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IEEE COMMUNICATIONS LETTERS, VOL. 6, NO. 12, DECEMBER 2002
Average Block Error Probability of Multicell CDMA Packet Networks With Fast Power Control Under Multipath Fading Margarita Ruiz-García, J. M. Romero-Jerez, C. Téllez-Labao, and A. Diaz-Estrella
Abstract—In this letter, we derive the average block error probability of multicell code-division multiple access (CDMA) packet networks with fast power control under multipath fading. Unlike many previous works, we consider that users are connected to a base station on a minimum attenuation basis. An analytical approach for the calculation of the intracell and intercell statistics is presented. By making use of these expressions, the mean block error probability is analyzed as a function of the number of resolvable paths and the number of base stations to which mobiles can connect. Index Terms—CDMA, fast power control, multipath fading, packet.
I. INTRODUCTION
F
UTURE wireless systems will require integrated services and flexible system architecture. Code-division multiple access (CDMA) and packet-switching are both attractive system design choices to accommodate these emerging demands. Third generation mobile radio systems use fast power control to compensate radio channel variations due to multipath fading for users moving at a low and even moderate speed. The performance of packet CDMA scheme in a Rayleigh fading environment has been analyzed in [1] and [2]. However, these studies assumed a single cell system where no intercell interference is considered In addition, it is commonly assumed in a multipath fading environment that users connect to the nearest base station [3]. In this letter, we estimate the average block error probability of multicell CDMA packet networks with fast power control under multipah fading. In [4] the derivation of the interference statistics for a CDMA system with fast power control is presented but the approach requires previous long and costly simulations. In [5] the effect of multipath fading on system capacity is implicitly considered in the required energy per bit to interfer. In this letter we present an analytence density ratio ical model for a characterization of the intercell and intracell interference in a cellular CDMA system, taking into account the effects of multipath fading, where cell selection is based on a minimum attenuation criterion. This interference characterization is used to derive the expression of the average block
error probability in multicell DS/CDMA packet transmission networks (UMTS). II. SYSTEM MODEL We consider the uplink channel of a multicell DS-CDMA packet transmission network with hexagonal cells and users per cell. Users generate and transmit -bits packets. The channel coherence time [1] is assumed to be greater than the packet transmission time, that is, the response of the channel does not change during a packet transmission. We use a block error correcting code able to correct up to errors. Each user communicates with the base station that provides the least closest base stations. average attenuation among a set of The area of the system will thus be divided in two regions: (points having the reference base station among the nearest base stations) and (points not having among nearest base stations). The radio channel is affected the by distance, path-loss exponent, lognormal shadowing and multipath fading. Power control is assumed to be fast enough to compensate the rapid fluctuations of the radio channel due equal strength signals to multipath fading. We consider that with Rayleigh distribution are received and optimally combined in RAKE receivers [3]. The power of the multipath fading degrees of will thus have a chi-squared distribution with freedom with probability density function (1) III. INTERCELL INTERFERENCE STATISTICS Let be the power received at a base station from a mobile connected to this base station. Assuming perfect compensation of multipath fading, will be constant, and the normalized indue to an active mobile located at tercell interference at in the region will be given by the point
(2) Manuscript received September 5, 2002. The associate editor coordinating the review of this letter and approving it for publication was Dr. S. Batalama.This work was supported by the Spanish CICYT project TIC2000-1120-C03-01. The authors are with the Departamento de Tecnología Electrónica, E.T.S.I. Telecomunicación, University of Málaga, 29071 Málaga, Spain (e-mail:
[email protected]). Digital Object Identifier 10.1109/LCOMM.2002.806461
, is the distance between mobile and base where is a random variable station , is the path-loss exponent, modeling the shadowing effect between mobile and base station , which is assumed to follow a Gaussian distribution with and is a random variable mean and standard deviation
1089-7798/02$17.00 © 2002 IEEE
RUIZ-GARCÍA et al.: AVERAGE BLOCK ERROR PROBABILITY OF MULTICELL CDMA PACKET NETWORKS
modeling the received power of the multipath fading process between mobile and base station . The moment of order of the will be interference generated by user in
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where and are, respectively, the areas of the regions and . In order to obtain expressions in a compact form, we is higher than 3, and that the power transmitted consider that by the mobiles is unlimited. With these considerations we have:
(3) (12) (4) and the dependence on has been where omitted for the sake of clarity. The first factor in (3) can be found to be given by [5], [6]
(13) For a path loss exponent of 4 and a deviation of the logof 6 dB, the values obtained for the internormal shadowing ference factors , and are 0.5844, 0.2662, 0.0549 for and 0.5658, 0.2013, 0.054 for . IV. INTRACELL INTERFERENCE STATISTICS
(5) where
, while for the second and third factors we have
The intracell interference generated at by an active moin the region (note that mobile located at the point cannot generate intracell interference) will biles in the region be given by
(6)
(14)
(7)
is a Bernoulli distributed random variable taking where ) and 1 (the movalues 0 (the mobile is not connected to ), with . Therebile is connected to fore
we proceed nearly as before, but For a mobile in the region for the mobile to generate intercell interference, the minimum base stations must be average attenuation to the nearest . Therefore lower than the attenuation to
(15) From (13), the probability that a mobile is connected to is gion
located in the re-
(8) (16) is equal to (4) for where factor in (8), [5], [6], is equal to (5) for
. The first
(9)
Therefore, the mean and the variance of the intracell interference can be found integrating over , that is (17)
Considering hexagonal cells with radius normalized to unity and uniform density of mobile users with magnitude users per unit area, the mean and variance of the total intercell interference can be found by integrating throughout the whole service area
(18) , for
where for
,
dB,
and
.
V. AVERAGE BLOCK ERROR PROBABILITY (10)
The average block error probability is given by (19)
(11)
is the probability of having a correctable block and where is the average bit error probability. With direct sequence
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IEEE COMMUNICATIONS LETTERS, VOL. 6, NO. 12, DECEMBER 2002
BPSK of spreading bandwidth , the expression for the ratio of bit energy to interference density for an user is (20) is the information bit rate, is the background noise where power spectral density (negligible compared to the interference is the processing gain power density due to mobile users) and . We model the total normalized interference by a lognormal random variable ( is Gaussian distributed) due to fast power control. The mean and variance of are (21) (22) The BER, for constant received signal power levels, is given by (Gaussian approximation [5]) (23) is approximated by another lognormal where the ratio random variable ( is a Gaussian random variable). The mean and variance of is given by (24) (25) Averaging over , we evaluate the average BER as (26) is the probability density function of . Using an where expansion in central differences for the estimation of (24), as in [6], we can write
M
Fig. 1. Average packet error probability for 2 cases. (a) Users connect to the = 3 and 4, (b) Users are connected to a base nearest base station [3] for = 4 and station on a minimum attenuation basis, for = 3, = 4, = 9. Comparison of these results with simulation results for = 4 and = 3.
N M
M
M
N N
decreases if increases from 4 to 9 for the values of M of 3 and 4. This is in contrast with the results in [6], where it is beyond four does not provide any claimed that increasing appreciable gain in performance. The reason for this is that in [6] only the average interference is used in the analysis. In this figure it is also clear that, as the number of resolvable paths increases, the packet error probability decreases. The reason for this is that the observed fluctuations of the radio channel due to fading are smoothed and consequently less interference is introduced in the system. This figure also shows that the packet and taking into acerror probability is higher for count the common minimum distance criterion [3]. Our results are more realistic and the curves show that the lowest packet and . Finally error probability is obtained for we estate that the simulations results are very approximated to the analytical ones as it is shown in this figure. REFERENCES
(27) VI. NUMERICAL RESULTS AND CONCLUSIONS This section presents curves showing the results obtained for the packet error probability. A processing gain of 256, a deviaof 6 dB, a path loss expotion of the log-normal shadowing of nent of 4, a number of resolvable paths M of 3 and 4 and 4 and 9 (for higher values of , the results are similar [5]) are considered for the Fig. 1. We compare our results with the ones obtained taking into account the usual assumption that users and . Beconnect to the nearest base station [3] for sides we compare our analytical results with the ones obtained and . by means of simulation for Fig. 1 shows the packet error probability for different values and . It can be seen that the packet error probability of
[1] J. Pérez-Romero, L. G. Alonso, and R. Agustí, “Average block error probability in the reverse link of a packet DS-CDMA system under Rayleigh fading channel conditions,” IEEE Comun. Lett., vol. 4, no. 4, pp. 116–118, April 2000. [2] W. Xu, A. Chockalingam, and L. B. Milstein, “Throughput-delay analysis of a multichannel packet CDMA scheme in a fading environment,” in Proc. IEEE ICUPC’97, vol. 1, San Diego, CA, Oct. 1997, pp. 183–187. [3] B. Hashem and E. Sousa, “Reverse link capacity and interference statistics of a fixed step power controlled DS/CDMA system under slow multipath fading,” IEEE Trans. Commun., vol. 47, no. 12, pp. 1905–1912, Dec. 1999. [4] J. M. Romero-Jerez, M. Ruiz-García, and A. Díaz-Estrella, “Effects of multipath fading on BER statistics in cellular CDMA networks with fast power control,” IEEE Commun. Lett., vol. 4, pp. 349–351, Nov. 2000. [5] G. E. Corazza, G. De Maio, and F. Vatalaro, “CDMA cellular system performance with fading, shadowing and imperfect power control,” IEEE Trans. Veh. Technol., vol. 47, pp. 450–459, May 1998. [6] J. Zhang and V. Aalo, “Performance analysis of a multicell DS-CDMA system with base station diversity,” Proc. IEE Communications, vol. 148, no. 2, pp. 112–118, Apr. 2001.
