A NOVEL ESTIMATOR FOR THE VELOCITY OF A MOBILE STATION IN A MICRO-CELLULAR SYSTEM
Ghasem Atemi, Bouchra Senadji and Boualem Boashash Signal Processing Research Centre Queensland University of Technology GPO Box 2434, Brisbane, QLD 4001, Australia Email:
[email protected] 3. MODEL A N D STATISTICS OF THE RECEIVED SIGNAL
1. ABSTRACT In this paper, a new estimator for the velocity of a mobile station in .a micro-cellular system is proposed. The proposed estimator is based on the instantaneous frequency of the received signal at the mobile station antenna. The performance of the proposed estimator in the presence of shadowing, additive noise, and nonisotropic scattering is analyzed, and compared with that of the conventional zero crossing rate based velocity estimator. We show that, unlike conventional estimators, the proposed estimator is robust to shadowing and additive noise.
2. INTRODUCTION
Micro-cells allow for increased capacity of mobile communication systems. In these systems, the velocity information can significantly improve the performance of the conventional received signal strength based handover algorithms by simultaneously reducing both the number of handovers and the handover delay 111. Reliable estimates of the mobile station (MS) velocity are also useful for effective dynamic channel assignment, and the optimization of adaptive multiple access wireless receivers. Conventional methods for estimating the velocity of an MS are based on the statistics of either the envelope or quadrature components of the received signal [l, 2, 31. The main drawback of those estimators is that their performance deteriorates in the presence of shadowing. Based on the instantaneous frequency (IF) of the received signal at the MS, we propose a new velocity estimator. We show that the proposed velocity estimator is robust to shadowing and its performance is mildly affected by the presence of additive white Gaussian noise (AWGN), and is similar to that of the zerocrossing rate (ZCR) method with respect to scattering distribution.
0-7803-7761-31031S17.00 0 2 0 0 3 lEEE
When an unmodulated carrier is transmitted, the bandpass signal received by an MS in the presence of additive noise can be modeled as 111:
where fc is the carrier frequency and n(t) represents the additive noise. The means, mi and m,, are due to the presence of a possible LOS component. In the absence of LOS component the model in (1) reduces to y ( t ) = s ( t ) n(t) where z ( t ) = zi(t)cosZxf,t s r ( t )sin27rfCtrepresents the scatter components of the received signal. The signal z ( t ) is the result of a constructive and destructive superposition of plane waves at the MS antenna. It is known that the envelope of s ( t ) has a Ricean distribution with Rice factor K = (mf + m i ) / 2 u Z where U’ = E[zf] = E[z:], with E[ ] the expectation operator. Also, the nth spectral m e ment of s ( t ) + n ( t ) is given by [l]:
+
b,
= ao(Znfm)”Lny(6’) cosn(8)d6‘
where ao = U ’ , fm is the maximum Doppler frequency shift, and p(6’) is the scattering distribution which is a function of the angle of incidence e of incoming waves. In a typical micro-cellular system, the scattering distribution is usually non-isotropic. Therefore, in order to capture the effects of the scattering distribution, the von Mises-Fisher density:
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where I I is the absolute value operator, w is the MS velocity, and A is the wavelength of the received signal. Using (8) and the assumption of local ergodicity, we propose the IF-based velocity estimator as:
K
5 = AJzexp(-)2
r,-
K
I(-)
2
< Ij,(t)l >
(9)
where k ( t ) is the estimated IF' of the received signal, I? is the estimated Ricean factor, and m
rm
x=o
x = 10
Figure 1: Polar plots ofp(8).
is used as a model for p ( 0 ) [4]. In (3), In(.)is the modified Bessel function of order n and determines the directivity of the incoming waves. For = 0 the scattering is isotropic and as x increases, the incoming wave becomes more directive (Figure 1). Using the scattering distribution in (3), bn can be written as:
x
is the time average of the IF over the duration T of the recorded signal. In the following section, assuming perfect estimation of f;(t) and K , we will study the effects of the mismatch caused by additive noise, nonisotropic scattering, and shadowing.
x
b, = ao(~rrfm)"qn(x)+ [l- (-l)n+l]No"nB~+l 4(n 1) (4) where:
+
In particular, it can be shown t h a t
5. P E R F O R M A N C E OF THE IF-BASED
VELOCITY ESTIMATOR 5.1. Effect of A W G N and Non-isotropic Scat-
tering
9,
The relative error, in estimating the MS velocity using the estimator in (9) can be expressed as:
where:
so(x) = 1 1--,
Using an envelope-phase description, the signal y ( t ) in (1) can be rewritten as
= r(t)cos(27rfct + $ ( t ) ) . (6) The velocity estimator which is proposed in the next section is based on the IF of y ( t ) , which is defined as [SI: y(t)
4.
and p ( ~ , $ , ? , $ ) is the joint p.d.f. Using (10) and (ll), the error can be computed numerically. However, closed form expression for the error can be obtained for K = 0 (Rayleigh fading). In this case, based on the results in [6],E[If;l]can be derived as:
Using (5a) and (5h), after some simple algebra, we ob-
THE P R O P O S E D V E L O C I T Y ESTIMATOR
The IF-based velocity estimator is derived in the ideal case, i.e. in the absence of shadowing and additive noise, and in the case of isotropic scattering. Based on the results in (61, it can he shown that in the ideal case, we have:
where y = A?L is the signal-bnoise ratio (SNR). "7 . Therefore, the re attve error can be written as:
Note that fm = X. In the following subsections, we will study separately the effect of AWGN and non-isotropic scattering on the IF-based velocity estimator.
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5.1.1. Effect of AWGN
The effect of AWGN alone is determined by setting x = 0 (isotropic scattering) in (13). In this case, (13) reduces to:
figure 2 shows the effect of AWGN on’the IF-based estimator, assuming BO = = 170 Hz, which allows for velocities up to vmoz = 100 km/h at j c = 900 MHz. It shows that a large XBo/v (low velocities) at low SNRs, results in a significant error. However, due to the parabolic characteristic of the noise at the output of the IF estimator 17, page: 2781, y is much higher than the received SNR. It follows that the IF-based estimator will still have a negligible error for small velocities even at low values of the received SNR.
9
5.1.2. Effect of the Scattering Distribution
The effect of the scattering distribution is examined in the absence of noise. When y + 00, (13) becomes:
IF-based velocity estimator also outperforms the other estimators in the presence of non-isotropic scattering. 5.2. Effect of shadowing
The effect of shadowing is studied in the absence of additive noise. Lee and Yeh, 181, suggest that, in the presence of shadowing, the composite received signal can be expressed as the product of the short-term multipath fading and long-term shadow fading. It follows that, in the absence of additive noise, the composite received signal a t the MS can be modeled as
Ydt) =“(t)
(16)
where m(t) represents the shadow variations caused by terrain configurations between the BS and the MS. Eq. (16) indicates that m ( t ) will cause a distortion in the amplitude and quadrature components of the received signal. Therefore the performance of all velocity estimators which are based on the statistics of the envelope and quadrature components of the received signal, deteriorates in the presence of shadowing. Because the shadowing produces no phase distortion, the IF of the received signal is not affected hy m(t) (both signals s ( t ) = r ( t )cos(Zirf,t $ ( t ) ) and m(l)r(t)cos(Zaf,t+$(t)) have the same IF). It follows that, the proposed estimator is robust to shadowing.
+
which is shown in Figure 3. Because the estimator in (9) was derived in the case of isotropic scattering, the error in estimating the MS velocity increases as increases. Based on the results in [l],the ZCR- and the IF-based velocity estimators have the same performance in the presence of non-isotopic scattering. Since it has been shown in [l]that the ZCR-based velocity estimator is generally more robust than the level crossing rate and covariance based methods in the presence of non-isotropic scattering, we conclude that the proposed
x
6. SIMULATIONS A N D DISCUSSIONS
The received signal at the MS was modeled taking into account multi-path fading, path-loss variation, and lognormal shadowing, as described in [9, chapter 21. The values of BO = 170 Hz and un = 8 d B were chosen for the system bandwidth and standard deviation of
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is robust t o shadowing. Simulations showed that the IF-based velocity estimator has superior performance in the presence of shadowing and AWGN than the conventional ZCR based one. This indicates that the Ilbased velocity estimator can significantly improve the performance of the velocity based handover decision algorithms in micrecellular and multi-tier systems. 8 . REFERENCES
Figure 4: Relative error as a function of the MS velocity in the presence of shadowing.
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[Z] A. Ahdi and M. Kaveh, “A new velocity estimator for cellular systems based on higher order crossings,” in Asilomar Conference o n Signals, Systems, and Computers, 1998, vol. 2, pp. 1423-1427. 13) C. Tepedelenlioglu and G. B. Giannakis, “On velocity estimation and correlation properties of narrow-band mobile communication channels,” IEEE Pansactions on Vehicular Technology, vol. 50, no. 4, pp. 1039-1052, Jul. 2001. [4] 3. Lin and J. G. Proakis, “A parametric method
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Figure 5: Relative error as a function of the MS velocity in the presence of AWGN with SNR=10 dE at the receiver input.
the shadowing. For each value of the MS velocity, the Ricean K-factor was estimated using the the momentmethod based estimator in [lo], and the estimated velocity was computed using (9). The performance of the IF-based estimator was compared with the conventional ZCR-based one by computing the average relative error over 100 realizations. The effects of shadowing (no additive noise) and of additive noise (no shadowing), in the case of isotropic scattering, are shown in Figures 4 and 5. They confirm that the performance of the proposed estimator is mildly affected by shadowing and AWGN.
7. CONCLUSION We proposed a new estimator for the velocity of a MS. Unlike conventional estimators, the proposed estimator
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