9 BONEK. E.

,
WEGER, P.,

SCHULTES, G., KREUZGRUBER, P., SIMBURGER. w., LESLIE, T.C., WPP. I., KNAPP, H., and ROHRINGER. N.:

'Personal communications transceiver architectures for monolithic integration'. IEEE Int. S p p . Personal, Indoor, and Mobfie Radio Comunications~The The Nether'ands, septmhr 1994. pp. 363-368

where ? ( k ) = d(k) + j i ( k ) is the receiver's decision about the real and imaginary components of data, p'(k) = p,(k) - jq,(k) is the complex conjugate of the real and imaginary components of the sampled matched filter output, and R(x) is the real part of the complex value x. By going through eqns. 2 - 7. the generalisation of the optimised algorithm becomes
p ( k ) = R{ (eik)- e(k-a)]p* (k-1) +?*(/I-1 )[p(/I)- p ( k - 2 ) ] )

(8:

Optimiwtion o modidid Mueller and Muller f slgorfthm

Optimisation of the modified Mueller and Muller (mM&M) timing error detection algorithm by cancelling its self-noise is presented. Simulation results show that not only is the new algorithm d f - n o i e fret, but there are also no symbol slips at medium to high SNR. Short acquisition time, operation on only one sample per symbol to eslimate the timing error, and a low complexity are other features of the new algorithm.

realsignal . , - complex signal m Fig. 1 Timing rrrur .swchronisarion h? uprimisr.d mM&M ulgorithm The block diagram of the optimised mM&M algorithm for the QPSK modulation scheme is shown in Fig. 1. The output of the combined matched filter and interpolator [2] is sampled at symbol rate. UT. Therefore, the operation of the optimised algorithm requires one sample per symbol. To detect the timing error, 2Nj+4 real multiplications and 2N,+5 real additions are performed per timing error estimate 5, where N , is the number of filter coeffcients in the interpolator FIR suhfilters.

Imp filter

Analysis: We are assuming a system whose output comprises nominally synchronised data symbols subject to additive white Gaussian noise, where the transmitter and the receiver use Nyquist root raised-cosine filters. With perfect carrier synchronisation, the sampled matched filter output is
m

p ( k ) = A,
2=-_

a ( i ) g ( ( k- i)T - T)

+ 'U@)

(1)

where a(i) is the data symbol, g(k) is the response of the receiver filter to the input pulse, A , is the amplitude of the received signal. T is the symbol priod, z is the timing error, and w(k) is additive white Gaussian noise. The mM&M algorithm [I] for the simple case of the BPSK modulation scheme is

pLl(k) = [B(k- 1) - q k

+ l)]p,(k)

(2)

where B(k) is the receiver's decision on a(!+ By substituting eqns. 1 and 2 for p(k), the mM&M algorithm can be expanded into 01(k) = A,[B(k-l)-iL(k+l)]

x {a(k+l)g(-T-T)+a(k-

I)g(T-T ) }
(3)
I
, I I . I i . I I I

+ A,[8(k- 1)- b ( k + l ) ] a ( k ) g ( - r )
+ A,[a(k- 1)-ii(k+
m

l)]

(L(Z)fJ((/I-Z)T-T)
i=~.t#k,~#kfl

+ W(k)

2000

symbol number

LOO0

6000

8000

Fig. 2 Performance o / m M & M ulgorithm

The terms on the first line contribute to the error voltage, which is proportional to the timing error z. The term on the second line is the self-noise which will not disappear, even when z = 0. With a Nyquist pulse shape, the summation term on the last line vanishes during tracking. To cancel the self-noise, the following is added to the self-noise:

[&(k)a(k 1 )

- & ( k ) a ( k- 1)]9(-T'I

(4)

At high SNR, the receiver's decisions are correct and, therefore, the self-noise entirely vanishes. From q n . 1 it can be deduced that adding eqn. 4 to eqn. 3 means adding the following to the original algorithm:

Sitnulation results: A QPSK modem was simulated using COSSAP, and the optimised algorithm was incorporated in the demodulator. Fig. 2 shows the normalised timing error of the data output for an initial timing error of half a symbol period and loop gain factor p = 0.18 using the standard mM&M algorithm. These results assume perfect carrier recovery, and high SNR at the input of the modem. It can be seen that although the timing loop has a fast acquisition, there is ii large tracking jitter due to self-noise. In addition. there are symbol slips which degrade the error performance of the receiver.

M ( k ) = B(k)lp,(k + 1 ) - p , ( k

1)1

(5)

The mM&M synchroniser and the algorithm in eqn. 5 generate sample outputs proportional to timing error, but the jitter components are in anti-phase so that if
T

= 0.5[pi(k)

+pz(k)]

(6)

Fig. 3u shows the performance under the same conditions when the optimised algorithm is used. The timing jitter caused by selfnoise has been greatly reduced, and the symbol slips have been eliminated. The fast acquisition characteristics of the mM&M algorithm have not been affected, and Fig. 3b shows the acquisition performance for an initial timing error of half a symbol period. The simulations have been repeated for signals subject to additive white Gaussian noise with SNR from 0 to 15dB, and results have shown consistently better results than those using the original algorithm [ 3 ] .These further results are being prepared for publication.

the jitter is minimised. To generalise eqn. 6 to include QPSK and OQPSK modulation schemes, the mM&M algorithm is

pT(k) = R{[i.(/I- 1 ) - ?(/I l ) ] p ' ( k ) l ] +

(7)

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ELECTRONICS L E T E R S 22nd June 7995 Vol. 31

No. 1 3

the subscriber terminal, voice segments are generated and transmitted sequentially in time slots. During silent periods, the transmission power can be disallowed [I], or alternatively reduced in steps according to a n indication in the system parameter overhead message [2, 31. These techniques are known a s discontinuous voice transmission (DTX). We present expressions for the outage probability calculation with discontinuous transmission in microcellular systems where the desired signal is described by a Rician model. Since a line of sight component is unlikely to exist between cochannel cells, the interferer signals are better described by a general Nakagami model. We refer to this condition as a Rician-Nakagami environment.
Outage crirerbnt Since a n excessive interference level degrades the demodulation process, outage probability is a useful performance criterion. The outage probability is defined as the probability that the carrier-to-joint noise plus the interference ratio (S/I+N) will drop below a specified threshold (4) which is often called the power protection ratio. However, since in high capacity systems it is interference ( I ) rather than noise (N) which limits the system performance. outage is usually described in terms of the S/fratio; this
is

0
b

25

50 75 symbol number

100
E d

Fig. 3 Pr.r/orniom c of optiini.s~~d mM&M ulgorithm

Condusitms. In this Letter the optimisation of the modified Muel-

ler and Muller liming error detection algorithm was presented. By analysis the source of the self-noise was determined and cancelled. The implementation of the new algorithm is simple. Fast acquisition, lo* complexity and self-noise free tracking performance make the algorithm a suitable candidate for implementation in digital receivers

Poutnge Prts 5 iP1 = E71Fs(zq)} =

(1)

where E, is the mean expected value averaged over all possible interference values (i) and F, is the cumulative distribution function (CDF) of the desired signal. Propagutrun model: In the Rician-Nakagami environment. the envelope of the desired signal is described by the Rician model where the instantaneous power (s) follows a noncentral chi-square F D P [4]:

0 IEE lY95
Electroni<s Letrrr s Onlinr No: IYP.50711

26 Muv /'I%

G.R. Daliesfahani and T.G. Jeans (Centre firr Surellirr Engineering Rrsmrdi. L'niver$i/y of' Surrey. Giridford, Surrey. .GU2 S H X , United
Kin,&m
1

References

'Tracking pcrformance comparison of clock synchronisation algorithms for digital implementatlon'. Proc. 1st Int. ESA Workshop on DSP Techniques Applied to Space Communications, The Netherlands, 1988. pp. 98-104 2 V F R D I Y I ) , .ind 'IOZER. T : 'Simulating asynchronous timing recovcry l o o ~ nusing multirate techniques'. IEE Colloquium on Comiiiunications Simulation and Modelling Techniques. York,
I
MOEPILCLAEY M.:

UK, 1993

D A N r w A H A h i C I K : ' A stud! in optimising a multicarrier demultiplexer demodulator (MCDD) for on-board processing (OBPI satellites'. PhD Thesis. University of Surrey. Guildford, Surrev. U K . March 1995

where S , and S, are the power of the direct and reflected components, respectively, whose relative proportion R , = SJS, is known as the rician factor and I,, designates tile modified Bessel function ' of the first kind and of order 2er.o. Note that the Rician model reduces to the Rayleigh model when the line of sight component vanishes (i.e. R, = 0). The envelope of each cochannel interferer signal is described by a Nakagami model where the instantaneous power follows a gamma F D P [4]. It has been found that a Nakagami model is general. since it can describe different fading severity levels and can also approximate diverse scenarios such as Rayleigh. log-normal and half-Gaussian conditions [SI.

Outage analysis in general Rician-Nakagami environments with DTX

In digital cellular technidogies, the use of discontinuous transmisvon (DTX) is a method of achieving p a t e r use of installed capacity and improved quality. The performance improvement that result\ from implementing DTX in microcellular systems is analysed and quantified. Closed form cxpressions are derived for outage probabilities for systems using discontinuous transmissioii in general Rician-Nakagami mvironnients

SI1 interferer, dB m Fig. 1 A verugr outage probability in Rician-Ruyleigh channels for differen1 D T X factors

Introdu<.rion: In digital systems, terminals transmit digitised voice segments imbedded in a frame structure. During the talkspurts of

Fading severity ni = I R = 7dB, w f = 40'4. 6 interferer\ - D 7 X = 0dB (illhigh) D T X = 4dB . _ _ _ . 8dB D7X = _ _ _ D T X = 16dB D 7 X = 32dB
~

ELECTRONICS LETTERS

22nd June 1995

Vol. 31

No. 13

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