where CO= /m0/*and Po = 02 are, respectively, the average power of the specular and the diffused components of the desired Rician signal. The PDF of Y, p( Y), can be found by convolving eqns. 2 and 3. Hence the outage probability P,,can be written as 0 IEE 1995 25 January 1995 Electronics Letters Online No: 19950375 J.T. Virtamo (VTT Information Technology, PO Box 1201, FIN-02044 VTT, Finland) Pout = References .I_”, p(Y)dY SYSKI. R.: ‘Introduction to congestion in telephone systems’ (Elsevier Science Publishers, Amsterdam, 2nd edition, 1986) 2 ROBERTS. J.W. (Ed.): ‘Performance evaluation and design of multiservice network. COST224 Final Report (CEC, Luxenbourg, 1992) 1 Making the change of variables Z = p 3 2 , y = P d / 2 in eqn. 4 and defining the parameters LC, = Pp2/2, CO= Pd2/2 and r = d[p,JPO],where aV2 = K,L, bY2 = &, we arrive at Outage probability for a Rician signal in L Rician interferers T.T. Tjhung, C.C. Chai and X. Dong This double integral is a special case of the integral evaluated by Price [4] (eqn. 2.5). Using eqns. 3.23 and 3.24 of [4], a new closed form expression of the outage probability for RiciadRician fading channel is found to be Indexing terms: Interference (signal), Mobile radio systems A new general outage probability expression for a Rician signal received among L Rician interferers is derived. This result is pout shown to cover previously published expressions involving Rayleigh signallinterferers as special cases. New RiciadRician outage probability curves are presented and discussed. Introduction: In microcellular mobile radio systems, channel models in which the signals are affected by fading only are often used [l, 21. In [I], a closed form expression is derived for the outage probability for a desired Rician signal and multiple Rayleigh interferers. In [2], the case of a Rayleigh desired signal with single Rician interferer is studied. For the case of a R i c h desired signal and multiple Rician interferers, no closed form expression for cochannel outage probability has so far been published. In this Letter, we derive a new closed form expression for outage probability for this case, and show that all the expressions for outage probability presented in [I, 21 are just special cases of our result. We also present new outage probability curves for different values of the Rician factor K , and different values of the protection ratio R,. = where 6 , = q Y d , 6, is the Kronecker delta: ,S , = 1 for m = 0 and , S, = 0 for m # 0, and Q(u,v) is the Marcum Q function. Special cases of eqn. 6: (i) Rayleigh desired signal, single Rician interferer: In this case, we let L = 1, & = 0 in eqn. 6 and obtain the result of Haug and Ucci 121: Derivation of outage probability f o r RiciadRician fading environment: Let X , (k = 0, .._,L)be a set of independent complex Gaussian random variables, with mean value m, and variance ok2.Let X , represent the desired Rician signal and E$=, X, represent the sum of L Rician interferers. The outage probability is expressed as (ii) Rician desired signal, L mutually independent Rayleigh interferers: For Rayleigh interferers K, = 0 using eqn. 3.21 of [4], we have Pout = Pr(Y 5 0) (1) where Y = Y, - Et=, Y,, Yo = IXo12,and Y, = R,IX,1*; k = 1, ..., L. Here, R , is the signal-to-interference protection ratio. We assume that all the signals X, (k = 0, .._,L) are independent and all the interferers have the same mean mi, = m, and the same variance o,* = d.This also implies that the Rice factor of each of the interfering signals is the same, K, = lm/*/02.The PDF of the sum of the interferers Y, = E:=, Y,, was obtained by Bello [3]: After some manipulation, it can be shown that Y/ < 0 (2) which is the result of ?ao and Sheikh ([I], eqn. 13). where I,,,(x) is the m order modified Bessel function of the first kind and C, = Rdml’, P, = R p 2 ; k = 1, ..., L. It is to be noted that C, and p, are, respectively, the average power multiplied by the protection ratio of the specular and the diffused components of the kth interferer. The PDF of the desired signal Y, is a special case of eqn. 2 with L = 1 and k = 0: (iii) Rician desired signal, single Rayleigh interferer: We let K , = 0, and L = 1 in eqn. 9 to obtain the result of Yao and Sheikh ([l], eqn.7). (iv) Rician desired signal and single Rician interferer: We let L = 1 and obtain a new expression for the case of a Rician desired signal and a single Rician interferer: 532 ELECTRONICS L E T E R S 30th March 1995 ~ Vol. 31 No. 7 ~ - -- Fig. 2 shows the effect of different R, and L on the outage probability. As expected, the outage probability increases as R, increases. The outage probability also increases with L, as the total interfering power becomes L times larger. Discussions: In the following we present outage probability curves as a function of the signal to interference ratio, SIR, defined as 25 Janwry I995 0 IEE 1995 Electronics Letters Online Nu: 19950362 T.T. Tjbung, C.C. Chai and X. Dong (Department of Electrica1 Engineering, National University of Singapore, I O Kent Ridge Crescent, Singapore 0511, Republic of Singapore) References YAO Y.D. and SHEIKH A.U.H.: 'Outage probability analysis for microcell mobile radio systems with co-channel interferers in RiciadRayleigh fading environment', Electron. Lett., 26, pp. 864866. 2 HAUG I.R. and UCCI D.R.: 'Outage probability of microcellular radio systems in a RayleighlRician fading environment'. Conf. Record, Int. Conf. on Communications ICC'92, pp. 312.4.1-312.4.5 3 BELLO P.A.: 'Binary error probabilities over selectively fading channels containing specular components', IEEE Trans., COM-14, pp. 400406. 4 PRICE R.: 'Some noncentral F-distributions expressed in closed form', Biometrika, 51, pp. 107-122. 1 lo( 10 1 >. -2 +lo s n eQl -3 0 a m 21 1 8 o5 Pitch detection of speech signals using segmented autocorrelation 1Ij6 0 5 10 15 SIR.dB 20 25 rn Fig. 1 Outage probability against SIR for various L, & and KI, wifh RI = 5 (7dB) LA. Atkinson. A.M. Kondoz and B.G. Evans Indexing terms: Speech analysis and processing, Correlation methods 101 1oo A pitch detection algorithm based on segmented autocorrelation is presented which exhibits improved rejection of formant interference and pitch period multiple errors, when compared to the standard autocorrelation method 121. In addition, the algorithm is wmputationally less intensive than a standard autocorrelation of the same window length. 2 1 04 ..- n {1 8 glo3 Q I 3 O -4 10 1 o5 -6 10 I 0 5 10 15 SIR, dB 20 25 30 Fig. 2 Outage probability against SIR for various L and R, & = lO,K,=5 -L= ---- 1 L=6 This SIR is the ratio of the average power of the desired signal to that of one interferer. In Fig. 1 we show outage probability curves for RI = 5 (7dB) and for various values of &, K, and L. The results of Haug and Ucci [2] and of Yao and Sheikh [I] are also shown for comparison. For the range of SIR of interest, say from 8 to 30dB, comparing the curves for Rician faded desired signal with KO= IO, and for one interferer, L = 1, with different K, values, it can be seen that as KI decreases, Po,, increases. The largest Po",occurs when K, = 0, which is the Rayleigh interferer case. At the other extreme, when the desired signal is Rayleigh faded and the interferer is Rician faded (& = 0, K, = S), Pouris much larger than the other interferer cases for which the desired signal is Rician faded. ELECTRONICS LE77ERS 30th March 1995 Vol. 31 - - .-. Introduction: Speech coders operating at bit rates of less than 4.8 kbiUs are usually based on parametric modelling of the human speech production system. Accurate and reliable detection of the pitch parameter is essential in order to maintain speech quality and preserve speaker identity. During highly voiced stationary sections of speech the pitch period is easily observed in the speech waveform, where the pitch period is readily obtained using pitch detection algorithms (PDAs) based on peak detection in the time domain [l] or autocorrelation lag domain [2]. Much of speech is nonstationary, exhibiting features such as rapid changes in energy, rapid evolution of the pitch cycle shape and mixed voicing. Preservation of correct speech characteristics over these regions is essential if high levels of speech intelligibility and quality are to be maintained. Unfortunately, it is over these regions that many PDAs fail. This Letter reports a new pitch detector, the segmented autocorrelation pitch detection algorithm (SAPDA). The SAPDA is autocorrelation based, however the autocorrelation is segmented into smaller units whose window length and lag are determined from the local maxima and minima of the speech signal. The autocorrelation function given by eqn. 1 is used as the basis for many PDAs, where S ( I ] is the ith speech sample of the analysis window and N is the autocorrelation window length. Eqn. 1 has the disadvantage that if the pitch period changes over the analysis window, then the peak corresponding to the correct pitch period becomes broader and reduced in height. In some cases, peaks corresponding to multiples of the pitch period become more pronounced than the required peak and are incorrectly selected as the pitch period. The SAPDA allows the autocorrelation lag to vary slightly over the analysis window, reducing this problem. No. 7 533

1/--страниц