The Performance Evaluation of Smart Antenna System Applied to Wireless
Bluetooth Systems
Shiann-Shiun Jeng, Chen Wan Tsung and Yen Hsu Chen
Department of Electrical Engineering, National Dong Hwa University
[email protected], [email protected], [email protected]
Abstract
In this paper, we evaluate the performance of the smart antenna beamforming algorithms applied to a Bluetooth system. The smart antenna system can decrease the multipath fading, increase the diversity gain, and suppress the co-channel interference between different devices. The simulation results show that the BER of Bluetooth with Pseudo-inverse DOA (PIDOA) and Dominant DOA (DDOA) beamforming interfered by the other pico nets can achieve about 10-4 and 10-3 respectively when the SNR=18dB and the number of pico nets is 4. When the error of DOAs is less than 10o, the performance of the Bluetooth with DDOA beamforming and PIDOA is still better than that without beamforming respectively.
Keywords: Bluetooth, smart antenna, PIDOA, DDOA I. Introduction
As communication technology develops, the short distance wireless communication techniques become more and more important. Ericsson proposed a wireless method to connect the mobile phone and other mobile devices to transmit voice and data. The transmission frequency of the Bluetooth is constrained to 2.4GHz ISM band. There are other wireless communication techniques performed in this band, such as IEEE 802.11b and Home RF. Thus, if the frequency hopping is utilized in this band, it will suffer from the co-channel interference from other wireless communication systems.
Besides, when the techniques of Bluetooth are improved, the cost of device is low. The Bluetooth is more and more popular and the number of Bluetooth network increases. Therefore, the co-channel interference between the different Bluetooth devices increases. In November 2003, Bluetooth SIG included the adaptive frequency hopping scheme in the new specification (version 1.2). Utilizing the Link Manage Protocol (LMP) runs link judgment to avoid bluetooth equipments utilizing the bandwidth occupied by other wireless devices and co-channel interference. In this paper, we use smart antenna systems to eliminate the co-channel interference. The smart antenna system utilizes antenna array and advanced array signal process algorithms to reduce co-channel interference. Furthermore, the smart antenna system can combat the multipath fading, increase the system capacity and diversity gain, and extend the transmission range. This work evaluates the performance of DOA based beamforming algorithms applied to Bluetooth system.
This paper is organized as follows: The second section describes the basic concepts of the smart antenna system. We introduce the simulation system platform in the third section and the simulation results are shown in the forth section. Some conclusions are made in the final section.
II. Description of Smart Antenna System Assume that the transmitted signal at each mobile unit is carried in plane wave and the antenna array at the base station is composed of M-element omnidirectional antenna arranged in a uniform linear fashion. The received signals contain both direct path and multipath signals. The array response vector to a transmitted signal s1(t) from a direction-of-arrival θ is given by
M T
a a
a ( ), ( ),..., ( )]
, 1 [ )
(θ = 1 θ 2 θ −1 θ
a (1)
where ai(θ) is a complex number denoting the amplitude gain and phase shift of signal at (i+1)-th antenna relative to that at the first antenna. For a uniform linear antenna array with separation D in free space, the array response vector due to the signals can be written as
T
c M D f c j
f D
j2 sin ),..,exp( 2 sin ( 1) )]
exp(
, 1 [ )
(θ = π θ π θ −
a (2)
where f, c, and T denote the carrier frequency, speed of light, and transpose operator, respectively.
In a typical wireless scenario, the antenna array is comprised of azimuthally broad coverage, even omnidirectional elements. Therefore, it not only receives a signal s1(t) propagated along the direct path but also many multipath echoes from different DOAs. With this in mind, the total signal vector received by the antenna array can be written as
) ( ) (
) ( ) ( ) ( )
( ) ( ) (
1 1
2
1 1
1
t t s
t t s t
s t
L l
l l
n a
n a
a x
+
=
+ θ α + θ
=
∑
= (3)
where L is the total path number containing direct path and multipath, the complex αk describes the phase and amplitude difference between the kth multipath and the direct path, n(t) is the background noise, and
∑
== L
l
l l 1
1 α a(θ )
a , which is referred to as the spatial signature(SS) associated with source one, s1(t). If there
are m sources, according to the superposition principle, the signal received by antenna array is
∑
=+
= m
k k
ks t t
t
1
) ( ) ( )
( a n
x (4)
From equation (3), we know that the spatial signature a1(t) is the linear combination of direct path and multipath and depends on the DOAs of direct path and multipath. Thus, we can utilize the direction-finding algorithm, such as DFT, ESPRIT, and MUSIC, to find the DOAs of direct path and multipath. According to these DOAs, we can calculate the complex weight used to perform beamforming algorithm [1] over the received signals to obtain the desired signal and suppress the interference from other users.
III. Description of System Platform
In the baseband processing, the Bluetooth executes the process on the data stream of the packet. In this paper, we choose the DM1 which is defined by ACL link as our transmitted packet type. This type of packet contains access code, packet header, and payload, as shown in Fig. 1. The packet header and payload are executed with some necessary process to increase the transmission security and reliability before transmission.
For example, the header error checking bits are added to the packet header to check the error of header. The symbols are whitened by scrambling. Finally, the symbols are encoded with 1/3 FEC code. The difference between the process of payload and packet header are security process and usage of the CRC (Cyclic Redundancy Check) code to check the error of payload.
Furthermore, the 1/3 or 2/3 FEC code is utilized at the payload. The selection of code rate depends on the definition of the Bluetooth packet.
Fig. 2 demonstrates the simulation block diagram.
The blocks are illustrated as follows:
1) transmitted signal
The modulation scheme utilized in Bluetooth is GFSK modulation. The transmitted signal can be represented as
) ) ( ) ( 2
2 cos(
)
(t =A fct+ hf
∫
∞tm ⊗h ds π π τ τ τ (5)
A is the amplitude of modulated signal,
f
c is the carrier frequency andh
f is the modulation index.)
(
)
( h t
m τ ⊗
is the output signal of Gaussian filter, where m(t) and h(t) can be represented respectively as follows.{ }
≤ ≤
= +
−
∈
−
=
∑
∞−∞
= 0 ,otherwise
0 , ) 1 ( , 1 , 1 , ) ( )
( t T
t p a
kT t p a t
m k
k
k (6)
−
= 2 2 2
2 ln exp 2 2 ln ) 2
(t B B t
h π π (7)
a
k is the input binary signal and p(t) is the rectangular pulse. B is the 3dB bandwidth of the Gaussian filter at the transmitter. T is the duration of a bit. According to [2], this convolution process can be represented as
+
−
−
= 2
1 2
ln erfc 2 2 1 2
ln erfc 2 2 ) 1
( T
BT t T
BT t t
g π π
(8) where BT is the bandwidth-bit duration product.
Therefore, the transmitted signal after modulating can be rewritten as
( )
{
() ()}
Re Re
) ( 2
2 cos ) (
) ( 2 2
t p t ca
t
k k
c d
j j
d kT g a f t j f j
t k
k d
c
e Ae
e Ae
d kT g a f
t f A t s
φ φ
τ τ π π
τ τ
π π
=
=
+ −
=
∫ ∑ −
∞
−
∞
−∞
=
∞
−
∞
−∞
=
∫ ∑
(9)
where
f
d is the frequency shift.2) channel model
The channel model proposed in [3] is adopted in this simulation and shown in Fig. 3. The impulse response can be represented as
∑∑
∞=
∞
=
−
−
=
0 0
) (
) exp(
) (
l k
kl l kl
kl j t T
t
c
β φ δ τ
(10)where
T
lis the arrival time of the l-th cluster;τ
klis the k-th multipath signal arriving at the receiver in the l-th cluster;φ
klis the phase of the received signals and is generated by normal distribution;β
klis the power gain of the k-th multipath signal in the l-th cluster. Fig. 4 shows that the mean square value of power gain,β
kl2, decreases when the total and cluster power-delay time constants,Γ
andγ
, increase. This channel model is an exponential decay.The amplitude of each multipath signal is generated from the Rayleigh distribution to model multipath fading [3]. The variance depends on the delay spread of each multipath signal. When the delay spread of the multipath signal is longer, the amplitude is smaller. The variance of each multipath signal can be represented as
) / exp(
2 1
0 = − −Ts TRMS
σ (11)
) /
2exp(
0 2
RMS s
k =σ −kT T
σ (12)
+
= 2 2
2 ,1 2 0
,1
0 k k
k N jN
h σ σ (13)
In the above equations, Ts is the sampling time; k is the index of the received multipath signals; TRMS is the
root mean square delay time, and N(0, 2 2 1
σk) is the
Gaussian distribution with mean and variance equal to 0 and 2
2 1
σk respectively.
Assume that there are two nonsynchronous piconets in the simulation. Fig. 4 demonstartes the collision of two nonsynchronous pico nets in the same bandwidth and area. TSTLS is the length of a Bluetooth time slot. The interference only exists when the pico net 1 is transmitted in the duration of T1 (T1=LT) and the rest of the time duration is utilized as frequency hopping channel. Assume that the length of the desired packet and interference packet is L and l symbol length respectively and the time shift JT+
τ
(TBST) is the time duration without other interference where the value of J is between –L+1~L-1. The length of TBST is generated randomly by uniform distribution. The multipath signals of the pico net interference are generated by the method mentioned above [4].3) received signal
Assume that there are N Bluetooth devices to compose N networks with the same operating frequency. The received signals at the antenna array can be represented as
) ( ) ( ) ( ) exp(
) ˆ(
1 1
, st t
j t
s
N i
L k
ik ik ik d ik
i a n
∑∑
= =+ Γ
−
= β φ θ (14)
L
i is the multipath number of the i-th Bluetooth device.β
ik,a ( θ
ik)
,φ
d ,ik andΓ
ik are the fading factor of the k-th path of the i-th Bluetooth device, antenna array response vector, phase shift and time delay, respectively.If the weighting vector of the N-th Bluetooth device is
w
N , the received signal after beamforming can be represented as
−Γ +
=
=
∑∑
= = N iL k
ik ik ik d ik T
N T N
t t
s j
t s t s
i
1 1
, '
) ( ) ( ) ( ) exp(
) ˆ( ) ˆ(
n a
w w
θ φ β
(15)
where T denotes the transpose. In this work, we evaluate the performance of DOA based beamforming algorithms applied to Bluetooth communication system and only consider the uplink transmission. The two DOA based beamforming algorithms are Dominant DOA (DDOA) and Pseudoinverse DOA (PIDOA) which are illustrated as following [1]:
i) Dominant DOA approach: The approach first captures the uplink spatial signature and then finds the DOA’s of the received signals using subspace based techniques such as MUSIC and ESPRIT. The amplitudes
{ }
αl associated with the DOA’s are also estimated. The DOA with the maximum amplitude,αl is selected and its array response vector a( )θl is chosen as the uplink weight vector.
ii) Pseudoinverse DOA approach: The approach is similar to the dominant DOA technique except that we take the pseudoinverse of the array response vectors of all the DOA’s except for the DOA of the desired user.
This method places nulls in all DOA’s except for our desired user, which should minimize interference.
In the demodulation, we adopt the phase-shift discrimination [5] to derive the desired signal and utilize the integrate and dump circuit and decision device to recover the data.
V. Simulation results
In this simulation, we choose DM1 packet as our transmitted packet. Assume that the bit duration estimation at the receiver and the transmission security are perfect. To save the simulation time, the FEC and CRC are all omitted and the modulation frequency is 1 MHz. The symbol duration is 1
µ s
. The sampling period is 10 ns and the modulation index is 0.35. The bandwidth-bit duration product of Gaussian low pass filter used at the receiver is 0.55 [6]. The number of antenna array at the receiver is 8 and the distance between each antenna element is2
λ
. The number ofmultipath of the desired signals is 4 and only the direct path of the pico net interference is considered. The root mean square delay (TRMS) is 50 ns [6]. The distribution of DOAs is uniform and the angle spread is 600. Assume that all the DOAs can be correctly estimated and the variation of the spatial signature can be ignored.
Fig. 5 is the performance of smart antenna applied to Bluetooth of DM1 packet transmitted over a multipath channel. When the transmitted signals suffer from multipath fading, the effect of ISI is minor. The BER (Bit Error Rate) without beamforming can achieve 10-3. Because a Gaussian filter is added at the Bluetooth transmitter to limit the bandwidth of the transmitted signals and the Bluetooth is a narrow band system, the delay spread of the multipath signal is much smaller.
Thus the performance of DM1 packet transmitted over multipath channel without beamforming still can achieve the required quality of Bluetooth. However, the SNR needs up to 21 dB. When the DOA based beamforming algorithms are applied to Bluetooth system, the performance of the Bluetooth is promoted significantly in Fig. 5. Fig. 5 demonstrates that the performance of pseudo inverse DOA (PIDOA) is better than that of dominant DOA (DDOA) because the PIDOA nulls the power at the directions of the multipath signals. When the number of the received antenna elements is eight, a smart antenna can provide 9 dB more diversity gain than that of a single omni-directional antenna over an AWGN channel theoretically. However, Fig. 5 demonstrates that the
diversity gain of PIDOA is only 8 dB better than that of a single antenna system due to fading of the direct path.
The DDOA only provides 5 dB more diversity gain than that of the single antenna. However, PIDOA and DDOA can provide 14 dB and 11 dB more diversity gain than that of the single antenna over multipath channel respectively.
Fig. 6 demonstrates the performance of different number of pico nets under the same SNR. The simulation results show that when the SNR is 18 dB, the performance without beamforming is significantly worse than that with beamforming. While the number of the pico nets is larger than 4, the BER of the system without beamforming will increase to 10-0.5. Thus, even the Bluetooth with the bit correction ability still can’t improve the performance. However, the BER of the system with DDOA and PIDOA is about 10-3 and 10-4 respectively when the number of pico nets is 4. At the same SNR and under the Bluetooth transmission quality criterion (BER=10-3), the numbers of pico nets can be 5 and 3 by using the PIDOA and DDOA respectively.
Therefore, the performance of PIDOA is better than that of DDOA.
As the same simulation setting in the above discussion, Fig. 7 and Fig. 8 demonstrate the performance degradation of DDOA and PIDOA respectively caused by error of DOAs. Fig. 7 and 8 show that when the error of DOAs is less than 10o, the performance of the Bluetooth with beamforming is still better than that without beamforming.
VI. Conclusion
This work evaluated the performance of two beamforming algorithms applied to a Bluetooth system.
The simulation results show that utilizing either of the two beamforming algorithms can reduce the interference caused by multipath transmission and suppress the co-channel interference between different devices. The performance of the PIDOA beamforming is better than that of the DDOA beamforming because the PIDOA beamforming can null the power at the direction of the interference and the DDOA beamforming only increase the power of the desired path. The error of DOAs causes the performance of the Bluetooth with beamforming worse. However, when the error of the DOAs is less than 10o, the performance of the Bluetooth with DDOA and PIDOA beamforming is still better than that without beamforming respectively over the channel model in [3]
and the uniform DOA distribution with angle spread 600. Thus, the smart antenna applied to the Bluetooth system can improve the performance.
Reference
[1] S. S. Jeng, G. T. Okamoto, G. Xu, H. P. Lin, and W. J.
Vogel, “Experimental evaluation of smart antenna system performance for wireless Communications,”
IEEE Trans. on Antennas and Propagation, Vol.46, No.6, pp.749-757, July 1998.
[2] S. Haykin, “Communication System,” John Wiley &
Sons, 2001.
[3] A. M. Saleh and R. A. Valenzuela, “A Statistical Model for Indoor Multipath Propagation,” IEEE Journal on Selected Areas in Comm., Vol.5, No. 2, pp. 128-137, 1987.
[4] K. Kim and G. L. Stiber, “Interference Mitigation in Asynchronous Slow Frequency Hopping Bluetooth Networks,” Wireless Personal Multimedia Communications, 2002. The 5th International Symposium on, Vol.1, pp.27-30 Oct. 2002.
[5] R. Schiphorst, F. W. Hoeksema and C. H. Slump,
“Bluetooth Demodulation Algorithms and Their Performance,” university of Twente, Department of Electrical Engineering, Lab. of Signals and Systems.
[6] A. Soltanian and R. E. V. Dyck, “Physical Layer Performance for Coexistence of Bluetooth and 802.11b,” National Ins. of Standards and Technology.
Access header Payload
LSB 68/72 54 0~2745 MSB
Fig.1 a Bluetooth packet format
Fig. 2 the Bluetooth simulation platform
) / exp(−T Γ
) / exp(−τ γ )
2(t β
Fig. 3 the exponential distribution of the multipath signals
Piconet 1
Piconet 2 τ
+ J×T TEST:
) ( duration Packet
2: l T
T ×
) ( duration Packet
1: L T
T ×
1 Piconet of duration Slot
SLTS: 0 T
= t
Fig. 4 the collision of two nonsynchronous piconet in the same bandwidth and area.
Fig. 5 the performance of a smart antenna applied to Bluetooth
s
ystem(DM1 packet)Fig. 7 the performance of a smart antenna applied to Bluetooth when the error of DOA exists (PIDOA and
DM1packet)
Fig. 8 the performance of a smart antenna applied to Bluetooth when the error of DOA exists (DDOA and
DM1packet)
Fig. 6 the performance of a smart antenna applied to a Bluetooth system when multi pico nets use the same frequency band (DM1 packet and SNR=18dB)