel, which negatively affects the performance of the system. The challenge is to evaluate the performance of the system, in terms of the average bit error probability (BEP). In this paper, through the use of the moment generating function, we derive expressions for the average BEP and an upper bound for M-ary phase-shift keying (M-PSK) modulation with maximal-ratio combining (MRC) diversity over the product RiciantimesRician channel. The results are expressed as double summations in terms of the generalized hypergeometric function, which can be computed using standard commercial software. For a large Rician factor, the expression is simplified to a single summation. Numerical results are obtained from the derived expressions and compared with simulation results. They show very good agreement for various Rician factors and the number of diversity branches. The upper bound is also evaluated and shown to be reasonably tight.

Asymptotic BEP and SEP of quadratic diversity combining receivers in correlated ricean fading, non-gaussian noise, and interference

In this paper, we study the asymptotic behavior of the bit-error probability (BEP) and the symbol-error probability (SEP) of quadratic diversity combining schemes such as coherent maximum-ratio combining (MRC), differential equal-gain combining (EGC), and noncoherent combining (NC) in correlated Ricean fading and non-Gaussian noise, which in our definition also includes interference. We provide simple and easy-to-evaluate asymptotic BEP and SEP expressions which show that at high signal-to-noise ratios (SNRs) the performance of the considered combining schemes depends on certain moments of the noise and interference impairing the transmission. We derive general rules for calculation of these moments and we provide closed-form expressions for the moments of several practically important types of noise such as spatially dependent and spatially independent Gaussian mixture noise, correlated synchronous and asynchronous co-channel interference, and correlated Gaussian interference. From our asymptotic results we conclude that (a) the asymptotic performance loss of binary frequency-shift keying (BFSK) with NC compared to binary phase-shift keying (BPSK) with MRC is always 6 dB independent of the type of noise and the number of diversity branches, (b) the asymptotic performance loss of differential EGC compared to MRC is always 3 dB for additive white Gaussian noise but depends on the number of diversity branches and may be larger or smaller than 3 dB for other types of noise, and (c) not only fading correlation but also noise correlation negatively affects the performance of quadratic diversity combiners.

Ergodic capacity of switch-and-examine combining under flat Rayleigh fading channels

Switch-and-examine combining (SEC) is an interesting diversity technique that is simpler than selection combining (SC), whereas its performances is similar in terms of bit error rate (BER) and diversity order. As ergodic capacity is also a key performance index in modern wireless systems, this article analyzes the ergodic capacity of the SEC system. The numerical results show that the ergodic capacity of SEC with optimal threshold is similar to that of SC for arbitrary number of diversity branches.

Analysis and Approximation of Statistical Distribution of Eigenvalues in i.i.d. MIMO Channels under Rayleigh Fading

In multiple input multiple output (MIMO) communication systems, eigenvalues of channel correlation matrices play an essential role for the performance analysis, and particularly the investigation about their behavior under time-variant environment ruled by a certain statistics is an important problem. This paper first gives the theoretical expressions for the marginal distributions of all the ordered eigenvalues of MIMO correlation matrices under i. i. d. (independent and identically distributed) Rayleigh fading environment. Then, an approximation method of those marginal distributions is presented: We show that the theory of SIMO space diversity using maximal ratio combining (MRC) is applicable to the approximation of statistical distributions of all eigenvalues in MIMO systems with the same number of diversity branches. The derived approximation has a monomial form suitable for the calculation of various performance measures utilized in MIMO systems. Through computer simulations, the effectiveness of the proposed method is demonstrated.

Unified asymptotic analysis of linearly modulated signals in fading, non-Gaussian noise, and interference

In this paper, we present a unified asymptotic symbol error rate (SER) analysis of linearly modulated signals impaired by fading and (possibly) non-Gaussian noise, which in our definition also includes interference. The derived asymptotic closed-form results are valid for a large class of fading and noise processes. Our analysis also encompasses diversity reception with equal gain and selection combining and is extended to binary orthogonal modulation. We show that for high signal-to-noise ratios (SNRs) the SER of linearly modulated signals depends on the Mellin transform of the probability density function (pdf) of the noise. Since the Mellin transform can be readily obtained for all commonly encountered noise pdfs, the provided SER expressions are easy and fast to evaluate. Furthermore, we show that the diversity gain only depends on the fading statistic and the number of diversity branches, whereas the combining gain depends on the modulation format, the type of fading, the number of diversity branches, and the type of noise. An exception are systems with a diversity gain of one, since their combining gain and asymptotic SER are independent of the type of noise. However, in general, in a log-log scale for high SNR the SER curves for different types of noise are parallel but not identical and their relative shift depends on the Mellin transforms of the noise pdfs.

A Pilot-Aided Multicode CDMA Transmission Over Wireless Channels

To adapt to the time-varying multipath fading associated with the wireless link, we address the use of a pilot-aided fade-resistant transmission scheme based on the multicode code division multiple access (CDMA) technology. In this system, all the information symbols along with the pilot symbol of a user are transmitted simultaneously over the wireless channel. We apply matched filter receivers to estimate time-varying multipath channel coefficients and the contribution of the pilot signals is subtracted from the received signal prior to decoding the information symbols. We analyze the tradeoff between the number of diversity branches and the channel estimation error in the performance. Our study indicates that, depending on the transmitter power and the channel condition, the proposed system is capable of outperforming the conventional CDMA system with known channel state information at the receiver.

Performance of Selection Combining Diversity in Weibull Fading with Cochannel Interference

We evaluate the performance of selection combining (SC) diversity in cellular systems where binary phase-shift keying (BPSK) is employed and the desired signal as well as the cochannel interferers (CCIs) is subject to Weibull fading. A characteristic function-(CF-) based approach is followed to evaluate the performance in terms of the outage probability. Two selection criteria are adopted at the diversity receiver: maximum desired signal power and maximum output signal-to-interference ratio (SIR). We study the effect of the fading parameters of the desired and interfering signals, the number of diversity branches, as well as the number of interferers on the performance. Numerical results are presented and the validity of our expressions is verified via Monte Carlo simulations.

SER of M-ary NCFSK with S + N Selection Combining in Nakagami Fading for Integer m

The performance of M-ary orthogonal noncoherent frequency-shift keying (NCFSK) with N branch signal-plus-noise (S + N) selection combining (SC) in Nakagami-m fading (m, integer) is studied. Both independent, identically distributed (i.i.d) and independent, nonidentically distributed (i.n.d) diversity branches are considered and two S + N SC receiver structures are examined. The performances of the S + N SC receivers are compared to those of classical SC and square-law combining (SLC) receivers. The effects of modulation order, fading parameter and the number of diversity branches on the performance of S + N SC are compared to the effects on the performances of classical SC and SLC. For example, it is shown that in an i.n.d fading channel, the value of signal-to-noise ratio (SNR) at which the error rate curves of classical SC and S + N SC cross, decreases as the modulation order, M, increases. Our results indicate that in i.n.d fading channels classical SC outperforms S + N SC for small ranges of SNR, while for moderate to large SNR values S + N SC has superior performance over classical SC. It is also shown that increasing the diversity order will increase the performance gap of S 4N SC over classical SC and over SLC in both i.i.d and i.n.d Nakagami-m fading channels