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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
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