Power Sum Distributions: An Easier Approach Using the Wald Distribution

Marcus, Allan H.

doi:10.2307/2285776

Cited by 8 publications

(11 citation statements)

References 4 publications

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“…To the best of our knowledge, there exists no closed-form expression for the average probability of detection when we substitute (8) and (10) into (9). The log-normal distribution can be closely approximated by the Wald distribution (also known as the inverse Gaussian distribution) [11], [12], whose PDF is given by…”

Section: Local Energy Detection In a Slow Fading Channelmentioning

confidence: 99%

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Computationally Tractable Model of Energy Detection Performance over Slow Fading Channels

2010

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Abstract-Energy detection (ED) has been widely used fordetecting unknown deterministic signals in many wireless communication applications, e.g., cognitive radio, and ultra-wideband (UWB). However, the performance analysis of ED over slow fading channels is cumbersome, because it is difficult to derive closed-form expressions for the average probability of detection involving the generalised Marcum Q-function and the log-normal distribution. In this letter, we derive an approximation of the average probability of detection over a slow fading channel by replacing the log-normal distribution with a Wald distribution. In addition, we analyze the detection performance of the ED using a square-law combining scheme over multiple independent and identically distributed slow fading channels.

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Section: Local Energy Detection In a Slow Fading Channelmentioning

confidence: 99%

“…Thus, the combined SNR under the SLC scheme, , will also follow the Wald distribution [14]. The PDF of can be easily obtained by replacing each with , each with , and each with in (11). Using a similar method to that of the single slow fading channel, we can obtain the average probability of detection as below…”

Section: Energy Detection Over Slow Fading Channelsmentioning

confidence: 99%

Computationally Tractable Model of Energy Detection Performance over Slow Fading Channels

2010

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“…The instantaneous SNR per received symbol is given by =X 2 E s /N 0 , and so the corresponding average SNR can be obtained as =E[X 2 ]E s /N 0 , where E[X 2 ] is obtained by setting n=2 in (20). For the receiver under consideration, the outage probability (P out ) defined as the probability that falls below a certain specified threshold, th , can be easily obtained by using (18), as follows:…”

Section: Outage Probability In Gg-l Shadowed Fading Channelmentioning

confidence: 99%

Performance analysis of lognormally shadowed generalized Gamma fading channels

Samimi

2010

Int J Communication

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SUMMARYA new composite channel model is proposed for the performance analysis of shadowed fading channels. This model is represented as a mixture of generalized Gamma (GG) multipath fading and lognormal shadowing. GG distribution includes the Rayleigh, Nakagami, and Weibull as special cases; hence the presented model, which is referred to as GG-L, is a generic model that covers many well-known composite fading models, including the Rayleigh-lognormal (R-L), Nakagami-lognormal (N-L), and Weibull-lognormal (W-L). The main drawback of the lognormal-based composite models is that the composite probability density function (PDF) is not in closed form, thereby making the performance evaluation of communication links in these channels cumbersome. To bypass this problem, an approximation method is developed which makes it possible to derive a closed-form, analytical expression for GG-L composite distribution. The proposed method only needs the mean and the variance of the underlying lognormal distribution, and hence, bypasses the required complicated integration needed to calculate the PDF of the received signal envelope in GG-L channel. Based on this method, the most statistical characteristics, such as cumulative density function (CDF) and moments of the GG-L composite distribution, are derived and used for the performance analysis of a single receiver operating over GG-L fading channel.

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“…Noting that IGD closely approximates lognormal distribution [7], we now consider IGD. The pdf of IG variate is…”

Section: Inverse Gaussian Distributionmentioning

confidence: 99%

“…One limitation, which this approximation suffers from, is that gamma distribution is not a good approximation for lognormal distribution with large variance. It has been reported that inverse Gaussian distribution (IGD) better approximates for lognormal distribution when long-tailed behavior is expected [7,8]. Noting this fact, Karmeshu and Agrawal [9] proposed a closedform expression for Equation (6) by replacing lognormal with IGD.…”

Section: Introductionmentioning

confidence: 99%

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Souto

Silva

Cercas³

et al. 2007

Wireless Communications

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SummaryFor studying performance characteristics of radio channels, the knowledge about the probability density function (pdf) of fading-shadowing effects is essential. K-distribution corresponding to Rayleigh-gamma distribution (RGD) is widely used to approximate a more realistic Rayleigh-lognormal distribution (RLD) which does not have a closed form expression. A new composite Rayleigh-inverse Gaussian distribution (RIGD), an alternative to Kdistribution, is analyzed with regards to its suitability and effectiveness in radio channels. Detailed investigations are made to study the performance characteristics of RIGD and K-distribution (RGD) in terms of Kullback-Leibler (KL) measure of divergence. Based on these investigations, it is found that RIGD is better suited for capturing fading-shadowing aspects of radio channels instead of K-distribution.

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Power Sum Distributions: An Easier Approach Using the Wald Distribution

Cited by 8 publications

References 4 publications

Computationally Tractable Model of Energy Detection Performance over Slow Fading Channels

Computationally Tractable Model of Energy Detection Performance over Slow Fading Channels

Performance analysis of lognormally shadowed generalized Gamma fading channels

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