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Performance of vector antennas with power control in CDMA under multipath Rayleigh fading channel
Int. J. Electron. Commun. (AEÜ) 65 (2011) 548–552
Contents lists available at ScienceDirect
International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.de/aeue
Performance of vector antennas with power control in CDMA under multipath Rayleigh fading channel Mahmud J. Alnaser ∗ , Salem Salamah The Public Authority for Applied Education and Training, Electronics Engineering, Alshuwaik, Kuwait, Kuwait
a r t i c l e
i n f o
Article history: Received 27 April 2010 Accepted 9 August 2010 Keywords: Polarization diversity Receiver diversity Power control Code division multiple access Multipath channels
a b s t r a c t Receivers currently employ single- or dual-polarized antennas, which measure one or two components of the received electromagnetic (EM) signal. In rich scattering environments, however, it may be possible to improve performance by using “vector antennas” as they can detect up to six independent components of the EM field. In this paper, theoretical and simulation results are obtained. We consider the design and analysis of vector-antenna receiver for code division multiple access (CDMA) signals. We consider a closed loop power control (CLPC) for a beamformer-Rake receiver for wireless CDMA multiuser system. We will investigate the performance enhancements in Bit Error Rate (BER) using various vector antennas that can respond to two polarization components combined in a frequency selective multipath fading channel. © 2010 Elsevier GmbH. All rights reserved.
1. Introduction In cellular communication system, it is known that code division multiple access CDMA system is interference limited. In the uplink from mobile to base station, multiple access interference (MAI) due to multipath fading and cross-correlation between users, results in power variation of the signal level between users located at different distances from base station. This is known as nearfar effect [1]. As a result of this, MAI decreases the received signal level and therefore reduces signal quality. This in turn limits the capacity of the CDMA system. One way to overcome the effect of interference is by monitoring the signal power and maintaining an acceptable level of signal-to-interference plusnoise ratio (SINR) by increasing or decreasing the transmitted power known as power control. In the last two decades, a lot of research has been devoted to different power control schemes. In the research study by Zander [2], Grandhi and Goodman [3] and Foschini and Miljanic [4], power control has been applied in a centralized or distributed way. On the other hand, to further mitigate interference, base stations were equipped with an antenna array structure known as a space–time receiver. This exploits the multipath signal arriving in space and time, and it was investigated by Naguib and Paularj [5]. To employ a power control with antenna arrays, a joint power control and beamforming was inves-
∗ Corresponding author at: College of technological studies, Department of Electronics Engineering, PAAET, Alshuwaik, Kuwait. E-mail addresses: [email protected] (M.J. Alnaser), [email protected] (S. Salamah). 1434-8411/$ – see front matter © 2010 Elsevier GmbH. All rights reserved. doi:10.1016/j.aeue.2010.08.001
tigated for a linear antenna system in a multiuser environment [6]. Most wireless systems currently employ single- or dualpolarized antennas, which can measure at most two components of the received electromagnetic (EM) signal. Since the signal consists of six field components (three electric and three magnetic), some potentially useful information may be neglected. Andrews et al. [7] have suggested that dramatic gains in wireless capacity might be possible by exploiting these extra components of the received signal. In principle, a “Vector antenna” can independently detect or excite all six EM field components enabling the communication system to access additional signaling dimensions, which may enhance performance in the same way as antenna arrays [5]. These extra dimensions can provide additional diversity to combat signal fading, alow the system to spatially leverage bandwidth by transmitting multiple separable signals in the same bandwidth, and improve the suppression of interference in a multiuser environment. A “tripole” antenna that consists of three mutually orthogonal dipoles by Andrew have shown through simulation, that this antenna improves on the capacity of scalar and dual-polarized antennas for a simple propagation example involving a line-ofsight component and one reflected path. A similar study of a three-element antenna system consisting of a loop and two dipoles was presented in [8] where coupling between antenna elements and return loss was investigated. In [9], Konanur et al. have shown an increase of capacity of vector antennas relative to a linear array antenna. Also, tripole antennas have been investigated for a different number of receivers in frequency selective multipath Rayleigh fading channels [10].
M.J. Alnaser, S. Salamah / Int. J. Electron. Commun. (AEÜ) 65 (2011) 548–552
549
neous, and isotropic medium, the received signal can be modeled by [11]:
Y(t) =
E(t) H(t)
= B(, ϕ)Z(t) + N(t),
where N(t) represents thermal noise, is the intrinsic impedance of the propagation medium, and:
⎡
Fig. 1. The orthonormal triad indicating the spherical coordinates (r, , ϕ) and the unit vectors ur , u and uϕ .
− sin
cos cos ϕ
⎢ cos sin cos ϕ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 0 − sin ϕ ⎥ ⎥. B(, ϕ) = ⎢ ⎢ cos cos ϕ ⎥ sin ⎢ ⎥ ⎢ ⎥ ⎣ sin cos ϕ − cos ⎦ − sin ϕ
Previous work on power control for a CDMA system has focused on employing uniform linear array diversity. In this paper, we will aim to use power control for a base station equipped with vector antenna in a multiuser system. The CLPC is used for a different number of vector antenna systems in frequency selective multipath fading channels. We will evaluate the performance of a CDMA system with vector antenna as a function of Bit Error Rate (BER) for different propagation conditions. The organization of this paper is as follows: in Section 2, we will introduce the system model, where the channel model and receiver using closed-loop power-control (CLPC) is proposed. In Section 3, simulation and results are presented, and finally a conclusion is drawn.
2. System model In this paper we will consider the application of power control for vector antennas in the uplink from mobile to base station in a direct sequence synchronous code division multiple access (DSCDMA) system. Consider a single vector antenna at the receiver. Each arriving multipath component is a two-dimensional vector R(t), consisting of horizontally and vertically polarized components of the electric field. For narrowband sinusoidal signals, it is convenient to write the signal in terms of its complex envelope Z, where R(t) = Re{exp(jωc t)Z}, and ωc is the carrier frequency. For any polarized signal, the complex envelope can be written as:
Z = Aej
cos˛ −sin˛
sin˛ cos˛
cosˇ jsin˛
,
where A, , ˛, ˇ, are the amplitude, phase, orientation angle, and ellipticity angle, respectively [11]. Since the signal is a function of the transmitted data, the amplitude, phase and polarization angles vary with time, and we write Z = Z(t). If the multipath component is reflected or scattered by an object in the far-field, then the signal can be approximated as a plane wave at the receiver. Let E(t) and H(t) denote the threedimensional complex envelopes of the electric and magnetic field vectors respectively at the receiver, and suppose that the multipath component arrives at the sensor from the direction ur , where:
ur =
cossinϕ sinsinϕ cosϕ
,
where and ϕ are the azimuth and elevation, respectively, of the incoming signal in the receiver coordinates (see Fig. 1). For a narrowband plane wave propagating in a nonconductive, homoge-
⎤
(1)
0
We are interested in using the antenna system described above to detect CDMA signals in the presence of a rich multipath and multiuser system. The transmitted signal of user i is a complex baseband signal of the form: Si (t) =
M
bi (m)ci (t − mT ),
m=1
where ci (t) is a unit-energy spreading waveform that vanishes outside the interval [0,T), and bi is a sequence of transmitted information bits for user i. When Si (t) is transmitted, the horizontally and vertically polarized components of each multipath component consist of Si (t) with some amplitude and phase shift, so that Zi (t) = Zi Si (t) for some fixed complex vector Zi . We assume that each user’s transmitted signal propagates to the receiver by multiple paths produced by L different scatterers. If the l-th path for user i arrives at the receiver from direction ( i,l , ϕi,l ), the superposition of the multipaths of all n users and noise at the receiver is given by: Y(t) =
L n
Pi B(i, , ϕi, )Zi, Si (t − i, ) + N(t),
(2)
i=1 =1
where Pi is the signal power of the i-th user, B(, ϕ) is the 6×2 antenna response given in Eq. (1), i, is the propagation delay of the l-th path of user i, and Zi, reflects the change in amplitude, phase, and polarization experienced by the l-th multipath component as it propagates from the transmitter of user i to the receiver. The noise N(t) is a zero-mean complex Gaussian vector with covariance 2 I. A tem -element vector antenna with tem ≤ 6 can sense only tem components of Y(t). The received signal in Eq. (2) above can be re-written as: Y(t) =
L n
Pi Gi, Si (t − i, ) + N(t),
(3)
i=1 =1
where Gi, consists of the appropriate tem components of B( i, , ϕi, )Zi, . The components of the vector Zi, are modeled as i.i.d. zero-mean complex Gaussian random variables and therefore the elements of Gi, are also zero-mean complex Gaussian random variables. Assuming we know the channel coefficients, delay spread and user’s spreading waveforms at the receiver, we can write the post-correlation signal of the first user for the m-th bit and -th, multipath as:
mT +1,
Y1, (m) = (m−1)T +1,
c1∗ (t − mT − 1, )Y(t)dt =
P1 G1, b1 (m)
550
M.J. Alnaser, S. Salamah / Int. J. Electron. Commun. (AEÜ) 65 (2011) 548–552
+ i1, + n1, ,
(4)
where c1 (t − 1, ) is the spreading code of the first user delayed by 1, , b1 (m) is the m-th data bit for the first user, and n1, is the thermal noise. The multiple-access interference (MAI) contributed from other users and self-interference is given by: L
i1, =
P1 G1,k I1,,1,k +
k=1,k = /
L n
Pi Gi,k I1,,i,k ,
(5)
i=2 k=1
mT +1,
I1,,i,k = (m−1)T +1,
bi (m)ci (t − mT − i,k ).c1∗ (t − mT − 1, )dt. (6)
˜ 1, = i1, + n1, and correlaSo the total undesired interference n tion can be written as: L
Rn˜ n,1, = ˜
P1,k G1,k G∗1,k +
k=1,k = /
L n
Pi Gi, G∗1,k + n2 I
(8)
and we can write the output of the space–time Rake receiver for path as: z1, (m) = w∗1, Y1, (m) =
˜ P1 w∗1, G1, bm + w∗1, n(m).
(9)
The combining of the Rake output is referred to as maximalratio combining (MRC), and the decision statistic is given as a scalar output:
L
z1, (m)
(10)
The for the desired user and path is given by: G1, , 1, = P1 G∗1, R−1 ˜ n˜ n,1,
(11)
and we can write b at the output of the space–time Rake receiver as: L
P,1 G∗1, R−1 G1, = ˜ n˜ n,1,
L
=1
1, .
(12)
=1
If the noise is white (Rn = 2 I) and G is a zero-mean complex Gaussian random variable, then b has a 2 probability density function (pdf) with 4L degrees of freedom [12]: f b ( ) =
2L−1 ( ) ¯ 2L (2L − 1)!
e− / ¯
where ¯ = /(L 2 ) is the average SNR-per-path-per-antenna. The average BER of BPSK modulation is therefore given by Proakis [12] and [13]:
∞
Pb =
Q(
2 )f b ( )d =
1 − u 2L 2L−1
0
×
1 + u 2
where for the tripole antenna:
u=
¯ 1 + ¯
−1, e(i) < 0 +1, e(i) > 0
cmd =
⎧ −n, ⎪ ⎪ ⎪ . ⎪ ⎪ ⎪ ⎨ −1,
0, ⎪ ⎪ 1, ⎪ ⎪ ⎪ ⎪ ⎩ . −n,
key ∈ (n − 0.5, ∞) key ∈ (0.5, 1.5] key ∈ (−0.5, 0.5], key ∈ (−1.5, −0.5] key ∈ (−∞, −n + 0.5)
The power control method is said to be in mode-n if cmd has the range of {−n, −(n − 1),. . .,−1, 0, 1, n − 1, n} and in mode-0 if cmd is either 1 or −1. Note that mode-0 is the SINR based power control scheme. 3. Simulation
.
=1
b =
(14)
In multi-step power control (MSPC) [14], the power control command (cmd) quantizes the difference between the received SINR and the threshold level set at the base station at multiple levels. The encoding of the error into power control command (cmd) can be explained as follows: we define key = error − p and then the cmd can be related to key given by:
i=2 =1
w1, = Rn−1 G1, , ˜ n,1, ˜
PCbit = sign[e(i)] =
(7)
The beamformer that maximizes SINR ( ) is given by:
bˆ = sgn
P(i + 1) = P(i) − e(i) p, where:
where the first term corresponds to self-interference due to multipath, and the second term is due to multiple-access interference and:
For closed loop power control, we compare for the desired user to a threshold th . The difference between the and th is compared, and the error command e = − th is evaluated. Then a power control command bit is sent to increase or decrease the transmitted power for the next sampling period Tp bits by a p increment. We can summarize the CLPC as:
2 =0
2L − 1 +
(13)
In this section we numerically plot the BER of the matched filter (MF) receiver for vector antenna at the receiver. We consider a single base station and the uplink from mobile users, where all users transmit to the same base station. We aim to determine the performance of vector antennas implemented at a base station which applies a CLPC scheme in a multipath environment when various antenna elements are used. We assume that the multipath components of the desired and interference signals are uniformly distributed on a sphere where the azimuth angle i, are i.i.d. and uniform on ∈[0, 2 ], and the elevation angles ϕi, are i.i.d. with probability density function:
P(ϕi, ) =
1 sin(ϕi, ), 2 0,
0 ≤ ϕi, ≤ otherwise
and the polarizations Zi, are i.i.d. CN(0, I). The noise N(t) is spatially and temporally white and Gaussian (i.e. E[N(t)N† (t + )] = 2 I). The fading channel is assumed to be a frequency-selective, slowly Rayleigh fading channel, and the multipath delays are set at discrete intervals, which is equivalent to one chip duration (Tc ). The scenario of synchronous users is assumed here. The number and values of the multipath delays L are equal for all users at the receiver and we assume the detection of first user. We will evaluate the performance of three different vector antennas that consist of 2, 3 and 6 elements. The 3-element tripole antenna proposed by Andrews et al. consists of three mutually orthogonal dipoles, where B( , ϕ ) are given by:
B( , ϕ ) =
−sin cos 0
cos cosϕ sin cosϕ −sinϕ
,
M.J. Alnaser, S. Salamah / Int. J. Electron. Commun. (AEÜ) 65 (2011) 548–552
Fig. 2. BER of the MF receiver for the tripole antenna (3-dipoles) versus dualpolarized antenna (2-dipoles) for L = 1,2 multipaths, n = 10 users, p = 1 dB.
and a dual-polarized antenna consisting of two orthogonal dipoles, where the elements of B( , ϕ ) are given by:
B( , ϕ ) =
−sin cos
cos cosϕ sin cosϕ
.
We first consider the case of two multipath components with delays 1 and 2 , respectively, such that 2 is delayed by one chip relative to 1 . At the transmitter we assume BPSK modulation and Gold spreading sequences of length 31 [15] and a unit-energy spreading waveform. In some cases, we consider random spreading sequences of length 31. The SNIR threshold th for the CLPC is considered for the desired user where other users are set to the same value. In Fig. 2 the performance of MF detector for desired user is plotted for dual antennas at a number of th values and n = 10 users. The two cases considered here are CLPC and no power control (NO PC). The performance in terms of the BER of CLPC with step size of 1 dB outperforms the case of NO PC. This improvement of BER is achieved over multipath L = 1,2. The figure also shows that more than 2 dB gain is attained for CLPC with respect to the NO PC case. Similarly, the BER of CLPC and NO PC is plotted for tripole antenna with multipath L = 1,2. Also, the theoretical BER for tripole antenna with L = 1,2 (Eq. (13)) and NO PC is plotted and shows a difference of 0.5 dB from the simulation curve. On the other hand, the CLPC with a step size of 1 dB has shown improvement over the NO PC case. When the number of multipaths increased, BER has further improved relative to the NO PC case. This shows that the joint use of tripole antenna with power control has further improved its performance and increased the ability to exploit multipath. In the same figure (Fig. 2), comparing the performance of dual and tripole antenna for L = 1,2 multipath and n = 10 users, we clearly notice a significant improvement of the tripole antenna over dual antenna at each multipath with CLPC and NO PC. From these results, we can conclude that tripole antennas can better exploit multipath when compared to a dual antenna with or without power control. Fig. 3 shows the BER performance with CLPC as a function of the number of interfering users for various numbers of vector antennas. In our simulation, we assume a fixed th of 7.5 dB, L = 2 multipaths and CLPC step size of 1 dB. As illustrated in the figure, we observed that increasing the number of users will increase the interference and degrade the BER. On the other hand, increasing the number of antennas has improved the BER, which means that tripole antennas
551
Fig. 3. BER of the MF receiver for the tripole antenna (3-dipoles), dual-polarized antenna (2-dipoles) and 6-element antenna at th = 7.5 dB for L = 1,2 multipaths, p = 1 dB.
can accommodate more users than dual antennas for lower BER, and the same is true for 6-element antennas over tripole antennas. Fig. 4 shows the effect of CLPC step size on the BER performance for dual and tripole antennas with th = 7.5 dB for 2 multipaths and n = 10 users. The performance of a 0.5 dB step size is less effective compared to the other PC step sizes and increasing the step size value further has improved the BER by a relatively small margin. Therefore, from these results, choosing a step size of 1 dB in all simulations will be optimal. Fig. 5 shows the performance of Multistep PC (MSPC) using dual and tripole antennas in terms of number of modes. Using mode 2 instead of mode 1 in MSPC will improve the BER in both types of antennas and therefore better tolerate fading channel. We also notice that the performance of a tripole antenna in mode 2 is even better than that of a dual antenna. Finally, we show in Fig. 6 the performance of Gold sequence versus random codes both of length 31 using dual and tripole antennas. Since cross-correlation of Gold sequence is much less than random codes, a lower interference is experienced between users. Hence we deduce that vector antenna can better resolve the mul-
Fig. 4. BER of the MF receiver for the tripole antenna (3-dipoles), dual-polarized antenna (2-dipoles) for MSPC at th = 7.5 and n = 10 users for L = 2 multipaths.
552
M.J. Alnaser, S. Salamah / Int. J. Electron. Commun. (AEÜ) 65 (2011) 548–552
4. Conclusions We have studied a MF receiver employing vector antennas with CLPC in multipath fading channel and a multiuser environment. We also observed various vector antennas showing a better performance of BER with power control than in the case without it. We found that tripole antenna have outperformed the dual antenna with CLPC. Also, the result of multi-step power control is evaluated for a different number of multipaths. Finally, comparing the BER for multiuser system using Gold and Random sequences for tripole and dual antennas shows that vector antenna can exploit multipath fading when we use higher correlated codes as compared with Gold codes. In a multiuser system and multipath channel, a tripole antenna is superior in terms of BER when compared with dual antenna for the same number of users. Also, for the same transmited power, tripole antenna have attained a lower BER than dual antenna. So the geometry of antenna with power control has a significant effect on receiver performance and hence signal quality. Fig. 5. BER of the MF receiver for the tripole antenna (3-dipoles), dual-polarized antenna (2-dipoles) for clpc with mode 1,2 and n = 10 users for L = 2 multipaths.
Fig. 6. BER of the MF receiver for the tripole antenna (3-dipoles), dual-polarized antenna (2-dipoles) and n = 10 users for L = 1 multipath with Gold and Random sequences and p = 1 dB.
tipath components where the BER for Gold codes is better than a system using random codes for the same number of users and th .
References [1] Prasad R, Jansen M. Near-far-effects on performance of DS/SS systems for personal communication networks. in Proc IEEE VTC 43;1993:710–713. [2] Zander J. Performance of optimum transmitter power control in cellular radio systems. IEEE Trans Veh Technol 1992;41:57–62. [3] Grandhi SA, R. Vijayan, Goodman DJ. Centralized power control in cellular radio systems. in IEEE Trans Veh Technol 1993;42(November):466–468. [4] Foschini GJ, Miljanic Z. A simple distributed autonomous pca and its convergence. IEEE Trans Veh Technol 1993;42(November):200–209. [5] Naguib AF, Paularj A. Performance of CDMA cellular networks with base-station antenna arrays. in Proc International Zurich Seminar on Digital Communications. [6] Rashid-Farrokhi F, L. Tassiulas, Liu K, J. R, Joint power control and beam forming in wireless networks using antenna arrays. IEEE Trans Comm. 1998;46:1313–1324. [7] Andrews MR, Mitra P. P., deCarvalho, R. Tripling the capacity of wireless communications using electromagnetic polarization. Nature 2001;409:316–318. [8] Konanur AS, Gosalia K, Krishnamurthy S. H., Hughes B., Lazzi, G. Investigation of the performance of co-polarized, co-located electric and magnetic dipoles for increasing channel capacity. in Proc of IEEE AP-S Int Conf 2003;(2 (June)):531–534. [9] Konanur AS, Gosalia K, Krishnamurthy S. H., Hughes B., Lazzi, G. Increasing wireless channel capacity through mimo systems employing co-located antennas. IEEE Trans Microw Theory Tech 2005;53(6 (June):721–729. [10] Al Naser, M. J., Hughes BL. Polarimetric vector receivers for CDMA multipath signals. in Proc CISS. 2006. [11] Nehorai A, Paldi E. Vector-sensor array processing for electromagnetic source localization. IEEE Trans Signal Proc. 1992. [12] Proakis JG. Digital communications. 4th ed. New York: McGraw-Hill. [13] Alnaser MJ. Polarimetric vector receivers for CDMA multipath signals. Dissertation. North Carolina State University, NC: Department of Electrical Engineering; 2006. [14] Chung-Ju Chang J-HL, Ren F-C. Design of power control mechanisms with pcm realization for the uplink of a DS-CDMA cellular mobile radio system. IEEE Trans Veh Technol 1996;45(3). [15] Spread spectrum systems. New York: Wiley; 1976.
Contents lists available at ScienceDirect
International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.de/aeue
Performance of vector antennas with power control in CDMA under multipath Rayleigh fading channel Mahmud J. Alnaser ∗ , Salem Salamah The Public Authority for Applied Education and Training, Electronics Engineering, Alshuwaik, Kuwait, Kuwait
a r t i c l e
i n f o
Article history: Received 27 April 2010 Accepted 9 August 2010 Keywords: Polarization diversity Receiver diversity Power control Code division multiple access Multipath channels
a b s t r a c t Receivers currently employ single- or dual-polarized antennas, which measure one or two components of the received electromagnetic (EM) signal. In rich scattering environments, however, it may be possible to improve performance by using “vector antennas” as they can detect up to six independent components of the EM field. In this paper, theoretical and simulation results are obtained. We consider the design and analysis of vector-antenna receiver for code division multiple access (CDMA) signals. We consider a closed loop power control (CLPC) for a beamformer-Rake receiver for wireless CDMA multiuser system. We will investigate the performance enhancements in Bit Error Rate (BER) using various vector antennas that can respond to two polarization components combined in a frequency selective multipath fading channel. © 2010 Elsevier GmbH. All rights reserved.
1. Introduction In cellular communication system, it is known that code division multiple access CDMA system is interference limited. In the uplink from mobile to base station, multiple access interference (MAI) due to multipath fading and cross-correlation between users, results in power variation of the signal level between users located at different distances from base station. This is known as nearfar effect [1]. As a result of this, MAI decreases the received signal level and therefore reduces signal quality. This in turn limits the capacity of the CDMA system. One way to overcome the effect of interference is by monitoring the signal power and maintaining an acceptable level of signal-to-interference plusnoise ratio (SINR) by increasing or decreasing the transmitted power known as power control. In the last two decades, a lot of research has been devoted to different power control schemes. In the research study by Zander [2], Grandhi and Goodman [3] and Foschini and Miljanic [4], power control has been applied in a centralized or distributed way. On the other hand, to further mitigate interference, base stations were equipped with an antenna array structure known as a space–time receiver. This exploits the multipath signal arriving in space and time, and it was investigated by Naguib and Paularj [5]. To employ a power control with antenna arrays, a joint power control and beamforming was inves-
∗ Corresponding author at: College of technological studies, Department of Electronics Engineering, PAAET, Alshuwaik, Kuwait. E-mail addresses: [email protected] (M.J. Alnaser), [email protected] (S. Salamah). 1434-8411/$ – see front matter © 2010 Elsevier GmbH. All rights reserved. doi:10.1016/j.aeue.2010.08.001
tigated for a linear antenna system in a multiuser environment [6]. Most wireless systems currently employ single- or dualpolarized antennas, which can measure at most two components of the received electromagnetic (EM) signal. Since the signal consists of six field components (three electric and three magnetic), some potentially useful information may be neglected. Andrews et al. [7] have suggested that dramatic gains in wireless capacity might be possible by exploiting these extra components of the received signal. In principle, a “Vector antenna” can independently detect or excite all six EM field components enabling the communication system to access additional signaling dimensions, which may enhance performance in the same way as antenna arrays [5]. These extra dimensions can provide additional diversity to combat signal fading, alow the system to spatially leverage bandwidth by transmitting multiple separable signals in the same bandwidth, and improve the suppression of interference in a multiuser environment. A “tripole” antenna that consists of three mutually orthogonal dipoles by Andrew have shown through simulation, that this antenna improves on the capacity of scalar and dual-polarized antennas for a simple propagation example involving a line-ofsight component and one reflected path. A similar study of a three-element antenna system consisting of a loop and two dipoles was presented in [8] where coupling between antenna elements and return loss was investigated. In [9], Konanur et al. have shown an increase of capacity of vector antennas relative to a linear array antenna. Also, tripole antennas have been investigated for a different number of receivers in frequency selective multipath Rayleigh fading channels [10].
M.J. Alnaser, S. Salamah / Int. J. Electron. Commun. (AEÜ) 65 (2011) 548–552
549
neous, and isotropic medium, the received signal can be modeled by [11]:
Y(t) =
E(t) H(t)
= B(, ϕ)Z(t) + N(t),
where N(t) represents thermal noise, is the intrinsic impedance of the propagation medium, and:
⎡
Fig. 1. The orthonormal triad indicating the spherical coordinates (r, , ϕ) and the unit vectors ur , u and uϕ .
− sin
cos cos ϕ
⎢ cos sin cos ϕ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 0 − sin ϕ ⎥ ⎥. B(, ϕ) = ⎢ ⎢ cos cos ϕ ⎥ sin ⎢ ⎥ ⎢ ⎥ ⎣ sin cos ϕ − cos ⎦ − sin ϕ
Previous work on power control for a CDMA system has focused on employing uniform linear array diversity. In this paper, we will aim to use power control for a base station equipped with vector antenna in a multiuser system. The CLPC is used for a different number of vector antenna systems in frequency selective multipath fading channels. We will evaluate the performance of a CDMA system with vector antenna as a function of Bit Error Rate (BER) for different propagation conditions. The organization of this paper is as follows: in Section 2, we will introduce the system model, where the channel model and receiver using closed-loop power-control (CLPC) is proposed. In Section 3, simulation and results are presented, and finally a conclusion is drawn.
2. System model In this paper we will consider the application of power control for vector antennas in the uplink from mobile to base station in a direct sequence synchronous code division multiple access (DSCDMA) system. Consider a single vector antenna at the receiver. Each arriving multipath component is a two-dimensional vector R(t), consisting of horizontally and vertically polarized components of the electric field. For narrowband sinusoidal signals, it is convenient to write the signal in terms of its complex envelope Z, where R(t) = Re{exp(jωc t)Z}, and ωc is the carrier frequency. For any polarized signal, the complex envelope can be written as:
Z = Aej
cos˛ −sin˛
sin˛ cos˛
cosˇ jsin˛
,
where A, , ˛, ˇ, are the amplitude, phase, orientation angle, and ellipticity angle, respectively [11]. Since the signal is a function of the transmitted data, the amplitude, phase and polarization angles vary with time, and we write Z = Z(t). If the multipath component is reflected or scattered by an object in the far-field, then the signal can be approximated as a plane wave at the receiver. Let E(t) and H(t) denote the threedimensional complex envelopes of the electric and magnetic field vectors respectively at the receiver, and suppose that the multipath component arrives at the sensor from the direction ur , where:
ur =
cossinϕ sinsinϕ cosϕ
,
where and ϕ are the azimuth and elevation, respectively, of the incoming signal in the receiver coordinates (see Fig. 1). For a narrowband plane wave propagating in a nonconductive, homoge-
⎤
(1)
0
We are interested in using the antenna system described above to detect CDMA signals in the presence of a rich multipath and multiuser system. The transmitted signal of user i is a complex baseband signal of the form: Si (t) =
M
bi (m)ci (t − mT ),
m=1
where ci (t) is a unit-energy spreading waveform that vanishes outside the interval [0,T), and bi is a sequence of transmitted information bits for user i. When Si (t) is transmitted, the horizontally and vertically polarized components of each multipath component consist of Si (t) with some amplitude and phase shift, so that Zi (t) = Zi Si (t) for some fixed complex vector Zi . We assume that each user’s transmitted signal propagates to the receiver by multiple paths produced by L different scatterers. If the l-th path for user i arrives at the receiver from direction ( i,l , ϕi,l ), the superposition of the multipaths of all n users and noise at the receiver is given by: Y(t) =
L n
Pi B(i, , ϕi, )Zi, Si (t − i, ) + N(t),
(2)
i=1 =1
where Pi is the signal power of the i-th user, B(, ϕ) is the 6×2 antenna response given in Eq. (1), i, is the propagation delay of the l-th path of user i, and Zi, reflects the change in amplitude, phase, and polarization experienced by the l-th multipath component as it propagates from the transmitter of user i to the receiver. The noise N(t) is a zero-mean complex Gaussian vector with covariance 2 I. A tem -element vector antenna with tem ≤ 6 can sense only tem components of Y(t). The received signal in Eq. (2) above can be re-written as: Y(t) =
L n
Pi Gi, Si (t − i, ) + N(t),
(3)
i=1 =1
where Gi, consists of the appropriate tem components of B( i, , ϕi, )Zi, . The components of the vector Zi, are modeled as i.i.d. zero-mean complex Gaussian random variables and therefore the elements of Gi, are also zero-mean complex Gaussian random variables. Assuming we know the channel coefficients, delay spread and user’s spreading waveforms at the receiver, we can write the post-correlation signal of the first user for the m-th bit and -th, multipath as:
mT +1,
Y1, (m) = (m−1)T +1,
c1∗ (t − mT − 1, )Y(t)dt =
P1 G1, b1 (m)
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+ i1, + n1, ,
(4)
where c1 (t − 1, ) is the spreading code of the first user delayed by 1, , b1 (m) is the m-th data bit for the first user, and n1, is the thermal noise. The multiple-access interference (MAI) contributed from other users and self-interference is given by: L
i1, =
P1 G1,k I1,,1,k +
k=1,k = /
L n
Pi Gi,k I1,,i,k ,
(5)
i=2 k=1
mT +1,
I1,,i,k = (m−1)T +1,
bi (m)ci (t − mT − i,k ).c1∗ (t − mT − 1, )dt. (6)
˜ 1, = i1, + n1, and correlaSo the total undesired interference n tion can be written as: L
Rn˜ n,1, = ˜
P1,k G1,k G∗1,k +
k=1,k = /
L n
Pi Gi, G∗1,k + n2 I
(8)
and we can write the output of the space–time Rake receiver for path as: z1, (m) = w∗1, Y1, (m) =
˜ P1 w∗1, G1, bm + w∗1, n(m).
(9)
The combining of the Rake output is referred to as maximalratio combining (MRC), and the decision statistic is given as a scalar output:
L
z1, (m)
(10)
The for the desired user and path is given by: G1, , 1, = P1 G∗1, R−1 ˜ n˜ n,1,
(11)
and we can write b at the output of the space–time Rake receiver as: L
P,1 G∗1, R−1 G1, = ˜ n˜ n,1,
L
=1
1, .
(12)
=1
If the noise is white (Rn = 2 I) and G is a zero-mean complex Gaussian random variable, then b has a 2 probability density function (pdf) with 4L degrees of freedom [12]: f b ( ) =
2L−1 ( ) ¯ 2L (2L − 1)!
e− / ¯
where ¯ = /(L 2 ) is the average SNR-per-path-per-antenna. The average BER of BPSK modulation is therefore given by Proakis [12] and [13]:
∞
Pb =
Q(
2 )f b ( )d =
1 − u 2L 2L−1
0
×
1 + u 2
where for the tripole antenna:
u=
¯ 1 + ¯
−1, e(i) < 0 +1, e(i) > 0
cmd =
⎧ −n, ⎪ ⎪ ⎪ . ⎪ ⎪ ⎪ ⎨ −1,
0, ⎪ ⎪ 1, ⎪ ⎪ ⎪ ⎪ ⎩ . −n,
key ∈ (n − 0.5, ∞) key ∈ (0.5, 1.5] key ∈ (−0.5, 0.5], key ∈ (−1.5, −0.5] key ∈ (−∞, −n + 0.5)
The power control method is said to be in mode-n if cmd has the range of {−n, −(n − 1),. . .,−1, 0, 1, n − 1, n} and in mode-0 if cmd is either 1 or −1. Note that mode-0 is the SINR based power control scheme. 3. Simulation
.
=1
b =
(14)
In multi-step power control (MSPC) [14], the power control command (cmd) quantizes the difference between the received SINR and the threshold level set at the base station at multiple levels. The encoding of the error into power control command (cmd) can be explained as follows: we define key = error − p and then the cmd can be related to key given by:
i=2 =1
w1, = Rn−1 G1, , ˜ n,1, ˜
PCbit = sign[e(i)] =
(7)
The beamformer that maximizes SINR ( ) is given by:
bˆ = sgn
P(i + 1) = P(i) − e(i) p, where:
where the first term corresponds to self-interference due to multipath, and the second term is due to multiple-access interference and:
For closed loop power control, we compare for the desired user to a threshold th . The difference between the and th is compared, and the error command e = − th is evaluated. Then a power control command bit is sent to increase or decrease the transmitted power for the next sampling period Tp bits by a p increment. We can summarize the CLPC as:
2 =0
2L − 1 +
(13)
In this section we numerically plot the BER of the matched filter (MF) receiver for vector antenna at the receiver. We consider a single base station and the uplink from mobile users, where all users transmit to the same base station. We aim to determine the performance of vector antennas implemented at a base station which applies a CLPC scheme in a multipath environment when various antenna elements are used. We assume that the multipath components of the desired and interference signals are uniformly distributed on a sphere where the azimuth angle i, are i.i.d. and uniform on ∈[0, 2 ], and the elevation angles ϕi, are i.i.d. with probability density function:
P(ϕi, ) =
1 sin(ϕi, ), 2 0,
0 ≤ ϕi, ≤ otherwise
and the polarizations Zi, are i.i.d. CN(0, I). The noise N(t) is spatially and temporally white and Gaussian (i.e. E[N(t)N† (t + )] = 2 I). The fading channel is assumed to be a frequency-selective, slowly Rayleigh fading channel, and the multipath delays are set at discrete intervals, which is equivalent to one chip duration (Tc ). The scenario of synchronous users is assumed here. The number and values of the multipath delays L are equal for all users at the receiver and we assume the detection of first user. We will evaluate the performance of three different vector antennas that consist of 2, 3 and 6 elements. The 3-element tripole antenna proposed by Andrews et al. consists of three mutually orthogonal dipoles, where B( , ϕ ) are given by:
B( , ϕ ) =
−sin cos 0
cos cosϕ sin cosϕ −sinϕ
,
M.J. Alnaser, S. Salamah / Int. J. Electron. Commun. (AEÜ) 65 (2011) 548–552
Fig. 2. BER of the MF receiver for the tripole antenna (3-dipoles) versus dualpolarized antenna (2-dipoles) for L = 1,2 multipaths, n = 10 users, p = 1 dB.
and a dual-polarized antenna consisting of two orthogonal dipoles, where the elements of B( , ϕ ) are given by:
B( , ϕ ) =
−sin cos
cos cosϕ sin cosϕ
.
We first consider the case of two multipath components with delays 1 and 2 , respectively, such that 2 is delayed by one chip relative to 1 . At the transmitter we assume BPSK modulation and Gold spreading sequences of length 31 [15] and a unit-energy spreading waveform. In some cases, we consider random spreading sequences of length 31. The SNIR threshold th for the CLPC is considered for the desired user where other users are set to the same value. In Fig. 2 the performance of MF detector for desired user is plotted for dual antennas at a number of th values and n = 10 users. The two cases considered here are CLPC and no power control (NO PC). The performance in terms of the BER of CLPC with step size of 1 dB outperforms the case of NO PC. This improvement of BER is achieved over multipath L = 1,2. The figure also shows that more than 2 dB gain is attained for CLPC with respect to the NO PC case. Similarly, the BER of CLPC and NO PC is plotted for tripole antenna with multipath L = 1,2. Also, the theoretical BER for tripole antenna with L = 1,2 (Eq. (13)) and NO PC is plotted and shows a difference of 0.5 dB from the simulation curve. On the other hand, the CLPC with a step size of 1 dB has shown improvement over the NO PC case. When the number of multipaths increased, BER has further improved relative to the NO PC case. This shows that the joint use of tripole antenna with power control has further improved its performance and increased the ability to exploit multipath. In the same figure (Fig. 2), comparing the performance of dual and tripole antenna for L = 1,2 multipath and n = 10 users, we clearly notice a significant improvement of the tripole antenna over dual antenna at each multipath with CLPC and NO PC. From these results, we can conclude that tripole antennas can better exploit multipath when compared to a dual antenna with or without power control. Fig. 3 shows the BER performance with CLPC as a function of the number of interfering users for various numbers of vector antennas. In our simulation, we assume a fixed th of 7.5 dB, L = 2 multipaths and CLPC step size of 1 dB. As illustrated in the figure, we observed that increasing the number of users will increase the interference and degrade the BER. On the other hand, increasing the number of antennas has improved the BER, which means that tripole antennas
551
Fig. 3. BER of the MF receiver for the tripole antenna (3-dipoles), dual-polarized antenna (2-dipoles) and 6-element antenna at th = 7.5 dB for L = 1,2 multipaths, p = 1 dB.
can accommodate more users than dual antennas for lower BER, and the same is true for 6-element antennas over tripole antennas. Fig. 4 shows the effect of CLPC step size on the BER performance for dual and tripole antennas with th = 7.5 dB for 2 multipaths and n = 10 users. The performance of a 0.5 dB step size is less effective compared to the other PC step sizes and increasing the step size value further has improved the BER by a relatively small margin. Therefore, from these results, choosing a step size of 1 dB in all simulations will be optimal. Fig. 5 shows the performance of Multistep PC (MSPC) using dual and tripole antennas in terms of number of modes. Using mode 2 instead of mode 1 in MSPC will improve the BER in both types of antennas and therefore better tolerate fading channel. We also notice that the performance of a tripole antenna in mode 2 is even better than that of a dual antenna. Finally, we show in Fig. 6 the performance of Gold sequence versus random codes both of length 31 using dual and tripole antennas. Since cross-correlation of Gold sequence is much less than random codes, a lower interference is experienced between users. Hence we deduce that vector antenna can better resolve the mul-
Fig. 4. BER of the MF receiver for the tripole antenna (3-dipoles), dual-polarized antenna (2-dipoles) for MSPC at th = 7.5 and n = 10 users for L = 2 multipaths.
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4. Conclusions We have studied a MF receiver employing vector antennas with CLPC in multipath fading channel and a multiuser environment. We also observed various vector antennas showing a better performance of BER with power control than in the case without it. We found that tripole antenna have outperformed the dual antenna with CLPC. Also, the result of multi-step power control is evaluated for a different number of multipaths. Finally, comparing the BER for multiuser system using Gold and Random sequences for tripole and dual antennas shows that vector antenna can exploit multipath fading when we use higher correlated codes as compared with Gold codes. In a multiuser system and multipath channel, a tripole antenna is superior in terms of BER when compared with dual antenna for the same number of users. Also, for the same transmited power, tripole antenna have attained a lower BER than dual antenna. So the geometry of antenna with power control has a significant effect on receiver performance and hence signal quality. Fig. 5. BER of the MF receiver for the tripole antenna (3-dipoles), dual-polarized antenna (2-dipoles) for clpc with mode 1,2 and n = 10 users for L = 2 multipaths.
Fig. 6. BER of the MF receiver for the tripole antenna (3-dipoles), dual-polarized antenna (2-dipoles) and n = 10 users for L = 1 multipath with Gold and Random sequences and p = 1 dB.
tipath components where the BER for Gold codes is better than a system using random codes for the same number of users and th .
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