Performance analysis of an opportunistic multi‐user cognitive network with multiple primary users

Consider a multi‐user underlay cognitive network where multiple cognitive users concurrently share the spectrum with a primary network with multiple users. The channel between the secondary network is assumed to have independent but not identical Nakagami‐m fading. The interference channel between the secondary users (SUs) and the primary users is assumed to have Rayleigh fading. A power allocation based on the instantaneous channel state information is derived when a peak interference power constraint is imposed on the secondary network in addition to the limited peak transmit power of each SU. The uplink scenario is considered where a single SU is selected for transmission. This opportunistic selection depends on the transmission channel power gain and the interference channel power gain as well as the power allocation policy adopted at the users. Exact closed form expressions for the moment‐generating function, outage performance, symbol error rate performance, and the ergodic capacity are derived. Numerical results corroborate the derived analytical results. The performance is also studied in the asymptotic regimes, and the generalized diversity gain of this scheduling scheme is derived. It is shown that when the interference channel is deeply faded and the peak transmit power constraint is relaxed, the scheduling scheme achieves full diversity and that increasing the number of primary users does not impact the diversity order. Copyright © 2014 John Wiley & Sons, Ltd.     

Performance analysis of opportunistic nonregenerative relaying

Opportunistic relaying in cooperative communication depends on careful relay selection. However, the traditional centralized method used for opportunistic amplify‐and‐forward protocols requires precise measurements of channel state information at the destination. In this paper, we adopt the max–min criterion as a relay selection framework for opportunistic amplify‐and‐forward cooperative communications, which was exhaustively used for the decode‐and‐forward protocol, and offer an accurate performance analysis based on exact statistics of the local signal‐to‐noise ratios of the best relay. Furthermore, we evaluate the asymptotical performance and deduce the diversity order of our proposed scheme. Finally, we validate our analysis by showing that performance simulation results coincide with our analytical results over Rayleigh fading channels, and we compare the max–min relay selection with their centralized channel state information‐based and partial relay selection counterparts. Copyright © 2013 John Wiley & Sons, Ltd.     

Joint adaptive modulation and diversity combining with feedback error compensation

This letter investigates the effect of feedback error on the performance of the joint adaptive modulation and diversity combining (AMDC) scheme which was previously studied with an assumption of error-free feedback channels. We also propose to utilize adaptive diversity to compensate for the performance degradation due to feedback error. We accurately quantify the performance of the joint AMDC scheme in the presence of feedback error, in terms of the average number of combined paths, the average spectral efficiency, and the average bit error rate. Selected numerical examples are presented and discussed to illustrate the effectiveness of the proposed feedback error compensation strategy with adaptive combining. It is observed that the proposed compensation strategy can offer considerable error performance improvement with little loss in processing power and spectral efficiency in comparison with the no compensation case.     

Average outage duration of multihop communication systems with regenerative relays

Closed-form expressions for the average outage duration (AOD) of multihop regenerative communication systems over generalized fading channels are presented. Both noise-limited and interference-limited systems are studied. To show the usefulness of the presented expressions, some specific fading scenarios are considered. In addition, some numerical examples of interest comparing direct versus relayed transmission and studying the effect of increasing the number of hops and/or cochannel interferers are plotted and discussed.     

Simplified noisy reference loss evaluation for digitalcommunication in the presence of slow fading and carrier phaseerror

Using a Maclaurin series expansion of the conditional (on the carrier phase error) bit error probability of binary and quaternary phase-shift keying (BPSK and QPSK, respectively) and then averaging this result over both the statistics of the carrier phase error and the channel fading, closed-form expressions for the average bit error probability are derived in a form that lend themselves toward obtaining simple formulas for the associated noisy reference loss. Numerical evaluation of this loss based on the use of these formulas is shown to provide excellent accuracy when compared with the exact evaluation, which requires two-fold numerical integration. Although the method is specifically applied to BPSK and QPSK, it is easily extended to other forms of modulation whose conditional bit error probability is known in a closed form     

On the Energy Detection of Unknown Signals Over Fading Channels

This letter addresses the problem of energy detection of an unknown signal over a multipath channel. It starts with the no-diversity case, and presents some alternative closed-form expressions for the probability of detection to those recently reported in the literature. Detection capability is boosted by implementing both square-law combining and square-law selection diversity schemes     

Cinetiques et mecanismes de l'action oxydative de l'hypochlorite sur les acides α-amines lors de la desinfection des eaux

In the field of water treatment, one increased concern over the quality of the environment requires an understanding of the fate of compounds generated by the addition of chemicals. One area of considerable interest is the stability of chlorine compounds produced when chlorine is added to natural water or swimming pool water. It is desirable to be able to predict the lifetimes of these harmful compounds under various conditions. In this study we examine for a range of hypochlorite α-amino acid ratios and pH, the kinetics and mechanism of the decomposition of α(N-chloro) and α(N,N-dichloro) amino acid, one of the products of chlorination.The interaction of chlorine with amino acids has been studied by several investigators Langheld (1909) was the first who discussed the decomposition of the α(N-chloro) amino acids. He noted that hypochlorous acid salts react with α-amino acids in the same manner as they do with amines to form monochlorinated or dichlorinated derivatives. Then, the decomposition of chloro-amino acids leads to the corresponding aldehydes or ketones, ammonia, carbonic acid, and sodium chloride. As an intermediate step Langheld assumed an imine formation.Wright (1936) and Pereira et al. (1973) have investigated the decomposition products of α(N,N-dichloro) amino acids. Their results indicate rapid formation of carbon dioxide, chloride ion, and the corresponding nitrile.Recently, many authors have investigated the rates of α(N-chloro) amino acids decomposition and the stability of its products (William and Wendy, 1979; Yoshiro et al., 1980; Le Cloirec-Renaud, 1984). However, they have neither differentiated between the decomposition of α(N-chloro) amino acid and α(N,N-dichloro) amino acid, nor have they demonstrated the combined effect of pH and molar ratio of hypochlorite and α-amino acid.In this study the hypochlorite oxidation of simple α-amino acids in aqueous solution has been investigated in the dark. The concentration of α(N-chloro) amino acid and α(N,N-dichloro) amino acid was monitored by DPD-fast titrimetric method and by measuring the absorbance at 255 and 293 nm respectively, this is illustrated in Figs 3 and 4. These results and the amino acids determination (O-phtalaldehyde—2 mercapto ethanol method) suggest that the intermediates α(N-chloro) and α(N,N-dichloro) amino acid are formed rapidly at an initial stage. Then, they decompose spontaneously by first order kinetics as shown in Table 1, to give a mixture of aldehyde and nitrile.When equimolar (1:1 mmol) amounts of hypochlorite and amino acid are used at pH 7, only aldehyde, carbon dioxide, chloride and ammonia are formed. However the corresponding nitrile compound appears, when operating condition allow the formation of α(N,N-dichloro) amino acid (acid pH or basic aqueous solutions with high molar ratio of hypochlorite and amino acid). This is illustrated in Table 2. The rate constant shows a dependence on pH, which is caused by the various forms that can arise from addition of protons to or removal of protons from the amino and carboxyl groups of the molecule William and Wendy, 1979). We assume an intermediate step of imine for the decomposition of both compounds: α(N-chloro) and α(N,N-dichloro) amino acid (scheme 6). The reaction should be considered as a spontaneous decarbonylation followed by a rapid hydrolysis of the imine. Scheme 7 illustrated how α(N,N-dichloro) amino acid can lead to the corresponding nitrile and aldehyde, however the α(N-chloro) amino acid gives only the corresponding aldehyde.The products of decomposition of α(N-chloro) amino acid are relatively stable in aqueous solution. Although we noted at pH = 3.5–5 that aldehyde react with chloramines and lead to the formation of corresponding nitrile, as shown in scheme 9.It appears that α(N-chloro) and α(N,N-dichloro) amino acid formed during the chlorination of natural or swimming pool water will degrade in a few hours to what are probably irritating products (like as aldehydes). The production of decomposition are a function of molar ratio of hypochlorite and amino acid and pH. However, since most natural water has a pH in the range of 5.5–9, there will be little variation of the rate of decomposition with pH. It seems that it is only temperature dependent.     

Sum and difference of two squared correlated Nakagami variates in connection with the McKay distribution

General formulas for the probability density function of the sum and the difference of two correlated, not necessarily identically distributed, squared Nakagami variates (or equivalently, gamma variates) are derived. These expressions are shown to be in the form of the McKay "Bessel function" distributions. In addition, formulas for the moments of these distributions, in terms of the Gauss hypergeometric function, are provided. An application of these new results relevant to the calculation of outage probability in the presence of self-interference is discussed.     

Dual tunable wavelength Er,Yb:glass laser for terahertz beatfrequency generation

Dual tunable wavelength operation of Er,Yb:phosphate glass laser is reported. The spatial separation of the laser eigenstates and the use of two properly designed intracavity etalons permit one to tune the two wavelengths independently from 1540.5 to 1562.7 nm. The generated beat note, monitored using a Michelson interferometer, is experimentally shown to be adjustable from dc to 2.7 THz. The linewidth of this beat note is found to be less than 10 kHz. Several applications are discussed     

End-to-end performance of transmission systems with relays over Rayleigh-fading channels

End-to-end performance of two-hop wireless communication systems with nonregenerative relays over flat Rayleigh-fading channels is presented. This is accomplished by deriving and applying some new closed-form expressions for the statistics of the harmonic mean of two independent exponential variates. It is shown that the presented results can either be exact or tight lower bounds on the performance of these systems depending on the choice of the relay gain. More specifically, average bit-error rate expressions for binary differential phase-shift keying, as well as outage probability formulas for noise limited systems are 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-ratio (SNR). They also show that the two systems have similar performance at high average SNR.