Performance Analysis of Multiple Access 60 GHz System ... - CiteSeerX
JOURNAL OF NETWORKS, VOL. 8, NO. 4, APRIL 2013
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Performance Analysis of Multiple Access 60 GHz System Using Frequency-shifted Gaussian Pulse and Non-carrier PSWF Pulse Hao Zhang1, Wei Shi1, Tingting Lu1, Jingjing Wang1,2，Xinjie Wang1,3 1
Department of Electrical Engineering, Ocean University of China, Qingdao, China College of information Science& Technology, Qingdao University of Science & Technology, Qingdao, China 3College of Communication and Electronic Engineering, Qingdao Technological University, Qingdao, China Email: [email protected], [email protected], [email protected], [email protected], [email protected]
2
Abstract—In this paper, a kind of impulse radio (IR) 60 GHz pulse based on Prolate Spheroidal Wave Functions (PSWF) is proposed. The capacity and performance for multiple access 60 GHz communication system based on carrier pulse and impulse radio pulse are analyzed separately. Both frequency-shifted Gaussian pulse and Prolate Spheroidal Wave Functions (PSWF) pulse are considered and devised according to the federal communication commission (FCC) power constraints. Pulse position modulation (PPM) with time hopping spread spectrum (THSS) is employed in the multiple access 60GHz communication system. The channel capacity and error probability for 60GHz communication system with different pulse waveforms over additive white Gaussian noise (AWGN) channel are compared and analyzed. The simulation results showed that the PSWF pulse 60GHz system with has better channel capacity and error probability performance than frequency-shifted Gaussian pulse 60GHz system. Index Terms—60 GHz, PSWF, frequency-shifted Gaussian pulse, multiple access, channel capacity, error probability
I. INTRODUCTION In recent years, a massive amount of unlicensed spectra around 60 GHz has drawn a growing interest in academic and industrial institutions. Similar to the microwave ultra wideband (UWB) radio, the up to 7 GHz of bandwidth is very suitable for short-range wireless communication, but it suffers from less chance of intersystem interference than the UWB. With 7 GHz of bandwidth, 2-3 Gbit/s high definition media interface (HDMI) or wireless gigabit Ethernet could be achieved even using simple modulation methods [1], like PSK ,PAM and QAM, etc. Furthermore, 60 GHz regulations allow a much higher transmit power (10W) compared to other existing wireless local area network (WLAN) and wireless personal area network (WPAN) This work is supported by the International S&T cooperation program of Qingdao, China under Grant No. 12-1-4-137-hz; National Nature Science Foundation (Youth Grant) under grant No. 60902005 and the natural science foundation of Shandong Province No. ZR2012FQ021.
© 2013 ACADEMY PUBLISHER doi:10.4304/jnw.8.4.761-768
systems. Higher transmit power is necessary to overcome the higher path loss at 60 GHz. In 2001, the United States Federal Communications Commission (FCC) set aside 7 GHz of contiguous spectrum between 57 and 64 GHz for unlicensed use. The IEEE 802.15.3 Task Group 3c had introduced some wireless Medium Access Control (MAC) and Physical Layer (PHY) restrictions including Effective Isotropic Radiated Power (EIRP) limit, mmWave PHY channelization and transmit spectral mask [2]. Some researches on channel capacity and error probability for 60GHz systems have been undertaken. The capacity analysis for 60 GHz wireless communication system over AWGN channel, frequency selective fading channel, Ricean fading channel, Nakagami-m fading channel and IEEE 802.15.3c channel were respectively presented in [3-7]. The performance analysis for 60 GHz wireless communication system was discussion in [8-10]. However, all the researches were based on single-user systems with carrier frequencyshifted pulse. The performance of Non-carrier pulse 60GHz system and multiple access 60 GHz-IR system have not been studied. In this paper a new Non-carrier 60GHz pulse based on Prolate Spheroidal Wave Functions (PSWF) are designed. Multiple access 60 GHz system capacity and error probability performance using PSWF pulse and frequency-shifted Gaussian pulse are compared and analyzed. The rest of this paper is organized as follows. Section II describes the design method and process for PSWF 60GHz pulse and frequency-shifted Gaussian 60GHz pulse. Meanwhile their power spectral densities (PSD) complying with the FCC frequency constraints are examined in this section. Multiple access 60 GHz system model is presented in Section III. The capacity and error probability performance of multiple access 60 GHz system are given and compared using these two types of waveforms in Section IV, these comparisons are based on pulse position modulation and under the AWGN channel. Finally, Section V concludes this paper. II. WAVEFORM DESIGN METHOD
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In this section, pulse waveforms for the 60GHz system are studied. The pulse waveforms are expected to use the 7 GHz frequency resources around 60 GHz as much as possible, so traditional Gaussian monocycles are not suitable. But a modulated Gaussian pulse can meet these requirements which can be written as [10]
= s j (t ) g= j 0,1,2,3... j (t )cos(2π f c t ).
(1)
Where f c is modulating frequency which decides the center frequency of s j (t), g j (t) is the Gaussian pulse (j=0) or its jth derivatives (j>1).
g 0 (t ) = Ae g1 (t= ) g 2 (t ) =
−
A(− A
2π t 2
α2
4π t
α2
4π
α
,
4
−
e
−
)e 2π t 2
α2
2π t 2
α2
,
(2)
[ −α 2 + 4π t 2 ],
Where the amplitude A can be used to normalize the pulse energy, and α is pulse shaping factor. In this paper, f c =60.5GHz, α =0.58ns. 1
∫ψ
k
( x) ⋅
sin[W (t − x)] dx = λkψ k (t ) (3) π (t − x)
Where ψ k ( x) is called the first k order PSWF waveform, λk is the corresponding energy concentration, λk is bigger, the energy concentration is better. W is bandwidth and pulse width is Tm. ψ k ( t ) is time limited signal and have the following form,
0.6 0.4 Amplitude(V)
T
−T
0.8
0.2 0 -0.2
T t < m p (t ) , ψ (t ) = 2 0, elsewhere
-0.4 -0.6 -0.8 -1 -5
-4
-3
2
1 0 -1 Times(1e-10s)
-2
3
5
4
The Gaussian pulse The 1st deriv ativ e
50
The 2nd deriv ativ e The 3rd deriv ativ e
45
The 4th deriv ativ e Transmit spectral mask
40
p ( t ) is the pulse waveform which meets the expected
spectrum masks.
sin[W (t − τ )] h(t − τ ) = , π (t − τ )
30
(5)
Because ψ ( t ) is nonzero only in limited scope, then (3) could be rewritten as
= λψ ( t )
35
∫
Tm 2
ψ (τ )h ( t − τ ) dτ .
−Tm 2
(6)
Although a closed-form solution, known as the prolate spheroidal function [12], [13], is difficult to find, our algorithm provides a numerical solution through the discretization of (6). By sampling at a rate of N samples per pulse period T m , (6) can be expressed as follows:
25 20 15 10 5 0 54
(4)
-10
x 10
Figure 1: The modulated Gaussian pulse with normalized amplitude
PSD [dBm/GHz]
Figure (1) describes pulse shapes of the modulated Gaussian pulse in time domain; figure (2) compares the PSD of the modulated Gaussian pulse and its derivatives with FCC transmit spectral mask. It shows that, with frequency shifting, the Gaussian pulse not only has no DC component, but also meets the transmitting spectral mask better than its derivatives. Since there is a gap in the center frequency, the PSD of Gaussian derivatives can not fully utilize the specified spectrum resources. However, systems using frequency-shifted pulse require carrier modulation module and carrier recovery module. This increases the complexity of transceiver system structure and power consumption. In order to resolve these problems, a new pulse without carrier for 60 GHz systems is proposed. This pulse is based on PSWF. Compared with frequency-shifted pulse, this pulse simplifies the system structure, but this scheme demands high level narrow pulse circuits. PSWF pulse has a good time-limited and frequencylimited characteristic, no matter in the time domain or frequency domain, and it also maintains orthogonal properties. PSWF expression is the following solution of differential equation [12].
α =0.58ns, fc=60.5GHz 56
58
60
62
64
66
Frequency [GHz] Figure 2: The PSD of modulated 60 GHz Gaussian pulse and their nth derivatives © 2013 ACADEMY PUBLISHER
N2 N N λψ ( n ) = ψ [ m]h [ n − m] , n = − ∑ 2 2 m =− N 2
(7)
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(7) could be abbreviate as
( n) ϕ ( n) ⋅ H ( n) λϕ=
1
(8)
0.8
where n and m take on integer values only. H(n) and ϕ (n) are converted to matrix form respectively
N ϕ (− 2 ) ϕ ( − N + 1) 2 ϕ ( n) = N − ϕ ( 1) 2 N ϕ ( ) 2
Amplitude(V)
(9)
-0.2 -0.4
-1 -0.5
-0.4
-0.3
-0.2
-0.1 0 0.1 Times(1e-10s)
0.2
0.3
0.4
0.5
Figure 3: The PSWF pulse with normalized amplitude for 60 GHz system
(10) 50 45 40
GHz. (11)
35 30 25 20 15 10 5 0 5.4
5.6
5.8
6 6.2 frequency(Hz)
6.4
6.6 10
x 10
Figure 4: The PSD of 60 GHz PSWF pulse
The design philosophy of 60 GHz pulse based on PSWF can be simply summarized as: Select appropriate pulse width T m , confirm the bandpass filter h(t) according to the FCC frequency mask, sample h(t) to h(n),expand h(n) to matrix form H(n), seek the eigenvectors ϕk (n) and eigenvalues λk of H(n), ϕ k (n) is the wanted pulse. But it is hard to get the exact pulse expression in time domain using this eigenvector method. III. 60 GHZ MULTIPLE ACCESS SYSTEM MODEL
(12)
This band is chosen to comply with FCC regulations. With N=256 and T m =1ns.Using MATLAB to generate the eigenvalue decomposition revealed the biggest eigenvalue. The corresponding eigenvector suggested for 60 GHz pulse design is plotted in figure 3. And the power spectrum of this pulse is presented in figure 4, which shows that the majority of PSD is concentrated in the FCC regulation. The PSWF pulse for 60 GHz presented in figure 3 is normalization pulse.
© 2013 ACADEMY PUBLISHER
0
-0.8
concentration λ is the eigenvalue corresponding the eigenvector ϕ (n) , the pulse corresponding the biggest eigenvalue is called 1 order PSWF pulse, the pulse corresponding the second biggest eigenvalue is called 2 order PSWF pulse, and so on. From (10), the N + 1 eigenvalues and their corresponding eigenvectors can be solved, that is the first N + 1 order PSWF pulse. So the number of PSWF pulse’s order is deciding by the sampling points of h(t). Given the desired frequency mask H(f) for 60 GHz, the pulse design algorithm utilizes the corresponding impulse response h(t). Numerical pulse is now provided for a band pass frequency mask between 57 and 64 GHz represented in the frequency domain by (11) and in the time domain by (12), where f L =57 GHz and f H =64
= h ( t ) 2 f H sin c ( 2 f H t ) − 2 f L sin c ( 2 f Lt )
0.2
-0.6
From the definition of eigenvector, the sampling pulse ϕ (n) is the eigenvector of H(n), and the energy
1, 57GHz < f < 64GHz H(f )= elsewhere 0,
0.4
PSD(dBm/Hz)
h(−1) h(− N ) h(0) H (n) = h( N / 2 ) h( N / 2 − 1) h(− N / 2 ) h( N ) h( N − 1) h(0)
0.6
A typical time-hopping M-ary PPM format for the output of the kth user in a IR 60 GHz system is given by [10] (k ) s= (t )
∞
∑A
(k )
j = −∞
q(t − jT f − c (jk )Tc − δ d ( k ) )
(13)
j / Ns
Where A(k) is the k user’s signal amplitude, q(t) represents the transmitted impulse waveform that nominally begins at time zero, and the quantities associated with (k) are transmitter dependent. T f is the frame time, which is typically a hundred to a thousand times the
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impulse width resulting in a signal with very low duty cycle. Each frame is divided into N h time slots with (k ) (k ) duration T c . The pulse shift pattern c j , 0 ≤ c j < Nh, is pseudorandom, which provides an additional shift in order to avoid catastrophic collisions due to multiple access interference. The sequence d is the N-ary data stream generated by the kth source after channel coding, and δd is the additional modulation time shift utilized for
where ε p is the average signal energy, WMAI is the MAI component given by Nu ( n +1) N s −1
WMAI = ∑
(t ) r=
∑s
(k )
k =1
=
Nu
∞
∑∑A
(k )
k =1 j =−∞
p(t − jT f − c T − δ i − τ 1 )
hi(1) (t ) = p (t − δ i − τ 1 )
i = 1,..., M .
The output of each cross-correlation receiver at the sample period [nN s T f ((n+1)N s -1)T f ] is ( n +1) N s −1
∑ ∫
j = nN s
jT f
( j −1)T f
r (t )hi(1) (t − jT f − c (1) j Tc − δ i ) dt ,
(16)
i = 1,..., M
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∑ ∫
jT f
( j −1)T f
n(t ) p(t − jT f − c (1)j Tc − δ i − τ1 )dt.
(20)
is the AWGN component. By defining the autocorrelation function of p(t) as
∫
Tf
0
p (t ) p (t − ∆)d ,t
(21)
(18) can be written as
WMAI =
Nu
Ns
∑∑ A
(k )
= k 2=j 1
γ ( ∆ (jk ) )
(22)
where
∆ (jk ) = (c (1)j − c (jk ) )Tc − (δ i(1) − δ d ( k ) ) − (τ 1 − τ k ) j / N s
(23)
is the time difference between user 1 and user k. Under the assumptions listed above, Δ can be modeled as a random variable uniformly distributed over [−T f , T f ]. As in [14], [15], [16], the MAI is modeled as a Gaussian random process for the multi-user environment. Note that N s >>1 justifies the Gaussian approximation even for a small number of users as illustrated in [16]. With the Gaussian approximation, we require the mean and variance of (17) to characterize the output of the crosscorrelators. It is easy to show that the AWGN component has zero mean and variance N s N 0 /2. However, the mean and variance of the MAI component are determined by the specific of pulse waveform. It will be shown that we assume that each information symbol only uses a single 60 GHz pulse, that is, N s = 1 for simplicity. And Without loss of generality, make (1) (k ) A= A= A , ε p = 1. From (17), when the signal exist, the mean of y i is
Assuming PPM signal is transmitted by user 1, (16) can be written as
N A(1) ε p + WMAI + W , yi = s WMAI + W
（n +1) N s −1
= γ (∆)
(15)
(19)
and
j / N s
To evaluate the average SNR, we make the following assumptions. (a) s(k)(t-τ k ), for k=1,2, …, N u , where N u is the number of active users, and the noise n(t) is assumed to be independent. (k ) (b) The time-hopping sequences c j are assumed to be independent and identically distributed (i.i.d) random variables uniformly distributed over the time interval [0, N h ]. (c) All M-ary PPM signals are equally likely a priori. (d) The time delay τ k is assumed to be i.i.d and uniformly distributed over [0, T f ]. (e) Perfect synchronization is assumed at the receiver, that is, τ k is known at the receiver. Without loss generality, we assume the desired user corresponds to k=1. The single user optimal receiver is an M-ary pulse correlation receiver followed by a detector. The M-ary cross-correlation receiver for user 1 consists of M filters matched to the basic functions defined as
= yi
j / N s
(1) j c
(t − τ k )'+ n(t ) p(t − jT f − c (jk )Tc −δ d ( k ) − τ k ) + n(t )
(18)
θ (= t ) A( k ) p(t − jT f − c (jk )Tc − δ d ( k ) − τ k ) ⋅
j = nN s
(14)
θ (t )dt
where
= W
Nu
jT f
( j −1)T f
k 2=j nN s =
(k ) j / N s
PPM determined by the input data d. If Ns>1, a repetition code is introduced, i.e., Ns pulses are used for the transmission of the same information symbol. The received signal can be modeled as the derivative of the transmitted pulse assuming propagation in free space [14], p(t) is the received pulse waveform.
∑ ∫
u1 =E ( N s A(1) ε p + WMAI + W ) =A + E (WMAI ) = A + A( Nu − 1) ⋅ E (γ (∆))
i = n exist signal
i ≠ n no signal
(17)
The variance of y i is
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= δ1 Var ( N s A(1) ε p + WMAI += W ) Var (WMAI + W ) (25)
N A2 = A ( Nu − 1) ⋅Var (γ (∆)) + 0 2
5
2
gauss-5users gauss-15users gauss-30users
4.5 4
When the signal does not exist, the mean and variance of y i separately are (26)
3 bits/s/Hz
u=2 E (WMAI + W=) E (WMAI=) A( Nu − 1) ⋅ E (γ (∆))
3.5
2.5 2
2
NA δ 2 Var (WMAI += = W ) A2 ( Nu − 1) ⋅Var (γ (∆)) + 0= δ1 2
1.5
(27)
1 0.5
With more than one user active in the system, MAI is a factor limiting the capacity and performance, especially for a large number of users. As shown in [17], if the number of users is large [18] or a repetition code is used with N s >> 1 , MAI caused by the undesired users at the output of the desired user’s correlation receiver can be modeled as a zero-mean Gaussian random variable. In this section, multiple access capacity and error probability are investigated with PPM. Assuming that δ ≥ Tp , that is, the M-ary PPM signal is an orthogonal signal with M dimensions.
0
8
4
=
N A2 A ( N u − 1) ⋅ Var (γ (∆ )) + 0 2
3 2.5 2 1.5 1 0.5 0
0
2
4
6
8
= ρ Where
N0
, Eg is the average signal energy.
Figure 5 and 6 shows the channel capacity of 60 GHz system with different number of users and the users are
© 2013 ACADEMY PUBLISHER
10 12 SNR(dB)
14
16
18
20
Figure 6: Channel capacity of 16-ary PPM 60 GHz system using PSWF pulse with different number of users
5 PSWF-30users PSWF-10users Gauss-30users Gauss-10users
4.5 4 3.5
bits/s/Hz
3 2.5
1
(29)
( N u − 1)Var[γ (∆ )]ρ + 1 2 Eg
20
1.5
ρ
A2 = N0 2
18
2
δ2
A2 2
=
A2
16
3.5
Vi , i = 2,3 M and V1 are Gaussian random variables with
( A(1) ) 2 = = γ MAI Var (WMAI + W )
14
PSWF-5users PSWF-15users PSWF-30users
4.5
M
distributions N ( γ ,1) and N (0,1) respectively. N ( x,1) denotes a Gaussian distribution with mean x and variance 1. (28) can be extended to the multiple access case by substituting γ MAI for γ ,
12 10 SNR(dB)
5
A. Multiple Access Capacity The theoretic capacity for a PPM system over an AWGN channel with a single user given in [19]
CM-PPM = log 2 M − E v|s1 log 2 ∑ exp[ γ (vi − v1 )] (28) i =1 bits/channel use where γ is the channel SNR per symbol,
6
4
2
0
Figure 5: Channel capacity of 16-ary PPM 60 GHz system using Gaussian pulse with different number of users
bits/s/Hz
IV. MULTIPLE ACCESS 60GHZ SYSTEM CAPACITY AND PERFORMANCE ANALYSIS BASED ON PSWF PULSE AND FREQUENCY-SHIFTED GAUSSIAN PULSE
0.5 0
0
2
4
6
8
10 12 SNR(dB)
14
16
18
20
Figure 7: Channel capacity comparison of 16-ary PPM 60 GHz system between PSWF pulse and frequency-shifted Gaussian pulse
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0
10
-1
10
-2
10
-3
10
B. Multiple Access Error Probability The theoretic error probability for a PPM system over an AWGN channel with a single user given in [19]
-4
10
-5
10
+∞
1 Pc = ∫ ( −∞ 2π
∫
r1 / N 0 /2
−∞
e
− x /2 2
dx)
M −1
p(r1 )dr1
(r1 − Eg ) 2 1 exp( − ) N0 πN0
where = p (r1 )
gauss-5users gauss-15users gauss-30users
SER
selected 5, 15, 30 respectively. It shows that the achievable channel capacity will decrease as the number of synchronous users increases due to the MAI. Figure 7 compares the channel capacity of 60 GHz system using PSWF pulse and frequency-shifted Gaussian pulse. Systems using PSWF pulse has better capacity performance than systems using Gaussian pulse. The simulation results also illustrate that the superiority of PSWF pulse become more and more apparent as the users increase.
0
2
4
6
8
10 12 Es/N0(db)
14
16
18
20
(30) Figure 8: Error probability of 2-ary PPM 60 GHz system using frequency-shifted Gaussian pulse with different number of users
(31) 0
the probability of a symbol error for an M-ary PPM is PM = 1 − Pc (32)
10
PSWF-5users PSWF-15users PSWF-30users
-1
10
+∞
Pc = ∫ ( −∞
1 2π
+∞
1 =∫ ( −∞ 2π +∞
1 =∫ ( −∞ 2π p(r1 ) =
∫
∫
r1 / δ 2
−∞
-2
10 SER
The error probability of multiple access PPM 60 GHz systems over AWGN channel can be obtained from (30) (31) by substituting δ 2 for N0/2,
-3
10
e− x /2 dx) M −1 p(r1 )dr1 2
r1 / A2 ( Nu −1)⋅Var ( γ ( ∆ )) +
N 0 A2 2
−∞
-4
10
e
− x 2 /2
dx)
M −1
p(r1 )dr1
(33) -5
10
∫
r1 / Eg ( Nu −1)⋅Var ( γ ( ∆ )) +
−∞
N 0 Eg 2
e
− x 2 /2
dx)
M −1
0
2
4
6
8
p(r1 )dr1
14
18
20
0
10
10users-PSWF 30users-PSWF 10users-Gauss 30users-Gauss
1
(34)
Figure 8 and 9 compare the error probability of 60 GHz system with different number of users and the users are selected 5, 15, 30 respectively. When Es / N 0 is small, the error probability mainly depends on thermal noise, so we can improve system performance through increasing each transmission pulse energy or increasing the transmission power. Once the transmission power increasing, the Es / N 0 will also increase in receiving terminal, and the SER will decrease. When Es / N 0 is large, the error probability mainly depends on MAI, and due to
-1
10
SER
(r1 − Eg )2 exp − N 0 Eg 2( E ( N − 1) ⋅Var (γ (∆)) + N 0 Eg ) 2π ( Eg ( Nu − 1) ⋅Var (γ (∆)) + ) g u 2 2 1
© 2013 ACADEMY PUBLISHER
16
Figure 9: Error probability of 2-ary PPM 60 GHz system using PSWF pulse carrier with different number of users
(r1 − Eg )2 1 exp(− ) 2δ 22 2πδ 2
(r1 − Eg )2 exp − 2 2 N A 2 NA 0 ) 2π ( A2 ( Nu − 1) ⋅Var (γ (∆)) + 0 ) 2( A ( Nu − 1) ⋅Var (γ (∆)) + 2 2
10 12 Es/N0(db)
-2
10
-3
10
-4
10
0
2
4
6
8
12 10 Es/N0(db)
14
16
18
20
Figure 10: Error probability of 2-ary PPM 60 GHz system comparison between PSWF pulse and frequency-shifted
the MAI, the error probability increases as the number of synchronous users increases.
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Figure 10 presents the error probability comparison between PSWF pulse and frequency-shifted Gaussian pulse 60 GHz system. In this paper, the numbers of users are selected 10, 30 respectively. PSWF pulse has better error probability performance than frequency-shifted Gaussian pulse as the same Es / N 0 . And the simulation result also illustrates that PSWF pulse has superior performance than frequency-shifted Gaussian pulse. From (28), (29), (33), (34), pulse waveforms impact the channel capacity and error probability of multiple access 60 GHz systems. The main reason for the diversity of channel capacity and error probability is different Var (γ (∆)) in (29), (33), (34). The pulse autocorrelation variance Var (γ (∆)) is smaller, the channel capacity is larger and the performance is better. In this paper, based on the calculation, the values of Var (γ (∆)) for PSWF pulse and frequency-shifted Gaussian pulse are 2.3646e-3 and 2.9554e-3 separately when the T m =1ns. Thus systems using the PSWF pulse have better capacity and error probability than systems using Gaussian pulse. V. CONCLUSION This paper provides an alternative IR 60GHz system other than carrier 60GHz system, and this subject is one rarely studied project in this field. This IR 60 GHz pulse design method is based on Prolate Spheroidal Wave Functions (PSWF). Meanwhile a carrier pulse design method using frequency-shifted Gaussian pulse is also presented. Multiple access 60GHz wireless communication system model using time-hopping spread spectrum based on impulse radio (IR) is proposed in this paper. Researching on capacity and error probability of multiple access 60 GHz system is significant for 60 GHz system multiuser access and anti-interference, so capacity and error probability of 60 GHz multiple access systems were analyzed and compared in this paper. The numerical results showed that pulse waveforms impact the channel capacity and error probability of multiple access 60 GHz systems, the multiple access channel capacity and SER performance of M-ary PPM systems using PSWF pulse are superior to that of systems using frequency-shifted Gaussian pulse. REFERENCE [1]
[2] [3]
[4]
[5]
N. Guo, R.C. Qiu, S.S. Mo, and K. Takahashi, “60 GHz millimeter-wave radio: Principle, technology, and new results,” EURASIP Journal on Wireless Communications and Networking, vol.2007, 2007. IEEE 802.15.3c, IEEE standard Part 15.3, pp58-147, 2009 H. Zhang and T.A. Gulliver, “On capacity of 60 GHz wireless communications over AWGN channels,” Proc. Canadian Conf. on Electrical and Computer Eng., pp. 936-939, May 2009. Li Na, Zhang Hao, Wang Jingjing, Gulliver T. Aaron . On Capacity of 60GHz TH-PPM Systems in Frequency Selective Fading Channels. MSIT2011, 2012:5506-5511. Zhang Hao, Wang Jingjing, Lv Tingting, Gulliver, T. Aaron. Capacity of 60 GHz Wireless Communication Systems over Ricean Fading Channels. Pacrim2011, 2011:437-440.
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[17]
[18] [19]
Hao Zhang, Ning Xu, Jingjing Wang, T. Aaron Gulliver .On Capacity of 60 GHz Wireless Communications over Nakagami-m Fading Channels. ICEEAC2010,2010:411-414. Zhang Hao, Xu Ning, Wang Jingjing, Gulliver T. Aaron. On Capacity of 60GHz wireless communications over IEEE 802.15.3c channel model. Pacrim2011,2011:680684. Li Na,Zhang Hao,Wang Jingjing,Cui Xuerong, Gulliver T. Aaron. Performance analysis of intra-vehicle 60G binary th-ppm systems over multipath fading channels.CIVS2010,2010:111-115. Zhang Hao, Li Na, Wang Jingjing, Gulliver T. Aaron. Energy detection receivers for 60 GHz binary PPM systems over IEEE 802.15.3c channels. Pacrim2011,2011:426-430. Hao Zhang, Ting ting Lu, Wei Wang, T. Aaron Gulliver, Error probability of 60GHz PAM systems with different pulse waveforms, 2011 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing, Victoria, B.C., Canada, pp. 441-446, Aug.23-26, 2011. PARR B, CHO B, WALLACE K.A Novel Ultrawideband Pulse Design Algorithm. IEEE Communication Letters, 2003,7(5):219-221. Slepian,D.and Pollak,H.O.,“Prolate spheroidal wave functions, Fourier analysis and uncertainty”, I, Bell System Tech. J.1961,40, Page(s):43-64. D. Slepian, “Prolate spheroidal wave functions, fourier analysis, and uncertainty-V: The discrete case,” Bell Syst. Tech. J., vol. 57, no. 5, pp.1371–1430, May 1978. R. A. Scholtz, “Multiple access with time-hopping impulse modulation,” in Proc. IEEE Military Communications Conference(MILCOM ’93), vol. 2, pp. 447–450, Boston, Mass, USA, October 1993. M. Z. Win and R. A. Scholtz, “Ultra-wide bandwidth time-hopping spread-spectrum impulse radio for wireless multiple-access communications,” IEEE Trans. Commun., vol.48, no. 4, pp.679-689, 2000. G. Durisi and G. Romano, “On the validity of Gaussian approximation to characterize the multiuser capacity of UWB TH PPM,” Proc. IEEE Conference on Ultra Wideband systems and Technologies( UWBST’02), pp. 157-161, May 2002. F. Ramirez-Mireles and R. A. Scholtz, “Multiple-access with time hopping and block waveform PPM modulation,” in Proc. IEEE International Conference on Communications (ICC ’98),vol. 2, pp. 775–779, Atlanta, Ga, USA, June 1998. J. G. Proakis, Digital Communications, McGraw-Hill, New York, NY, USA, 4th edition, 2001. H. Zhang and T. A. Gulliver, “Performance and capacity of PAM and PPM UWB time-hopping multiple access communications with receive diversity,” EURASIP J. on Applied Signal Processing, pp. 306-315, Mar. 2005.
Hao Zhang was born in Jiangsu, China, in 1975. He received his B.S. degree in telecom engineering and industrial management from Shanghai Jiaotong University, Shanghai, China, in 1994, the M.B.A. degree from New York Institute of Technology, Old westbury, NY, in 2001, and the Ph.D. degree in electrical and computer engineering from the University of Victoria, Victoria, BC, Canada, in 2004. From 1994 to 1997, he was the Assistant President of ICO (China) Global Communication Company, Beijing ,China .He was the Founder and CEO of Beijing Parco Company, Ltd.,
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Beijing, China, from 1998 to 2000. In 2000, he joined Microsoft Canada, Vancouver, BC, as a Software Engineer, and was Chief Engineer at Dream Access Information Technology, Victoria, BC, Canada, from 2001 to 2002. He is currently an Adjunct Assistant Professor with the Department of Electrical and Computer Engineering, University of Victoria. His research interests include UWB, MIMO wireless systems, and spectrum communications. Wei Shi was born in Shandong, China, in 1986. He received his B.S. degree in Ludong University, Yantai, China, in 2009. From 2009 to now, he is a student of department of electrical engineering, Ocean University of China. His research interests include OFDM, UWB and 60 GHz wireless communication. Tingting Lu was born in Shandong, China, in 1983. She received her B.E degree in HuNan University, Changsha, China, in 2006. the M.E. degree from Ocean University of China, Qingdao, China in 2009. From 2009 to now, she is a student of department of electrical engineering, Ocean University of China. Her research interests include UWB and 60 GHz wireless communication.
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Jingjing Wang was born in Anhui, China, in 1975. She received her B.S. degree in industrial automation from Shandong University, Jinan, China, in 1993, the M.Sc. degree from control theory and control engineering, Qingdao University of Science& Technology, Qingdao, China in 2002 and the Ph.D. degree in department of electrical engineering, Ocean University of China in 2012. From 1997 to 1999, she was the assistant engineer of Shengli Oilfield, Dongying, China. From 2002 to now, she is an associate professor at the College of information Science& Technology, Qingdao University of Science & Technology. Her research interests include 60 GHz wireless communication, and UWB radio systems. Xinjie Wang was pursuing his Ph.D degree in Ocean University of China now. He was born in 1980. He received his B.S. Degree in Electrical and Information from Qufu Normal University, China in 2003, and the Master Degree in Signal and Information processing from Sun Yat-sen University, China in 2005. From 2005 to now, he is an lecturer in College of Communication and Electronics, Qingdao Technological University. His research interests include cooperative communication networks, cognitive radio networks, cross-layer design, ultra wideband radio systems and digital communication over fading channels, etc.
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Performance Analysis of Multiple Access 60 GHz System Using Frequency-shifted Gaussian Pulse and Non-carrier PSWF Pulse Hao Zhang1, Wei Shi1, Tingting Lu1, Jingjing Wang1,2，Xinjie Wang1,3 1
Department of Electrical Engineering, Ocean University of China, Qingdao, China College of information Science& Technology, Qingdao University of Science & Technology, Qingdao, China 3College of Communication and Electronic Engineering, Qingdao Technological University, Qingdao, China Email: [email protected], [email protected], [email protected], [email protected], [email protected]
2
Abstract—In this paper, a kind of impulse radio (IR) 60 GHz pulse based on Prolate Spheroidal Wave Functions (PSWF) is proposed. The capacity and performance for multiple access 60 GHz communication system based on carrier pulse and impulse radio pulse are analyzed separately. Both frequency-shifted Gaussian pulse and Prolate Spheroidal Wave Functions (PSWF) pulse are considered and devised according to the federal communication commission (FCC) power constraints. Pulse position modulation (PPM) with time hopping spread spectrum (THSS) is employed in the multiple access 60GHz communication system. The channel capacity and error probability for 60GHz communication system with different pulse waveforms over additive white Gaussian noise (AWGN) channel are compared and analyzed. The simulation results showed that the PSWF pulse 60GHz system with has better channel capacity and error probability performance than frequency-shifted Gaussian pulse 60GHz system. Index Terms—60 GHz, PSWF, frequency-shifted Gaussian pulse, multiple access, channel capacity, error probability
I. INTRODUCTION In recent years, a massive amount of unlicensed spectra around 60 GHz has drawn a growing interest in academic and industrial institutions. Similar to the microwave ultra wideband (UWB) radio, the up to 7 GHz of bandwidth is very suitable for short-range wireless communication, but it suffers from less chance of intersystem interference than the UWB. With 7 GHz of bandwidth, 2-3 Gbit/s high definition media interface (HDMI) or wireless gigabit Ethernet could be achieved even using simple modulation methods [1], like PSK ,PAM and QAM, etc. Furthermore, 60 GHz regulations allow a much higher transmit power (10W) compared to other existing wireless local area network (WLAN) and wireless personal area network (WPAN) This work is supported by the International S&T cooperation program of Qingdao, China under Grant No. 12-1-4-137-hz; National Nature Science Foundation (Youth Grant) under grant No. 60902005 and the natural science foundation of Shandong Province No. ZR2012FQ021.
© 2013 ACADEMY PUBLISHER doi:10.4304/jnw.8.4.761-768
systems. Higher transmit power is necessary to overcome the higher path loss at 60 GHz. In 2001, the United States Federal Communications Commission (FCC) set aside 7 GHz of contiguous spectrum between 57 and 64 GHz for unlicensed use. The IEEE 802.15.3 Task Group 3c had introduced some wireless Medium Access Control (MAC) and Physical Layer (PHY) restrictions including Effective Isotropic Radiated Power (EIRP) limit, mmWave PHY channelization and transmit spectral mask [2]. Some researches on channel capacity and error probability for 60GHz systems have been undertaken. The capacity analysis for 60 GHz wireless communication system over AWGN channel, frequency selective fading channel, Ricean fading channel, Nakagami-m fading channel and IEEE 802.15.3c channel were respectively presented in [3-7]. The performance analysis for 60 GHz wireless communication system was discussion in [8-10]. However, all the researches were based on single-user systems with carrier frequencyshifted pulse. The performance of Non-carrier pulse 60GHz system and multiple access 60 GHz-IR system have not been studied. In this paper a new Non-carrier 60GHz pulse based on Prolate Spheroidal Wave Functions (PSWF) are designed. Multiple access 60 GHz system capacity and error probability performance using PSWF pulse and frequency-shifted Gaussian pulse are compared and analyzed. The rest of this paper is organized as follows. Section II describes the design method and process for PSWF 60GHz pulse and frequency-shifted Gaussian 60GHz pulse. Meanwhile their power spectral densities (PSD) complying with the FCC frequency constraints are examined in this section. Multiple access 60 GHz system model is presented in Section III. The capacity and error probability performance of multiple access 60 GHz system are given and compared using these two types of waveforms in Section IV, these comparisons are based on pulse position modulation and under the AWGN channel. Finally, Section V concludes this paper. II. WAVEFORM DESIGN METHOD
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In this section, pulse waveforms for the 60GHz system are studied. The pulse waveforms are expected to use the 7 GHz frequency resources around 60 GHz as much as possible, so traditional Gaussian monocycles are not suitable. But a modulated Gaussian pulse can meet these requirements which can be written as [10]
= s j (t ) g= j 0,1,2,3... j (t )cos(2π f c t ).
(1)
Where f c is modulating frequency which decides the center frequency of s j (t), g j (t) is the Gaussian pulse (j=0) or its jth derivatives (j>1).
g 0 (t ) = Ae g1 (t= ) g 2 (t ) =
−
A(− A
2π t 2
α2
4π t
α2
4π
α
,
4
−
e
−
)e 2π t 2
α2
2π t 2
α2
,
(2)
[ −α 2 + 4π t 2 ],
Where the amplitude A can be used to normalize the pulse energy, and α is pulse shaping factor. In this paper, f c =60.5GHz, α =0.58ns. 1
∫ψ
k
( x) ⋅
sin[W (t − x)] dx = λkψ k (t ) (3) π (t − x)
Where ψ k ( x) is called the first k order PSWF waveform, λk is the corresponding energy concentration, λk is bigger, the energy concentration is better. W is bandwidth and pulse width is Tm. ψ k ( t ) is time limited signal and have the following form,
0.6 0.4 Amplitude(V)
T
−T
0.8
0.2 0 -0.2
T t < m p (t ) , ψ (t ) = 2 0, elsewhere
-0.4 -0.6 -0.8 -1 -5
-4
-3
2
1 0 -1 Times(1e-10s)
-2
3
5
4
The Gaussian pulse The 1st deriv ativ e
50
The 2nd deriv ativ e The 3rd deriv ativ e
45
The 4th deriv ativ e Transmit spectral mask
40
p ( t ) is the pulse waveform which meets the expected
spectrum masks.
sin[W (t − τ )] h(t − τ ) = , π (t − τ )
30
(5)
Because ψ ( t ) is nonzero only in limited scope, then (3) could be rewritten as
= λψ ( t )
35
∫
Tm 2
ψ (τ )h ( t − τ ) dτ .
−Tm 2
(6)
Although a closed-form solution, known as the prolate spheroidal function [12], [13], is difficult to find, our algorithm provides a numerical solution through the discretization of (6). By sampling at a rate of N samples per pulse period T m , (6) can be expressed as follows:
25 20 15 10 5 0 54
(4)
-10
x 10
Figure 1: The modulated Gaussian pulse with normalized amplitude
PSD [dBm/GHz]
Figure (1) describes pulse shapes of the modulated Gaussian pulse in time domain; figure (2) compares the PSD of the modulated Gaussian pulse and its derivatives with FCC transmit spectral mask. It shows that, with frequency shifting, the Gaussian pulse not only has no DC component, but also meets the transmitting spectral mask better than its derivatives. Since there is a gap in the center frequency, the PSD of Gaussian derivatives can not fully utilize the specified spectrum resources. However, systems using frequency-shifted pulse require carrier modulation module and carrier recovery module. This increases the complexity of transceiver system structure and power consumption. In order to resolve these problems, a new pulse without carrier for 60 GHz systems is proposed. This pulse is based on PSWF. Compared with frequency-shifted pulse, this pulse simplifies the system structure, but this scheme demands high level narrow pulse circuits. PSWF pulse has a good time-limited and frequencylimited characteristic, no matter in the time domain or frequency domain, and it also maintains orthogonal properties. PSWF expression is the following solution of differential equation [12].
α =0.58ns, fc=60.5GHz 56
58
60
62
64
66
Frequency [GHz] Figure 2: The PSD of modulated 60 GHz Gaussian pulse and their nth derivatives © 2013 ACADEMY PUBLISHER
N2 N N λψ ( n ) = ψ [ m]h [ n − m] , n = − ∑ 2 2 m =− N 2
(7)
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(7) could be abbreviate as
( n) ϕ ( n) ⋅ H ( n) λϕ=
1
(8)
0.8
where n and m take on integer values only. H(n) and ϕ (n) are converted to matrix form respectively
N ϕ (− 2 ) ϕ ( − N + 1) 2 ϕ ( n) = N − ϕ ( 1) 2 N ϕ ( ) 2
Amplitude(V)
(9)
-0.2 -0.4
-1 -0.5
-0.4
-0.3
-0.2
-0.1 0 0.1 Times(1e-10s)
0.2
0.3
0.4
0.5
Figure 3: The PSWF pulse with normalized amplitude for 60 GHz system
(10) 50 45 40
GHz. (11)
35 30 25 20 15 10 5 0 5.4
5.6
5.8
6 6.2 frequency(Hz)
6.4
6.6 10
x 10
Figure 4: The PSD of 60 GHz PSWF pulse
The design philosophy of 60 GHz pulse based on PSWF can be simply summarized as: Select appropriate pulse width T m , confirm the bandpass filter h(t) according to the FCC frequency mask, sample h(t) to h(n),expand h(n) to matrix form H(n), seek the eigenvectors ϕk (n) and eigenvalues λk of H(n), ϕ k (n) is the wanted pulse. But it is hard to get the exact pulse expression in time domain using this eigenvector method. III. 60 GHZ MULTIPLE ACCESS SYSTEM MODEL
(12)
This band is chosen to comply with FCC regulations. With N=256 and T m =1ns.Using MATLAB to generate the eigenvalue decomposition revealed the biggest eigenvalue. The corresponding eigenvector suggested for 60 GHz pulse design is plotted in figure 3. And the power spectrum of this pulse is presented in figure 4, which shows that the majority of PSD is concentrated in the FCC regulation. The PSWF pulse for 60 GHz presented in figure 3 is normalization pulse.
© 2013 ACADEMY PUBLISHER
0
-0.8
concentration λ is the eigenvalue corresponding the eigenvector ϕ (n) , the pulse corresponding the biggest eigenvalue is called 1 order PSWF pulse, the pulse corresponding the second biggest eigenvalue is called 2 order PSWF pulse, and so on. From (10), the N + 1 eigenvalues and their corresponding eigenvectors can be solved, that is the first N + 1 order PSWF pulse. So the number of PSWF pulse’s order is deciding by the sampling points of h(t). Given the desired frequency mask H(f) for 60 GHz, the pulse design algorithm utilizes the corresponding impulse response h(t). Numerical pulse is now provided for a band pass frequency mask between 57 and 64 GHz represented in the frequency domain by (11) and in the time domain by (12), where f L =57 GHz and f H =64
= h ( t ) 2 f H sin c ( 2 f H t ) − 2 f L sin c ( 2 f Lt )
0.2
-0.6
From the definition of eigenvector, the sampling pulse ϕ (n) is the eigenvector of H(n), and the energy
1, 57GHz < f < 64GHz H(f )= elsewhere 0,
0.4
PSD(dBm/Hz)
h(−1) h(− N ) h(0) H (n) = h( N / 2 ) h( N / 2 − 1) h(− N / 2 ) h( N ) h( N − 1) h(0)
0.6
A typical time-hopping M-ary PPM format for the output of the kth user in a IR 60 GHz system is given by [10] (k ) s= (t )
∞
∑A
(k )
j = −∞
q(t − jT f − c (jk )Tc − δ d ( k ) )
(13)
j / Ns
Where A(k) is the k user’s signal amplitude, q(t) represents the transmitted impulse waveform that nominally begins at time zero, and the quantities associated with (k) are transmitter dependent. T f is the frame time, which is typically a hundred to a thousand times the
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impulse width resulting in a signal with very low duty cycle. Each frame is divided into N h time slots with (k ) (k ) duration T c . The pulse shift pattern c j , 0 ≤ c j < Nh, is pseudorandom, which provides an additional shift in order to avoid catastrophic collisions due to multiple access interference. The sequence d is the N-ary data stream generated by the kth source after channel coding, and δd is the additional modulation time shift utilized for
where ε p is the average signal energy, WMAI is the MAI component given by Nu ( n +1) N s −1
WMAI = ∑
(t ) r=
∑s
(k )
k =1
=
Nu
∞
∑∑A
(k )
k =1 j =−∞
p(t − jT f − c T − δ i − τ 1 )
hi(1) (t ) = p (t − δ i − τ 1 )
i = 1,..., M .
The output of each cross-correlation receiver at the sample period [nN s T f ((n+1)N s -1)T f ] is ( n +1) N s −1
∑ ∫
j = nN s
jT f
( j −1)T f
r (t )hi(1) (t − jT f − c (1) j Tc − δ i ) dt ,
(16)
i = 1,..., M
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∑ ∫
jT f
( j −1)T f
n(t ) p(t − jT f − c (1)j Tc − δ i − τ1 )dt.
(20)
is the AWGN component. By defining the autocorrelation function of p(t) as
∫
Tf
0
p (t ) p (t − ∆)d ,t
(21)
(18) can be written as
WMAI =
Nu
Ns
∑∑ A
(k )
= k 2=j 1
γ ( ∆ (jk ) )
(22)
where
∆ (jk ) = (c (1)j − c (jk ) )Tc − (δ i(1) − δ d ( k ) ) − (τ 1 − τ k ) j / N s
(23)
is the time difference between user 1 and user k. Under the assumptions listed above, Δ can be modeled as a random variable uniformly distributed over [−T f , T f ]. As in [14], [15], [16], the MAI is modeled as a Gaussian random process for the multi-user environment. Note that N s >>1 justifies the Gaussian approximation even for a small number of users as illustrated in [16]. With the Gaussian approximation, we require the mean and variance of (17) to characterize the output of the crosscorrelators. It is easy to show that the AWGN component has zero mean and variance N s N 0 /2. However, the mean and variance of the MAI component are determined by the specific of pulse waveform. It will be shown that we assume that each information symbol only uses a single 60 GHz pulse, that is, N s = 1 for simplicity. And Without loss of generality, make (1) (k ) A= A= A , ε p = 1. From (17), when the signal exist, the mean of y i is
Assuming PPM signal is transmitted by user 1, (16) can be written as
N A(1) ε p + WMAI + W , yi = s WMAI + W
（n +1) N s −1
= γ (∆)
(15)
(19)
and
j / N s
To evaluate the average SNR, we make the following assumptions. (a) s(k)(t-τ k ), for k=1,2, …, N u , where N u is the number of active users, and the noise n(t) is assumed to be independent. (k ) (b) The time-hopping sequences c j are assumed to be independent and identically distributed (i.i.d) random variables uniformly distributed over the time interval [0, N h ]. (c) All M-ary PPM signals are equally likely a priori. (d) The time delay τ k is assumed to be i.i.d and uniformly distributed over [0, T f ]. (e) Perfect synchronization is assumed at the receiver, that is, τ k is known at the receiver. Without loss generality, we assume the desired user corresponds to k=1. The single user optimal receiver is an M-ary pulse correlation receiver followed by a detector. The M-ary cross-correlation receiver for user 1 consists of M filters matched to the basic functions defined as
= yi
j / N s
(1) j c
(t − τ k )'+ n(t ) p(t − jT f − c (jk )Tc −δ d ( k ) − τ k ) + n(t )
(18)
θ (= t ) A( k ) p(t − jT f − c (jk )Tc − δ d ( k ) − τ k ) ⋅
j = nN s
(14)
θ (t )dt
where
= W
Nu
jT f
( j −1)T f
k 2=j nN s =
(k ) j / N s
PPM determined by the input data d. If Ns>1, a repetition code is introduced, i.e., Ns pulses are used for the transmission of the same information symbol. The received signal can be modeled as the derivative of the transmitted pulse assuming propagation in free space [14], p(t) is the received pulse waveform.
∑ ∫
u1 =E ( N s A(1) ε p + WMAI + W ) =A + E (WMAI ) = A + A( Nu − 1) ⋅ E (γ (∆))
i = n exist signal
i ≠ n no signal
(17)
The variance of y i is
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JOURNAL OF NETWORKS, VOL. 8, NO. 4, APRIL 2013
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= δ1 Var ( N s A(1) ε p + WMAI += W ) Var (WMAI + W ) (25)
N A2 = A ( Nu − 1) ⋅Var (γ (∆)) + 0 2
5
2
gauss-5users gauss-15users gauss-30users
4.5 4
When the signal does not exist, the mean and variance of y i separately are (26)
3 bits/s/Hz
u=2 E (WMAI + W=) E (WMAI=) A( Nu − 1) ⋅ E (γ (∆))
3.5
2.5 2
2
NA δ 2 Var (WMAI += = W ) A2 ( Nu − 1) ⋅Var (γ (∆)) + 0= δ1 2
1.5
(27)
1 0.5
With more than one user active in the system, MAI is a factor limiting the capacity and performance, especially for a large number of users. As shown in [17], if the number of users is large [18] or a repetition code is used with N s >> 1 , MAI caused by the undesired users at the output of the desired user’s correlation receiver can be modeled as a zero-mean Gaussian random variable. In this section, multiple access capacity and error probability are investigated with PPM. Assuming that δ ≥ Tp , that is, the M-ary PPM signal is an orthogonal signal with M dimensions.
0
8
4
=
N A2 A ( N u − 1) ⋅ Var (γ (∆ )) + 0 2
3 2.5 2 1.5 1 0.5 0
0
2
4
6
8
= ρ Where
N0
, Eg is the average signal energy.
Figure 5 and 6 shows the channel capacity of 60 GHz system with different number of users and the users are
© 2013 ACADEMY PUBLISHER
10 12 SNR(dB)
14
16
18
20
Figure 6: Channel capacity of 16-ary PPM 60 GHz system using PSWF pulse with different number of users
5 PSWF-30users PSWF-10users Gauss-30users Gauss-10users
4.5 4 3.5
bits/s/Hz
3 2.5
1
(29)
( N u − 1)Var[γ (∆ )]ρ + 1 2 Eg
20
1.5
ρ
A2 = N0 2
18
2
δ2
A2 2
=
A2
16
3.5
Vi , i = 2,3 M and V1 are Gaussian random variables with
( A(1) ) 2 = = γ MAI Var (WMAI + W )
14
PSWF-5users PSWF-15users PSWF-30users
4.5
M
distributions N ( γ ,1) and N (0,1) respectively. N ( x,1) denotes a Gaussian distribution with mean x and variance 1. (28) can be extended to the multiple access case by substituting γ MAI for γ ,
12 10 SNR(dB)
5
A. Multiple Access Capacity The theoretic capacity for a PPM system over an AWGN channel with a single user given in [19]
CM-PPM = log 2 M − E v|s1 log 2 ∑ exp[ γ (vi − v1 )] (28) i =1 bits/channel use where γ is the channel SNR per symbol,
6
4
2
0
Figure 5: Channel capacity of 16-ary PPM 60 GHz system using Gaussian pulse with different number of users
bits/s/Hz
IV. MULTIPLE ACCESS 60GHZ SYSTEM CAPACITY AND PERFORMANCE ANALYSIS BASED ON PSWF PULSE AND FREQUENCY-SHIFTED GAUSSIAN PULSE
0.5 0
0
2
4
6
8
10 12 SNR(dB)
14
16
18
20
Figure 7: Channel capacity comparison of 16-ary PPM 60 GHz system between PSWF pulse and frequency-shifted Gaussian pulse
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0
10
-1
10
-2
10
-3
10
B. Multiple Access Error Probability The theoretic error probability for a PPM system over an AWGN channel with a single user given in [19]
-4
10
-5
10
+∞
1 Pc = ∫ ( −∞ 2π
∫
r1 / N 0 /2
−∞
e
− x /2 2
dx)
M −1
p(r1 )dr1
(r1 − Eg ) 2 1 exp( − ) N0 πN0
where = p (r1 )
gauss-5users gauss-15users gauss-30users
SER
selected 5, 15, 30 respectively. It shows that the achievable channel capacity will decrease as the number of synchronous users increases due to the MAI. Figure 7 compares the channel capacity of 60 GHz system using PSWF pulse and frequency-shifted Gaussian pulse. Systems using PSWF pulse has better capacity performance than systems using Gaussian pulse. The simulation results also illustrate that the superiority of PSWF pulse become more and more apparent as the users increase.
0
2
4
6
8
10 12 Es/N0(db)
14
16
18
20
(30) Figure 8: Error probability of 2-ary PPM 60 GHz system using frequency-shifted Gaussian pulse with different number of users
(31) 0
the probability of a symbol error for an M-ary PPM is PM = 1 − Pc (32)
10
PSWF-5users PSWF-15users PSWF-30users
-1
10
+∞
Pc = ∫ ( −∞
1 2π
+∞
1 =∫ ( −∞ 2π +∞
1 =∫ ( −∞ 2π p(r1 ) =
∫
∫
r1 / δ 2
−∞
-2
10 SER
The error probability of multiple access PPM 60 GHz systems over AWGN channel can be obtained from (30) (31) by substituting δ 2 for N0/2,
-3
10
e− x /2 dx) M −1 p(r1 )dr1 2
r1 / A2 ( Nu −1)⋅Var ( γ ( ∆ )) +
N 0 A2 2
−∞
-4
10
e
− x 2 /2
dx)
M −1
p(r1 )dr1
(33) -5
10
∫
r1 / Eg ( Nu −1)⋅Var ( γ ( ∆ )) +
−∞
N 0 Eg 2
e
− x 2 /2
dx)
M −1
0
2
4
6
8
p(r1 )dr1
14
18
20
0
10
10users-PSWF 30users-PSWF 10users-Gauss 30users-Gauss
1
(34)
Figure 8 and 9 compare the error probability of 60 GHz system with different number of users and the users are selected 5, 15, 30 respectively. When Es / N 0 is small, the error probability mainly depends on thermal noise, so we can improve system performance through increasing each transmission pulse energy or increasing the transmission power. Once the transmission power increasing, the Es / N 0 will also increase in receiving terminal, and the SER will decrease. When Es / N 0 is large, the error probability mainly depends on MAI, and due to
-1
10
SER
(r1 − Eg )2 exp − N 0 Eg 2( E ( N − 1) ⋅Var (γ (∆)) + N 0 Eg ) 2π ( Eg ( Nu − 1) ⋅Var (γ (∆)) + ) g u 2 2 1
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16
Figure 9: Error probability of 2-ary PPM 60 GHz system using PSWF pulse carrier with different number of users
(r1 − Eg )2 1 exp(− ) 2δ 22 2πδ 2
(r1 − Eg )2 exp − 2 2 N A 2 NA 0 ) 2π ( A2 ( Nu − 1) ⋅Var (γ (∆)) + 0 ) 2( A ( Nu − 1) ⋅Var (γ (∆)) + 2 2
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Figure 10: Error probability of 2-ary PPM 60 GHz system comparison between PSWF pulse and frequency-shifted
the MAI, the error probability increases as the number of synchronous users increases.
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Figure 10 presents the error probability comparison between PSWF pulse and frequency-shifted Gaussian pulse 60 GHz system. In this paper, the numbers of users are selected 10, 30 respectively. PSWF pulse has better error probability performance than frequency-shifted Gaussian pulse as the same Es / N 0 . And the simulation result also illustrates that PSWF pulse has superior performance than frequency-shifted Gaussian pulse. From (28), (29), (33), (34), pulse waveforms impact the channel capacity and error probability of multiple access 60 GHz systems. The main reason for the diversity of channel capacity and error probability is different Var (γ (∆)) in (29), (33), (34). The pulse autocorrelation variance Var (γ (∆)) is smaller, the channel capacity is larger and the performance is better. In this paper, based on the calculation, the values of Var (γ (∆)) for PSWF pulse and frequency-shifted Gaussian pulse are 2.3646e-3 and 2.9554e-3 separately when the T m =1ns. Thus systems using the PSWF pulse have better capacity and error probability than systems using Gaussian pulse. V. CONCLUSION This paper provides an alternative IR 60GHz system other than carrier 60GHz system, and this subject is one rarely studied project in this field. This IR 60 GHz pulse design method is based on Prolate Spheroidal Wave Functions (PSWF). Meanwhile a carrier pulse design method using frequency-shifted Gaussian pulse is also presented. Multiple access 60GHz wireless communication system model using time-hopping spread spectrum based on impulse radio (IR) is proposed in this paper. Researching on capacity and error probability of multiple access 60 GHz system is significant for 60 GHz system multiuser access and anti-interference, so capacity and error probability of 60 GHz multiple access systems were analyzed and compared in this paper. The numerical results showed that pulse waveforms impact the channel capacity and error probability of multiple access 60 GHz systems, the multiple access channel capacity and SER performance of M-ary PPM systems using PSWF pulse are superior to that of systems using frequency-shifted Gaussian pulse. REFERENCE [1]
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N. Guo, R.C. Qiu, S.S. Mo, and K. Takahashi, “60 GHz millimeter-wave radio: Principle, technology, and new results,” EURASIP Journal on Wireless Communications and Networking, vol.2007, 2007. IEEE 802.15.3c, IEEE standard Part 15.3, pp58-147, 2009 H. Zhang and T.A. Gulliver, “On capacity of 60 GHz wireless communications over AWGN channels,” Proc. Canadian Conf. on Electrical and Computer Eng., pp. 936-939, May 2009. Li Na, Zhang Hao, Wang Jingjing, Gulliver T. Aaron . On Capacity of 60GHz TH-PPM Systems in Frequency Selective Fading Channels. MSIT2011, 2012:5506-5511. Zhang Hao, Wang Jingjing, Lv Tingting, Gulliver, T. Aaron. Capacity of 60 GHz Wireless Communication Systems over Ricean Fading Channels. Pacrim2011, 2011:437-440.
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Hao Zhang, Ning Xu, Jingjing Wang, T. Aaron Gulliver .On Capacity of 60 GHz Wireless Communications over Nakagami-m Fading Channels. ICEEAC2010,2010:411-414. Zhang Hao, Xu Ning, Wang Jingjing, Gulliver T. Aaron. On Capacity of 60GHz wireless communications over IEEE 802.15.3c channel model. Pacrim2011,2011:680684. Li Na,Zhang Hao,Wang Jingjing,Cui Xuerong, Gulliver T. Aaron. Performance analysis of intra-vehicle 60G binary th-ppm systems over multipath fading channels.CIVS2010,2010:111-115. Zhang Hao, Li Na, Wang Jingjing, Gulliver T. Aaron. Energy detection receivers for 60 GHz binary PPM systems over IEEE 802.15.3c channels. Pacrim2011,2011:426-430. Hao Zhang, Ting ting Lu, Wei Wang, T. Aaron Gulliver, Error probability of 60GHz PAM systems with different pulse waveforms, 2011 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing, Victoria, B.C., Canada, pp. 441-446, Aug.23-26, 2011. PARR B, CHO B, WALLACE K.A Novel Ultrawideband Pulse Design Algorithm. IEEE Communication Letters, 2003,7(5):219-221. Slepian,D.and Pollak,H.O.,“Prolate spheroidal wave functions, Fourier analysis and uncertainty”, I, Bell System Tech. J.1961,40, Page(s):43-64. D. Slepian, “Prolate spheroidal wave functions, fourier analysis, and uncertainty-V: The discrete case,” Bell Syst. Tech. J., vol. 57, no. 5, pp.1371–1430, May 1978. R. A. Scholtz, “Multiple access with time-hopping impulse modulation,” in Proc. IEEE Military Communications Conference(MILCOM ’93), vol. 2, pp. 447–450, Boston, Mass, USA, October 1993. M. Z. Win and R. A. Scholtz, “Ultra-wide bandwidth time-hopping spread-spectrum impulse radio for wireless multiple-access communications,” IEEE Trans. Commun., vol.48, no. 4, pp.679-689, 2000. G. Durisi and G. Romano, “On the validity of Gaussian approximation to characterize the multiuser capacity of UWB TH PPM,” Proc. IEEE Conference on Ultra Wideband systems and Technologies( UWBST’02), pp. 157-161, May 2002. F. Ramirez-Mireles and R. A. Scholtz, “Multiple-access with time hopping and block waveform PPM modulation,” in Proc. IEEE International Conference on Communications (ICC ’98),vol. 2, pp. 775–779, Atlanta, Ga, USA, June 1998. J. G. Proakis, Digital Communications, McGraw-Hill, New York, NY, USA, 4th edition, 2001. H. Zhang and T. A. Gulliver, “Performance and capacity of PAM and PPM UWB time-hopping multiple access communications with receive diversity,” EURASIP J. on Applied Signal Processing, pp. 306-315, Mar. 2005.
Hao Zhang was born in Jiangsu, China, in 1975. He received his B.S. degree in telecom engineering and industrial management from Shanghai Jiaotong University, Shanghai, China, in 1994, the M.B.A. degree from New York Institute of Technology, Old westbury, NY, in 2001, and the Ph.D. degree in electrical and computer engineering from the University of Victoria, Victoria, BC, Canada, in 2004. From 1994 to 1997, he was the Assistant President of ICO (China) Global Communication Company, Beijing ,China .He was the Founder and CEO of Beijing Parco Company, Ltd.,
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Beijing, China, from 1998 to 2000. In 2000, he joined Microsoft Canada, Vancouver, BC, as a Software Engineer, and was Chief Engineer at Dream Access Information Technology, Victoria, BC, Canada, from 2001 to 2002. He is currently an Adjunct Assistant Professor with the Department of Electrical and Computer Engineering, University of Victoria. His research interests include UWB, MIMO wireless systems, and spectrum communications. Wei Shi was born in Shandong, China, in 1986. He received his B.S. degree in Ludong University, Yantai, China, in 2009. From 2009 to now, he is a student of department of electrical engineering, Ocean University of China. His research interests include OFDM, UWB and 60 GHz wireless communication. Tingting Lu was born in Shandong, China, in 1983. She received her B.E degree in HuNan University, Changsha, China, in 2006. the M.E. degree from Ocean University of China, Qingdao, China in 2009. From 2009 to now, she is a student of department of electrical engineering, Ocean University of China. Her research interests include UWB and 60 GHz wireless communication.
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Jingjing Wang was born in Anhui, China, in 1975. She received her B.S. degree in industrial automation from Shandong University, Jinan, China, in 1993, the M.Sc. degree from control theory and control engineering, Qingdao University of Science& Technology, Qingdao, China in 2002 and the Ph.D. degree in department of electrical engineering, Ocean University of China in 2012. From 1997 to 1999, she was the assistant engineer of Shengli Oilfield, Dongying, China. From 2002 to now, she is an associate professor at the College of information Science& Technology, Qingdao University of Science & Technology. Her research interests include 60 GHz wireless communication, and UWB radio systems. Xinjie Wang was pursuing his Ph.D degree in Ocean University of China now. He was born in 1980. He received his B.S. Degree in Electrical and Information from Qufu Normal University, China in 2003, and the Master Degree in Signal and Information processing from Sun Yat-sen University, China in 2005. From 2005 to now, he is an lecturer in College of Communication and Electronics, Qingdao Technological University. His research interests include cooperative communication networks, cognitive radio networks, cross-layer design, ultra wideband radio systems and digital communication over fading channels, etc.
