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J. H. Hwang et al.: Performance Analysis of PO-THMA UWB System Using Mutually Orthogonal MHP Pulses
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Performance Analysis of PO-THMA UWB System Using Mutually Orthogonal MHP Pulses Jun Hyeok Hwang, Suk Chan Kim, Senior Member, IEEE, Seokho Yoon, Member, IEEE, Bongsoon Kang, Member, IEEE, and, Ju Sung Park Abstract — In this paper, we propose a pulse ordered time
hopping multiple access (PO-THMA) ultra- wideband (UWB) system using modified Hermite polynomial (MHP) pulses. The MHP pulses have a mutually orthogonal property between different ordered pulses and that property makes simultaneous transmission at the same time slot without collision in the THMA UWB system, and this result in increasing transmission capacity or improving bit error rate (BER). We analyze BER of the proposed system and show that the BER performance and the transmission capacity are improved dramatically when compared with those of conventional THMA UWB system. Index Terms — UWB, PO-THMA, MHP pulses, WPAN
I. INTRODUCTION An ultra-wideband (UWB) technology has been recently proposed as a solution for wireless personal area network (WPAN) and home networking areas, because of high transmission speed, robustness to severe multi-path, low implementation cost, and low power consumption [1]-[3]. An UWB communication system transmits information using very short duration pulses which result in wide signal bandwidth, and thus needs no carrier unlike conventional communication systems. Although UWB promises a very high data rate, there is limitation of power spectral density such as federal communication committee (FCC) part 15 rules, resulting in reliable communications only over small to medium distances [1]-[3]. WPAN requires high data transmission and excellent bit error ratio (BER) for indoor multiple-access environment. To solve these problems in UWB systems, one approach is based on modulation which means multi-band UWB system like direct sequence code division multiple access (DS-CDMA) and multi-band orthogonal frequency division multiplexing (MB-OFDM). The other approach is using specific pulse which have good correlation property called single-band impulse radio UWB system [2], [3]. Since single-band impulse radio UWB system is based on Jun Hyeok Hwang is supported by the Brain Korea 21. Jun Hyeok Hwang, Suk Chan Kim, and Ju Sung Park are with the Department of Electronics Engineering, Pusan National University, Busan 609-735, Korea (e-mail: [email protected]). Seokho Yoon is with the School of Information and Communication Engineering, Sungkyunkwan University, Suwon 440-746, Korea. Bongsoon Kang is with the School of Electronics Engineering, Dong-a University, Busan 604-714, Korea. Manuscript received January 10, 2007
carrierless, the structure of system is very simple and implemented with much lower cost than multi-band system. However, single-band UWB system uses pseudo random time-hopping code for multiple-access. Therefore as the number of users in the system increases, the data transmission rate goes down and the BER is getting worse, since the assigned data rate to each user goes low and the probability of collision which means more than two pulses of different users are in same chip simultaneously goes high although those pulses are no synchronized in time. This is the reason that most UWB standards pursue the multi-band in spite of high complexity instead of single-band [2]-[4]. In this paper, we propose a new pulse ordered time hopping multiple-access (PO-THMA) UWB system which is using orthogonality of the modified Hermite polynomial (MHP) pulses to overcome collisions if any. That is, the orthogonal property among different ordered MHP pulses allows multiple pulses at the same time. These make the proposed system overcome the drawbacks of low transmission rate comparing to multi-band system. We derive the theoretical BER of the proposed system and show that the BER and transmission capacity are improved dramatically when compared with that of conventional THMA UWB. In addition, we also analyze the jitter performance which is important point in the UWB synchronization. The organization of this paper is as follows. In Section Ⅱ , the MHP and PO-THMA UWB system model are introduced. In Section Ⅲ , BER performance of proposed system in the presence of timing jitter is derived. In Section Ⅳ, there are some performance comparisons with conventional THMA UWB system. Finally, conclusions are presented in Sections Ⅴ. II. POSED PO-THMA UWB SYSTEM MODEL A. MHP Pulses A variety of pulse shapes has been proposed for the UWB impulse radio system, including the Gaussian pulse, Gaussian monocycle pulse, and Hermite polynomial (HP) pulses [5]-[7]. These pulses are designed to have a desired transmission spectrum and to avoid a DC component. The Hermite transform has already been used to shed light on spatiotemporal relationships in image processing. Today, HP is widely used in mathematics and physics as a root of Hermite differential equations [5], [6]. And it is modified to
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Ψ1 (t − τ 1 )
d ⎣⎢(1)j / N s ⎦⎥ Ψ 2 (t − τ 2 )
d ⎣⎢(2) j / N s ⎦⎥
∫
dˆ (1)
∫
dˆ (2)
∫
dˆ ( K )
Tf
Tf
Ψ N (t − τ K )
d⎣⎢( Kj/ )Ns ⎦⎥
Tf
Fig. 1. Transmitter and receiver structure of the proposed PO-THMA UWB system.
K
r(t) = ∑αk s(k ) (t −τ k ) + n(t)
MHP having orthogonal property and defined as
⎛ t2 ⎞ d n H n (t ) = ( −1) exp ⎜ ⎟ n ⎝ 4 ⎠ dt n
⎡ ⎛ t 2 ⎞⎤ ⎢exp ⎜ − ⎟ ⎥ , ⎝ 2 ⎠⎦ ⎣
k =1
(1)
K
∞
= ∑ ∑α d k =1 j =−∞
(k ) k ⎣⎢ j / Ns ⎦⎥
(3)
p (t − jTf − c T −τ k ) + n(t ), ( n)
( m) j c
where n is pulse order. B. Proposed PO-THMA System In order to make the UWB signal carry any information the signal must be modulated by the information using pulse position modulation (PPM) or pulse amplitude modulation (PAM) [3], [4]. Target BER and transmission rate of UWB impulse radio system are adjusted by the number of pulse repetition. In this paper, the time-hopping codes and various ordered MHP pulses are used together to expand the dimension. Fig. 1 is transmitter and receiver structure of proposed POTHMA UWB system. And Fig. 2 is the proposed multipleaccess scheme which is the case of 4 MHP pulses and 4 timehopping codes. Transmit signal of the k-th user in the proposed PAM PO-THMA UWB system is given by
sm( k,n) (t ) =
∞
∑
j =−∞
d ⎣⎢( kj /) N s ⎦⎥ p ( n ) (t − jT f − c (jm )Tc ),
(2)
where Tf is frame duration and Tc is chip duration. Ns and Nc are the number of frame for a symbol and the number of chips for a frame, respectively. d ⎢⎣( kj /) N s ⎥⎦ is the signal amplitude which
Fig. 2. Multiple-access scheme of the proposed PO-THMA (4 MHP pulses and 4 time-hopping codes)
where α k denotes path-loss and τ k is the propagation delay for the k-th user, respectively. n(t) is AWGN with power spectral density of N0/2 and p(t) is the received pulse waveform which is the derivative form of the transmitted pulse.
has values of ±1, p(n)(t) is one of the MHP pulse, and cj(m) is
III. PERFORMANCE ANALYSIS
one of the time-hopping codes having the range, 0 ≤ c (jm ) ≤ N c
A. Correlation of MHP Pulses To get the BER with multiple access interference (MAI) under the assumption of perfect synchronization, exact correlation should be obtained. The detection is achieved by
[2], [4]. Assuming K users are transmitting asynchronously on an AWGN channel, the received signal, r(t) is given by
J. H. Hwang et al.: Performance Analysis of PO-THMA UWB System Using Mutually Orthogonal MHP Pulses
correlating the received signal with a template signal for the pulse duration. The correlator output is given by Tf
Z = ∫ r (t )ψ (t )dt ,
(4)
0
where ψ (t ) is the template signal [4], [8], and it needs the orthogonal correlation property between MHP pulses. Therefore, we calculate the cross-correlation function of MHP pulses. We considering the multiple-access time delay for k-th user as follows Tf
R(m, n, Δ) = ∫ Hm (t ) Hn (t − Δ)dt,
TABLE I CROSS-CORRELATON FUNCTION BETWEEN MHP PULSES. R( m,n,Δ)
R(m,1,Δ)
R(m,2,Δ)
R(m,3,Δ)
R(m,4,Δ)
R(1,n,Δ)
Ω(-η2+1)
Ω(η3-2η)
Ω(-η4+3η2)
Ω(η5-3η3-2η)
R(2,n,Δ)
Ω(-η3+2η)
Ω(η4-4η2+2)
Ω(-η5+6η3-6η)
Ω(η6-7η4+8η2-5)
R(3,n,Δ)
Ω(-η4+3η2)
Ω(η5-6η3+6η)
Ω(-η6+9η4 -18η2+6) Ω(-η7+11η5 -13η3+η)
Ω(η7-11η5+13η3 -η) Ω(η8-16η6+72η4 -96η2+24)
R(4 ,n, Δ) Ω(-η5+3η3+2η) Ω(η6-7η4+8η2-5)
where Ω is
2π exp(−η 2 / 2) .
1
(5)
0
41
n= n= n= n=
MHP pulse order, and Δ is time delay between m-th user and n-th user. From [5], [6], and (1), it can be shown that MHP satisfy the following
H0 (t ) = s(t )
Normalized Amplitude
where H m (t ) is the m-th MHP pulse order, H n (t ) is the n-th
1 2 3 4
0.5
0
H1 (t ) = t ⋅ s(t ) M Hn (t ) = s(t ) ⋅ Hen (t )
(6)
Hn+1 (t ) = s(t ) {t ⋅ Hn (t ) − n ⋅ Hn−1 (t )} ,
-0.5 -1
-0.8
-0.6
-0.4
-0.2
0 0.2 Time [ns]
0.4
0.6
0.8
1
Fig. 3. Autocorrelation property of the MHP pulses (n = 1 ~ 4).
where s (t ) and H en (t ) are the modified term and the n-th
1 n= n= n= n=
⎛ −t 2 ⎞ s (t ) = exp ⎜ ⎟ ⎝ 4 ⎠
(7)
⎛ t2 ⎞ d n ⎛ −t 2 ⎞ H en (t ) = (−1) exp ⎜ ⎟ n exp ⎜ ⎟, ⎝ 2 ⎠ dt ⎝ 2 ⎠ n
Normalized Amplitude
degree HP, respectively, and given by
1 vs. 1 vs. 1 vs. 1 vs.
n= n= n= n=
1 2 3 4
0.5
0
Finally, using (6), and (7) we derive the cross-correlation as follows: -0.5
∞
R(m, n, Δ) = ∫ Hm (t)Hn (t −Δ)dt
-1
−∞ ∞
= ∫ Hm (t +η)Hn (t −η)dt
(8)
−∞
}
where notational convenience η = Δ / 2 and Et {
}
-0.6
-0.4
-0.2
0 0.2 Time [ns]
0.4
0.6
0.8
1
Fig. 4. Cross-correlation property of the MHP pulses (n =1 vs. n = 1 ~ 4)
Proposed system is determined correlation value for perfect synchronization between m-th MHP pulse and n-th MHP pulse as follows
⎛ −η2 ⎞ = 2π exp⎜ ⎟ Et Hem (t +η)Hen (t −η) , ⎝ 2 ⎠
{
-0.8
denote
expectation. The third equality is derived by letting t a Gaussian random variable with zero mean and unit variance. Table I shows the cross-correlation functions for m = 1, 2, 3, 4 and n = 1, 2, 3, 4.
Tf ⎧1, if m = n R(m, n) = ∫ Hm (t ) Hn (t )dt = ⎨ , 0 ⎩0, if m ≠ n
(9)
Fig. 3 and 4 show the auto and cross correlation property of the MHP pulses, respectively. The auto-correlation becomes narrower as pulse orders n increased, and this means that the
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effect of timing jitter is increased. Fig. 4 shows the crosscorrelation property between the order 1 and order 1 ~ 4. B. Performance Analysis of PO-THMA System To evaluate the SNR, we make the following assumptions. First, the received signal and the noise signal are assumed to be independent for all users. And, the time-hopping sequences are assumed to be independent, identically distributed (i.i.d.) random variables which is uniformly distributed over time interval [0, Nh]. Each information symbol uses more than one pulse, which justifies a Gaussian approximation of the MAI [8], [9]. The time delay of the k-th user is assumed to be i.i.d. and uniformly distributed over one frame width. Finally, between the transmitter and the receiver is assumed perfect synchronization. The correlator output is composed of desired received signal component Zd, MAI signal component ZMAI, and thermal noise signal component Zn. When the first user is active in the proposed system, the composite received signal is expressed as
Z (1) = Z d + Z MAI + Z n ,
(10)
(k ) where Δ (jk ) = (c (1) j − c j )Tc − (τ 1 − τ k ) is the time difference
between user 1 and user k. Above assumptions, Δ can be modeled as a random variable uniformly distributed over [−T f , T f ] . As in [2], [9], MAI is modeled by zero mean white Gaussian and its variance depends on auto-correlation of timehopping code and cross-correlation of MHP pulse orders as Ns
( l +1) N s
∑ ∫
and Ns
∑ ∫
jT f
( j −1)T f
k = 2 j = lN s +1
⎡⎣ p (1) (t ) ⎤⎦ dt ,
p ( k ) (t − τ k ) p (1) (t )dt ,
(11)
j =1 k = 2
Ns Q ⎛ P ⎞ = ∑ E[( d ( k ) ) 2 ] ⎜ ∑ E[γ 2 (Δ (j p ) )] + ∑ E[γ 2 (Δ (jq ) )] ⎟, j =1 q =2 ⎝ p =2 ⎠
Zn =
∑ ∫
jT f
(k ) 2 Var[ Z MAI ] as σ MAI , the theoretical BER of the proposed a PAM PO-THMA UWB system is expressed as
( j −1)T f
j =lN s +1
n(t ) p (t )dt .
(13)
noise component Z n has mean zero and NsN0/2 variance. However, because the mean and variance of the MAI component are determined by the specific pulse waveform, we should determine the auto and cross correlation function of the transmitted pulse as follows
∫
Tf
0
p n ( t ) p m (t − Δ ) dt .
Ns
K
∑∑d j =1 k = 2
(k )
γ ( Δ (jk ) ) ,
( l +1) N s
∑ ∫
j = lN s +1
jT f
( j −1) T f
p (t − ε j ) p ( t ) dt ,
(19)
means time difference between the ideal pulse position and the actual received pulse position. Then, the theoretical BER performance with timing jitter for PAM PO-THMA UWB system is derived as
⎛ Es Pb _ jitter = Q ⎜⎜ 2 2 σ σ MAI + n ⎝
⎞ ⎟⎟ , ⎠
(20)
where Es = N s2 Eε . IV. NUMERICAL RESULTS
(14)
Therefore, the equation (12) can be written as
Z MAI =
(18)
where ε j is the timing jitter of the j-th frame pulse which
Since, Ns pulses are transmitted for each symbol, the desired signal component is Z d = N s2 E p = Eb and the thermal
R (m , n, Δ ) =
⎞ ⎟⎟ . ⎠
When there is timing jitter in the propose system, the BER performance degrades, since timing jitter decreases correlator output [10], [11]. Correlation between the template and the received pulse for fixed value of timing jitter is calculated as
Eε =
(1)
(17)
where P is the number of MHP pulse and Q is the number of time-hopping code. We find out that Z MAI has zero mean and when we let
(12)
and ( l +1) N s
K
(k ) Var[ Z MAI ] = ∑∑ E[(d ( k ) ) 2 ]E[γ 2 (Δ (jk ) )]
⎛ Eb Pb = Q ⎜⎜ 2 2 ⎝ σ n + σ MAI 2
( j −1)T f
j = lN s +1
K ( l +1) N s
Z MAI = ∑
jT f
(16)
j =1 k = 2
where each terms are obtained as
Zd =
K
(k ) E[ Z MAI ] = ∑∑ E[d ( k ) ]E[γ (Δ (jk ) )] ,
(15)
In this section, we show some numerical results under perfect synchronization and the presence of timing jitter in the proposed system and conventional the THMA system. Timing jitter is uniformly distributed between 0 ~ 0.1ns. The computer simulation results verify the theoretical results and some simulation parameters are as followings in Table II.
J. H. Hwang et al.: Performance Analysis of PO-THMA UWB System Using Mutually Orthogonal MHP Pulses TABLE II COMPUTER SIMULATION PARAMETERS
Parameters
Value
Pulse width Bandwidth normalization Sampling frequency Data rate PPM shift Number of users Channel
2 ns 0.15 ns 10 GHz 20 Mbps 0.5 ns 16, 32, 64, 128 AWGN
codes in two dimensionally. So, we can expect that the proposed system has better BER performance for fixed data rate and increased capacity for fixed BER. If it transmits a more pulses simultaneously, the system capacity will be increased. However, high order MHP pulses are sensitive to timing jitter. Therefore, we must select appropriate order and the number of MHP pulses in the real system. Fig. 6 shows the BER performance of the proposed UWB system with PAM versus the number of users for the various 0
10
0
10
-1
10
-1
10
-2
10
-2
BER
BER
10
16 user (N = 1) 32 user (N = 1) 64 user (N = 1) 128 user (N = 1) 16 user (N = 2) 32 user (N = 2) 64 user (N = 2) 128 user (N = 2) 16 user (N = 4) 32 user (N = 4) 64 user (N = 4) 128 user (N = 4)
-3
10
-4
10
-5
10
-6
10
-10
-5
0
-3
10
-4
-5
10
-6
10
5 Eb/N0
10
15
-5
0
5
10 Eb/N0
15
20
25
Fig. 7. BER performance of the proposed system with PPM.
20
0
10
0
10
-1
10
-1
10
-2
10
-2
BER
10
BER
16 user (N = 1) 32 user (N = 1) 64 user (N = 1) 128 user (N = 1) 16 user (N = 2) 32 user (N = 2) 64 user (N = 2) 128 user (N = 2) 16 user (N = 4) 32 user (N = 4) 64 user (N = 4) 128 user (N = 4)
10
Fig. 5. BER performance of the proposed system versus Eb/No for various number of users with PAM (The number of MHP pulses are 1, 2, and 4).
-3
10
-3
10
SNR 5dB (N = 1) SNR 10dB (N = 1) SNR 15dB (N = 1) SNR 5dB (N = 2) SNR 10dB (N = 2) SNR 15dB (N = 2) SNR 5dB (N = 4) SNR 10dB (N = 4) SNR 15dB (N = 4)
-4
10
SNR 5dB (N = 1) SNR 10dB (N = 1) SNR 15dB (N = 1) SNR 5dB (N = 2) SNR 10dB (N = 2) SNR 15dB (N = 2) SNR 5dB (N = 4) SNR 10dB (N = 4) SNR 15dB (N = 4)
-4
10
-5
10
-6
10
43
0
10
20
30
40 50 60 Number of Users
70
80
90
-5
10
-6
10
100
Fig. 6. BER performance of the proposed system versus the number of users for various SNR with PAM.
Fig. 5 shows the BER performance of the proposed UWB system and the THMA UWB system with PAM. In this figure, we use 1, 2, 3, and 4 orders of MHP pulses. From now on, it means the results of THMA that the pulse order N equals to 1 in the all results. This figure shows the proposed scheme have good performance. We can know that the resources are increased by considering orthogonal property of MHP pulses and it means we have more flexibility in assignment of resources including pulse orders as well as time-hopping
0
10
20
30
40 50 60 Number of Users
70
80
90
100
Fig. 8. BER performance of the proposed system versus number of users with PPM for various SNR.
SNR of 5, 10, and 15dB. This figure shows that the error probability is increased as the number of users increased. In this figure, we can get the maximum number of users for given BER and SNR. Fig. 7 shows the BER performance of the proposed system and conventional the THMA system with PPM. We show that the BER performance of the PAM scheme is better than PPM scheme. And Fig. 8 shows the BER performance of the proposed UWB system with PPM versus the number of users for the various SNR of 5, 10, and 15dB. Fig. 9 and 10 show the BER performance of the proposed UWB system with PAM in
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the presence of timing jitter. These figures show the BER performance in the presence of timing jitters of 0.05ns and 0.1ns, respectively. We find out that the BER is decreased according to increased the timing offset value and the number of users. Therefore, we can find out the appropriate number of users and pulse orders from those results for the desired BER and data rate.
REFERENCES [1] [2]
[3]
0
10
-1
10
[4]
-2
BER
10
-3
10
-4
10
-5
10
-6
10
-10
[5]
16 user (N = 1) 32 user (N = 1) 64 user (N = 1) 128 user (N = 1) 16 user (N = 2) 32 user (N = 2) 64 user (N = 2) 128 user (N = 2) 16 user (N = 4) 32 user (N = 4) 64 user (N = 4) 128 user (N = 4) -5
0
[6]
5 Eb/N0
10
15
20
Fig. 9. BER performance of the proposed system with timing jitter 0.05ns.
0
10
-1
10
-2
BER
10
-3
10
-4
10
-5
10
-6
10
-10
16 user (N = 1) 32 user (N = 1) 64 user (N = 1) 128 user (N = 1) 16 user (N = 2) 32 user (N = 2) 64 user (N = 2) 128 user (N = 2) 16 user (N = 4) 32 user (N = 4) 64 user (N = 4) 128 user (N = 4) -5
0
5 Eb/N0
10
15
20
Fig. 10. BER performance of the proposed system with timing jitter 0.1ns.
V. CONCLUSIONS In this paper, we proposed a PO-THMA UWB system which used mutually orthogonal MHP pulses. The proposed scheme had more flexibility in assignment of resources to users including mutually orthogonal MHP pulses as well as time-hopping codes in two dimensionally. We analyzed BER of the proposed system and showed that the BER performance and the transmission capacity were improved dramatically when it compared with those of conventional THMA UWB system. The proposed system could be expected to be utilized in the high data rate indoor wireless communication system requiring low power and simple complexity. ACKNOWLEDGMENT This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD), (KRF-2006-311-D00664).
M. Z. Win and R. A. Scholtz. “Impulse of Radio: How it works,” IEEE Trans. Commun. Lett., vol. 2, pp 51-53, Feb. 1998. M. A. 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. 679-691, Apr. 2000. P. Runkle, J. McCorkle, T. Miller, and M. Welborn, “DS-CDMA: the modulation technology of choice for UWB communications,” in Proc. IEEE Conf. Ultra Wideband Syst. Technol., pp. 364-368, Nov. 16–19, 2003. G. Durisi and S. Benedetto, “Performance evaluation and comparison of different modulation schemes for UWB multi-access systems,” Proc. IEEE Int. Conf. Comm., Anchorage, AK, pp. 2187-2191, May 2003. M. Ghavami, L. B. Michael and R. Kohno “ Hermite function based Orthogonal Pulse for UWB Communications,” Proc. Wireless Personal Multimedia Conf., Aalbog, Denmark, pp. 437-440, Sep. 2001. L. B. Michael, M. Ghavami, and R. Kohno, “Multiple pulse generator for ultra-wideband communication using Hermite Polynomial based
orthogonal pulses, ” Proc. 2002 IEEE Conf. on Ultra Wideband Systems and Technologies, Baltimore, MA, USA, May 2002. [7] M. G. Di Benedetto, G. Giancola, Understanding Ultra WideBand Radio Fundamentals, Prentice Hall. 2004. [8] H. Zhang and T. A. Gulliver, “Biorthogonal pulse position modulation for time hopping multiple-access UWB communications,” IEEE Trans. Wireless Commun., vol. 4, no 3, pp. 1154-1162, May 2005. [9] G. Durisi and G. Romano, “On the validity of Gaussian approximation to characterize the multiuser capacity of UWB TH PPM,” Proc. IEEE Conf. Ultra Wideband Systems and Technology, pp. 157-161, 2002. [10] J. R. Foerster, “The effects of multipath interference on the performance of UWB systems in an indoor wireless channel,” Proc. IEEE Vehicular Technology Conf., pp. 1176-1180, May 2001. [11] M. Ghavami, L. B. Michael, and R. Kohno, “Effect of Timing Jitter on Hermite Function Based Orthogonal Pulse for Ultra Wideband Communication,” Proc. Wireless Personal Multimedia Conf., Aalborag, Denmark, pp.437-440, Sep. 2001. [12] J. G. Proakis, Digital Communications, 4th ed., McGraw Hill, 2001.
Jun Hyeok Hwang received the B.S. degree in electronics engineering from Jinju National University, Jinju, Korea, in February 1999, and the M.S. degree in electrical engineering form the Pukyong National University, Busan, Korea, in February 2003. He is currently working towards the Ph.D. degree at the Communication System Laboratory, Department of Electronics Engineering at Pusan National University, Busan, Korea. His research interests include ultra-wideband system, digital communication, and wireless communications. Suk Chan Kim was born in Namhae, Korea, on February 10, 1971. He received the B.S. (summa cum laude) degree in electronics engineering from Pusan National University (PNU), Busan, Korea, in February 1993, and the M.S.E. and Ph.D. degrees in electrical engineering from Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea, in February 1995 and 2000, respectively. He was a teaching and research assistant at the Department of Electrical Engineering, KAIST, in 1993-1999, and a post doctoral researcher at the Electronics and Telecommunications Research Institute (ETRI), Princeton University, and Lehigh University, in 2000-2001, respectively. He is now an Associate Professor at the Department of electronics engineering, PNU from March 2002. He is a Member of the Research Institute of Computer, Information and Communication (RICIC), Institute of Electronics Engineers of Korea (IEEK), Korean Institute of Communication Sciences (KICS), and a Senior Member of the Institute of Electrical and Electronics Engineers (IEEE). His research interests include mobile communications, statistical signal processing, and communication networks.
J. H. Hwang et al.: Performance Analysis of PO-THMA UWB System Using Mutually Orthogonal MHP Pulses Seokho Yoon (S’99-M’02) received the B.S.E. (summa cum laude), M.S.E., and Ph.D. degrees in electrical engineering from Korea Advanced Institute of Science and Technology (KAIST) in 1997, 1999, and 2002, respectively. From April 2002 to June 2002, he was with the Department of Electrical Engineering and Computer Sciences, Massachusetts Institute of Technology (MIT), Cambridge, MA, and from July 2002 to February 2003, he was with the Department of Electrical Engineering, Harvard University, Cambridge, MA, as a Postdoctoral Research Fellow. In March 2003, he joined the School of Information and Communication Engineering, Sungkyunkwan University, where he is currently an Assistant Professor. His research interests include spread spectrum systems, mobile communications, detection and estimation theory, and statistical signal processing. Dr. Yoon is a Member of the Institute of Electrical and Electronics Engineers (IEEE), Institute of Electronics Engineers of Korea (IEEK), and Korean Institute of Communication Sciences (KICS). He was the recipient of a Bronze Prize at Samsung Humantech Paper Contest in 2000. Bongsoon Kang (M’76) received the B.S. degree in Electronic Engineering from Yonsei University, Seoul, Korea, in 1985, and the M.S. degree in Electrical Engineering. from University of Pennsylvania, Pennsylvania, USA, in 1987, and the Ph.D. degree in Electrical and Computer Engineering from Drexel University, Philadelphia, USA, in 1990. From Dec. 1989 to Feb. 1999, he had worked as a senior staff researcher at the Samsung Electronics Co., Ltd., Korea. Since March 1999, he has been with the School of Electronic Engineering, Dong-A Univ., Busan, Korea. He is the director of the Multimedia Research Center of the University. His research interests include VLSI algorithm/architecture design, image/video processing, and wireless communication.
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Ju Sung Park received was born in Junju, Korea, on December 19, 1953. He received the B.S degree in electronics engineering from Pusan National University, Busan, Korea, in 1976 and the M.S. degree in electrical engineering from the KAIST, Seoul, Korea, in 1978, and the Ph.D. degree in electrical engineering from University of Florida, Gainsville, in 1989, USA. From March 1978 to March 1991, he was with the ETRI, Taejun, Korea, where he work as a Principal Research Engineer and as the manger and the director of IC design group. While at ETRI he designed several bipolar analog IC’s and was in charge of developing VCR IC’s, CMOS 8 bit microprocessor, and telecommunication chips. In 1991, he joined the Electronics Department of Pusan National University, Pusan, Korea, where he is now a professor of Electrical Engineering. His current research interests are microprocessor and DSP core design, digital audio algorithm implementation by hardware and software co-design.
39
Performance Analysis of PO-THMA UWB System Using Mutually Orthogonal MHP Pulses Jun Hyeok Hwang, Suk Chan Kim, Senior Member, IEEE, Seokho Yoon, Member, IEEE, Bongsoon Kang, Member, IEEE, and, Ju Sung Park Abstract — In this paper, we propose a pulse ordered time
hopping multiple access (PO-THMA) ultra- wideband (UWB) system using modified Hermite polynomial (MHP) pulses. The MHP pulses have a mutually orthogonal property between different ordered pulses and that property makes simultaneous transmission at the same time slot without collision in the THMA UWB system, and this result in increasing transmission capacity or improving bit error rate (BER). We analyze BER of the proposed system and show that the BER performance and the transmission capacity are improved dramatically when compared with those of conventional THMA UWB system. Index Terms — UWB, PO-THMA, MHP pulses, WPAN
I. INTRODUCTION An ultra-wideband (UWB) technology has been recently proposed as a solution for wireless personal area network (WPAN) and home networking areas, because of high transmission speed, robustness to severe multi-path, low implementation cost, and low power consumption [1]-[3]. An UWB communication system transmits information using very short duration pulses which result in wide signal bandwidth, and thus needs no carrier unlike conventional communication systems. Although UWB promises a very high data rate, there is limitation of power spectral density such as federal communication committee (FCC) part 15 rules, resulting in reliable communications only over small to medium distances [1]-[3]. WPAN requires high data transmission and excellent bit error ratio (BER) for indoor multiple-access environment. To solve these problems in UWB systems, one approach is based on modulation which means multi-band UWB system like direct sequence code division multiple access (DS-CDMA) and multi-band orthogonal frequency division multiplexing (MB-OFDM). The other approach is using specific pulse which have good correlation property called single-band impulse radio UWB system [2], [3]. Since single-band impulse radio UWB system is based on Jun Hyeok Hwang is supported by the Brain Korea 21. Jun Hyeok Hwang, Suk Chan Kim, and Ju Sung Park are with the Department of Electronics Engineering, Pusan National University, Busan 609-735, Korea (e-mail: [email protected]). Seokho Yoon is with the School of Information and Communication Engineering, Sungkyunkwan University, Suwon 440-746, Korea. Bongsoon Kang is with the School of Electronics Engineering, Dong-a University, Busan 604-714, Korea. Manuscript received January 10, 2007
carrierless, the structure of system is very simple and implemented with much lower cost than multi-band system. However, single-band UWB system uses pseudo random time-hopping code for multiple-access. Therefore as the number of users in the system increases, the data transmission rate goes down and the BER is getting worse, since the assigned data rate to each user goes low and the probability of collision which means more than two pulses of different users are in same chip simultaneously goes high although those pulses are no synchronized in time. This is the reason that most UWB standards pursue the multi-band in spite of high complexity instead of single-band [2]-[4]. In this paper, we propose a new pulse ordered time hopping multiple-access (PO-THMA) UWB system which is using orthogonality of the modified Hermite polynomial (MHP) pulses to overcome collisions if any. That is, the orthogonal property among different ordered MHP pulses allows multiple pulses at the same time. These make the proposed system overcome the drawbacks of low transmission rate comparing to multi-band system. We derive the theoretical BER of the proposed system and show that the BER and transmission capacity are improved dramatically when compared with that of conventional THMA UWB. In addition, we also analyze the jitter performance which is important point in the UWB synchronization. The organization of this paper is as follows. In Section Ⅱ , the MHP and PO-THMA UWB system model are introduced. In Section Ⅲ , BER performance of proposed system in the presence of timing jitter is derived. In Section Ⅳ, there are some performance comparisons with conventional THMA UWB system. Finally, conclusions are presented in Sections Ⅴ. II. POSED PO-THMA UWB SYSTEM MODEL A. MHP Pulses A variety of pulse shapes has been proposed for the UWB impulse radio system, including the Gaussian pulse, Gaussian monocycle pulse, and Hermite polynomial (HP) pulses [5]-[7]. These pulses are designed to have a desired transmission spectrum and to avoid a DC component. The Hermite transform has already been used to shed light on spatiotemporal relationships in image processing. Today, HP is widely used in mathematics and physics as a root of Hermite differential equations [5], [6]. And it is modified to
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Ψ1 (t − τ 1 )
d ⎣⎢(1)j / N s ⎦⎥ Ψ 2 (t − τ 2 )
d ⎣⎢(2) j / N s ⎦⎥
∫
dˆ (1)
∫
dˆ (2)
∫
dˆ ( K )
Tf
Tf
Ψ N (t − τ K )
d⎣⎢( Kj/ )Ns ⎦⎥
Tf
Fig. 1. Transmitter and receiver structure of the proposed PO-THMA UWB system.
K
r(t) = ∑αk s(k ) (t −τ k ) + n(t)
MHP having orthogonal property and defined as
⎛ t2 ⎞ d n H n (t ) = ( −1) exp ⎜ ⎟ n ⎝ 4 ⎠ dt n
⎡ ⎛ t 2 ⎞⎤ ⎢exp ⎜ − ⎟ ⎥ , ⎝ 2 ⎠⎦ ⎣
k =1
(1)
K
∞
= ∑ ∑α d k =1 j =−∞
(k ) k ⎣⎢ j / Ns ⎦⎥
(3)
p (t − jTf − c T −τ k ) + n(t ), ( n)
( m) j c
where n is pulse order. B. Proposed PO-THMA System In order to make the UWB signal carry any information the signal must be modulated by the information using pulse position modulation (PPM) or pulse amplitude modulation (PAM) [3], [4]. Target BER and transmission rate of UWB impulse radio system are adjusted by the number of pulse repetition. In this paper, the time-hopping codes and various ordered MHP pulses are used together to expand the dimension. Fig. 1 is transmitter and receiver structure of proposed POTHMA UWB system. And Fig. 2 is the proposed multipleaccess scheme which is the case of 4 MHP pulses and 4 timehopping codes. Transmit signal of the k-th user in the proposed PAM PO-THMA UWB system is given by
sm( k,n) (t ) =
∞
∑
j =−∞
d ⎣⎢( kj /) N s ⎦⎥ p ( n ) (t − jT f − c (jm )Tc ),
(2)
where Tf is frame duration and Tc is chip duration. Ns and Nc are the number of frame for a symbol and the number of chips for a frame, respectively. d ⎢⎣( kj /) N s ⎥⎦ is the signal amplitude which
Fig. 2. Multiple-access scheme of the proposed PO-THMA (4 MHP pulses and 4 time-hopping codes)
where α k denotes path-loss and τ k is the propagation delay for the k-th user, respectively. n(t) is AWGN with power spectral density of N0/2 and p(t) is the received pulse waveform which is the derivative form of the transmitted pulse.
has values of ±1, p(n)(t) is one of the MHP pulse, and cj(m) is
III. PERFORMANCE ANALYSIS
one of the time-hopping codes having the range, 0 ≤ c (jm ) ≤ N c
A. Correlation of MHP Pulses To get the BER with multiple access interference (MAI) under the assumption of perfect synchronization, exact correlation should be obtained. The detection is achieved by
[2], [4]. Assuming K users are transmitting asynchronously on an AWGN channel, the received signal, r(t) is given by
J. H. Hwang et al.: Performance Analysis of PO-THMA UWB System Using Mutually Orthogonal MHP Pulses
correlating the received signal with a template signal for the pulse duration. The correlator output is given by Tf
Z = ∫ r (t )ψ (t )dt ,
(4)
0
where ψ (t ) is the template signal [4], [8], and it needs the orthogonal correlation property between MHP pulses. Therefore, we calculate the cross-correlation function of MHP pulses. We considering the multiple-access time delay for k-th user as follows Tf
R(m, n, Δ) = ∫ Hm (t ) Hn (t − Δ)dt,
TABLE I CROSS-CORRELATON FUNCTION BETWEEN MHP PULSES. R( m,n,Δ)
R(m,1,Δ)
R(m,2,Δ)
R(m,3,Δ)
R(m,4,Δ)
R(1,n,Δ)
Ω(-η2+1)
Ω(η3-2η)
Ω(-η4+3η2)
Ω(η5-3η3-2η)
R(2,n,Δ)
Ω(-η3+2η)
Ω(η4-4η2+2)
Ω(-η5+6η3-6η)
Ω(η6-7η4+8η2-5)
R(3,n,Δ)
Ω(-η4+3η2)
Ω(η5-6η3+6η)
Ω(-η6+9η4 -18η2+6) Ω(-η7+11η5 -13η3+η)
Ω(η7-11η5+13η3 -η) Ω(η8-16η6+72η4 -96η2+24)
R(4 ,n, Δ) Ω(-η5+3η3+2η) Ω(η6-7η4+8η2-5)
where Ω is
2π exp(−η 2 / 2) .
1
(5)
0
41
n= n= n= n=
MHP pulse order, and Δ is time delay between m-th user and n-th user. From [5], [6], and (1), it can be shown that MHP satisfy the following
H0 (t ) = s(t )
Normalized Amplitude
where H m (t ) is the m-th MHP pulse order, H n (t ) is the n-th
1 2 3 4
0.5
0
H1 (t ) = t ⋅ s(t ) M Hn (t ) = s(t ) ⋅ Hen (t )
(6)
Hn+1 (t ) = s(t ) {t ⋅ Hn (t ) − n ⋅ Hn−1 (t )} ,
-0.5 -1
-0.8
-0.6
-0.4
-0.2
0 0.2 Time [ns]
0.4
0.6
0.8
1
Fig. 3. Autocorrelation property of the MHP pulses (n = 1 ~ 4).
where s (t ) and H en (t ) are the modified term and the n-th
1 n= n= n= n=
⎛ −t 2 ⎞ s (t ) = exp ⎜ ⎟ ⎝ 4 ⎠
(7)
⎛ t2 ⎞ d n ⎛ −t 2 ⎞ H en (t ) = (−1) exp ⎜ ⎟ n exp ⎜ ⎟, ⎝ 2 ⎠ dt ⎝ 2 ⎠ n
Normalized Amplitude
degree HP, respectively, and given by
1 vs. 1 vs. 1 vs. 1 vs.
n= n= n= n=
1 2 3 4
0.5
0
Finally, using (6), and (7) we derive the cross-correlation as follows: -0.5
∞
R(m, n, Δ) = ∫ Hm (t)Hn (t −Δ)dt
-1
−∞ ∞
= ∫ Hm (t +η)Hn (t −η)dt
(8)
−∞
}
where notational convenience η = Δ / 2 and Et {
}
-0.6
-0.4
-0.2
0 0.2 Time [ns]
0.4
0.6
0.8
1
Fig. 4. Cross-correlation property of the MHP pulses (n =1 vs. n = 1 ~ 4)
Proposed system is determined correlation value for perfect synchronization between m-th MHP pulse and n-th MHP pulse as follows
⎛ −η2 ⎞ = 2π exp⎜ ⎟ Et Hem (t +η)Hen (t −η) , ⎝ 2 ⎠
{
-0.8
denote
expectation. The third equality is derived by letting t a Gaussian random variable with zero mean and unit variance. Table I shows the cross-correlation functions for m = 1, 2, 3, 4 and n = 1, 2, 3, 4.
Tf ⎧1, if m = n R(m, n) = ∫ Hm (t ) Hn (t )dt = ⎨ , 0 ⎩0, if m ≠ n
(9)
Fig. 3 and 4 show the auto and cross correlation property of the MHP pulses, respectively. The auto-correlation becomes narrower as pulse orders n increased, and this means that the
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42
effect of timing jitter is increased. Fig. 4 shows the crosscorrelation property between the order 1 and order 1 ~ 4. B. Performance Analysis of PO-THMA System To evaluate the SNR, we make the following assumptions. First, the received signal and the noise signal are assumed to be independent for all users. And, the time-hopping sequences are assumed to be independent, identically distributed (i.i.d.) random variables which is uniformly distributed over time interval [0, Nh]. Each information symbol uses more than one pulse, which justifies a Gaussian approximation of the MAI [8], [9]. The time delay of the k-th user is assumed to be i.i.d. and uniformly distributed over one frame width. Finally, between the transmitter and the receiver is assumed perfect synchronization. The correlator output is composed of desired received signal component Zd, MAI signal component ZMAI, and thermal noise signal component Zn. When the first user is active in the proposed system, the composite received signal is expressed as
Z (1) = Z d + Z MAI + Z n ,
(10)
(k ) where Δ (jk ) = (c (1) j − c j )Tc − (τ 1 − τ k ) is the time difference
between user 1 and user k. Above assumptions, Δ can be modeled as a random variable uniformly distributed over [−T f , T f ] . As in [2], [9], MAI is modeled by zero mean white Gaussian and its variance depends on auto-correlation of timehopping code and cross-correlation of MHP pulse orders as Ns
( l +1) N s
∑ ∫
and Ns
∑ ∫
jT f
( j −1)T f
k = 2 j = lN s +1
⎡⎣ p (1) (t ) ⎤⎦ dt ,
p ( k ) (t − τ k ) p (1) (t )dt ,
(11)
j =1 k = 2
Ns Q ⎛ P ⎞ = ∑ E[( d ( k ) ) 2 ] ⎜ ∑ E[γ 2 (Δ (j p ) )] + ∑ E[γ 2 (Δ (jq ) )] ⎟, j =1 q =2 ⎝ p =2 ⎠
Zn =
∑ ∫
jT f
(k ) 2 Var[ Z MAI ] as σ MAI , the theoretical BER of the proposed a PAM PO-THMA UWB system is expressed as
( j −1)T f
j =lN s +1
n(t ) p (t )dt .
(13)
noise component Z n has mean zero and NsN0/2 variance. However, because the mean and variance of the MAI component are determined by the specific pulse waveform, we should determine the auto and cross correlation function of the transmitted pulse as follows
∫
Tf
0
p n ( t ) p m (t − Δ ) dt .
Ns
K
∑∑d j =1 k = 2
(k )
γ ( Δ (jk ) ) ,
( l +1) N s
∑ ∫
j = lN s +1
jT f
( j −1) T f
p (t − ε j ) p ( t ) dt ,
(19)
means time difference between the ideal pulse position and the actual received pulse position. Then, the theoretical BER performance with timing jitter for PAM PO-THMA UWB system is derived as
⎛ Es Pb _ jitter = Q ⎜⎜ 2 2 σ σ MAI + n ⎝
⎞ ⎟⎟ , ⎠
(20)
where Es = N s2 Eε . IV. NUMERICAL RESULTS
(14)
Therefore, the equation (12) can be written as
Z MAI =
(18)
where ε j is the timing jitter of the j-th frame pulse which
Since, Ns pulses are transmitted for each symbol, the desired signal component is Z d = N s2 E p = Eb and the thermal
R (m , n, Δ ) =
⎞ ⎟⎟ . ⎠
When there is timing jitter in the propose system, the BER performance degrades, since timing jitter decreases correlator output [10], [11]. Correlation between the template and the received pulse for fixed value of timing jitter is calculated as
Eε =
(1)
(17)
where P is the number of MHP pulse and Q is the number of time-hopping code. We find out that Z MAI has zero mean and when we let
(12)
and ( l +1) N s
K
(k ) Var[ Z MAI ] = ∑∑ E[(d ( k ) ) 2 ]E[γ 2 (Δ (jk ) )]
⎛ Eb Pb = Q ⎜⎜ 2 2 ⎝ σ n + σ MAI 2
( j −1)T f
j = lN s +1
K ( l +1) N s
Z MAI = ∑
jT f
(16)
j =1 k = 2
where each terms are obtained as
Zd =
K
(k ) E[ Z MAI ] = ∑∑ E[d ( k ) ]E[γ (Δ (jk ) )] ,
(15)
In this section, we show some numerical results under perfect synchronization and the presence of timing jitter in the proposed system and conventional the THMA system. Timing jitter is uniformly distributed between 0 ~ 0.1ns. The computer simulation results verify the theoretical results and some simulation parameters are as followings in Table II.
J. H. Hwang et al.: Performance Analysis of PO-THMA UWB System Using Mutually Orthogonal MHP Pulses TABLE II COMPUTER SIMULATION PARAMETERS
Parameters
Value
Pulse width Bandwidth normalization Sampling frequency Data rate PPM shift Number of users Channel
2 ns 0.15 ns 10 GHz 20 Mbps 0.5 ns 16, 32, 64, 128 AWGN
codes in two dimensionally. So, we can expect that the proposed system has better BER performance for fixed data rate and increased capacity for fixed BER. If it transmits a more pulses simultaneously, the system capacity will be increased. However, high order MHP pulses are sensitive to timing jitter. Therefore, we must select appropriate order and the number of MHP pulses in the real system. Fig. 6 shows the BER performance of the proposed UWB system with PAM versus the number of users for the various 0
10
0
10
-1
10
-1
10
-2
10
-2
BER
BER
10
16 user (N = 1) 32 user (N = 1) 64 user (N = 1) 128 user (N = 1) 16 user (N = 2) 32 user (N = 2) 64 user (N = 2) 128 user (N = 2) 16 user (N = 4) 32 user (N = 4) 64 user (N = 4) 128 user (N = 4)
-3
10
-4
10
-5
10
-6
10
-10
-5
0
-3
10
-4
-5
10
-6
10
5 Eb/N0
10
15
-5
0
5
10 Eb/N0
15
20
25
Fig. 7. BER performance of the proposed system with PPM.
20
0
10
0
10
-1
10
-1
10
-2
10
-2
BER
10
BER
16 user (N = 1) 32 user (N = 1) 64 user (N = 1) 128 user (N = 1) 16 user (N = 2) 32 user (N = 2) 64 user (N = 2) 128 user (N = 2) 16 user (N = 4) 32 user (N = 4) 64 user (N = 4) 128 user (N = 4)
10
Fig. 5. BER performance of the proposed system versus Eb/No for various number of users with PAM (The number of MHP pulses are 1, 2, and 4).
-3
10
-3
10
SNR 5dB (N = 1) SNR 10dB (N = 1) SNR 15dB (N = 1) SNR 5dB (N = 2) SNR 10dB (N = 2) SNR 15dB (N = 2) SNR 5dB (N = 4) SNR 10dB (N = 4) SNR 15dB (N = 4)
-4
10
SNR 5dB (N = 1) SNR 10dB (N = 1) SNR 15dB (N = 1) SNR 5dB (N = 2) SNR 10dB (N = 2) SNR 15dB (N = 2) SNR 5dB (N = 4) SNR 10dB (N = 4) SNR 15dB (N = 4)
-4
10
-5
10
-6
10
43
0
10
20
30
40 50 60 Number of Users
70
80
90
-5
10
-6
10
100
Fig. 6. BER performance of the proposed system versus the number of users for various SNR with PAM.
Fig. 5 shows the BER performance of the proposed UWB system and the THMA UWB system with PAM. In this figure, we use 1, 2, 3, and 4 orders of MHP pulses. From now on, it means the results of THMA that the pulse order N equals to 1 in the all results. This figure shows the proposed scheme have good performance. We can know that the resources are increased by considering orthogonal property of MHP pulses and it means we have more flexibility in assignment of resources including pulse orders as well as time-hopping
0
10
20
30
40 50 60 Number of Users
70
80
90
100
Fig. 8. BER performance of the proposed system versus number of users with PPM for various SNR.
SNR of 5, 10, and 15dB. This figure shows that the error probability is increased as the number of users increased. In this figure, we can get the maximum number of users for given BER and SNR. Fig. 7 shows the BER performance of the proposed system and conventional the THMA system with PPM. We show that the BER performance of the PAM scheme is better than PPM scheme. And Fig. 8 shows the BER performance of the proposed UWB system with PPM versus the number of users for the various SNR of 5, 10, and 15dB. Fig. 9 and 10 show the BER performance of the proposed UWB system with PAM in
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44
the presence of timing jitter. These figures show the BER performance in the presence of timing jitters of 0.05ns and 0.1ns, respectively. We find out that the BER is decreased according to increased the timing offset value and the number of users. Therefore, we can find out the appropriate number of users and pulse orders from those results for the desired BER and data rate.
REFERENCES [1] [2]
[3]
0
10
-1
10
[4]
-2
BER
10
-3
10
-4
10
-5
10
-6
10
-10
[5]
16 user (N = 1) 32 user (N = 1) 64 user (N = 1) 128 user (N = 1) 16 user (N = 2) 32 user (N = 2) 64 user (N = 2) 128 user (N = 2) 16 user (N = 4) 32 user (N = 4) 64 user (N = 4) 128 user (N = 4) -5
0
[6]
5 Eb/N0
10
15
20
Fig. 9. BER performance of the proposed system with timing jitter 0.05ns.
0
10
-1
10
-2
BER
10
-3
10
-4
10
-5
10
-6
10
-10
16 user (N = 1) 32 user (N = 1) 64 user (N = 1) 128 user (N = 1) 16 user (N = 2) 32 user (N = 2) 64 user (N = 2) 128 user (N = 2) 16 user (N = 4) 32 user (N = 4) 64 user (N = 4) 128 user (N = 4) -5
0
5 Eb/N0
10
15
20
Fig. 10. BER performance of the proposed system with timing jitter 0.1ns.
V. CONCLUSIONS In this paper, we proposed a PO-THMA UWB system which used mutually orthogonal MHP pulses. The proposed scheme had more flexibility in assignment of resources to users including mutually orthogonal MHP pulses as well as time-hopping codes in two dimensionally. We analyzed BER of the proposed system and showed that the BER performance and the transmission capacity were improved dramatically when it compared with those of conventional THMA UWB system. The proposed system could be expected to be utilized in the high data rate indoor wireless communication system requiring low power and simple complexity. ACKNOWLEDGMENT This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD), (KRF-2006-311-D00664).
M. Z. Win and R. A. Scholtz. “Impulse of Radio: How it works,” IEEE Trans. Commun. Lett., vol. 2, pp 51-53, Feb. 1998. M. A. 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. 679-691, Apr. 2000. P. Runkle, J. McCorkle, T. Miller, and M. Welborn, “DS-CDMA: the modulation technology of choice for UWB communications,” in Proc. IEEE Conf. Ultra Wideband Syst. Technol., pp. 364-368, Nov. 16–19, 2003. G. Durisi and S. Benedetto, “Performance evaluation and comparison of different modulation schemes for UWB multi-access systems,” Proc. IEEE Int. Conf. Comm., Anchorage, AK, pp. 2187-2191, May 2003. M. Ghavami, L. B. Michael and R. Kohno “ Hermite function based Orthogonal Pulse for UWB Communications,” Proc. Wireless Personal Multimedia Conf., Aalbog, Denmark, pp. 437-440, Sep. 2001. L. B. Michael, M. Ghavami, and R. Kohno, “Multiple pulse generator for ultra-wideband communication using Hermite Polynomial based
orthogonal pulses, ” Proc. 2002 IEEE Conf. on Ultra Wideband Systems and Technologies, Baltimore, MA, USA, May 2002. [7] M. G. Di Benedetto, G. Giancola, Understanding Ultra WideBand Radio Fundamentals, Prentice Hall. 2004. [8] H. Zhang and T. A. Gulliver, “Biorthogonal pulse position modulation for time hopping multiple-access UWB communications,” IEEE Trans. Wireless Commun., vol. 4, no 3, pp. 1154-1162, May 2005. [9] G. Durisi and G. Romano, “On the validity of Gaussian approximation to characterize the multiuser capacity of UWB TH PPM,” Proc. IEEE Conf. Ultra Wideband Systems and Technology, pp. 157-161, 2002. [10] J. R. Foerster, “The effects of multipath interference on the performance of UWB systems in an indoor wireless channel,” Proc. IEEE Vehicular Technology Conf., pp. 1176-1180, May 2001. [11] M. Ghavami, L. B. Michael, and R. Kohno, “Effect of Timing Jitter on Hermite Function Based Orthogonal Pulse for Ultra Wideband Communication,” Proc. Wireless Personal Multimedia Conf., Aalborag, Denmark, pp.437-440, Sep. 2001. [12] J. G. Proakis, Digital Communications, 4th ed., McGraw Hill, 2001.
Jun Hyeok Hwang received the B.S. degree in electronics engineering from Jinju National University, Jinju, Korea, in February 1999, and the M.S. degree in electrical engineering form the Pukyong National University, Busan, Korea, in February 2003. He is currently working towards the Ph.D. degree at the Communication System Laboratory, Department of Electronics Engineering at Pusan National University, Busan, Korea. His research interests include ultra-wideband system, digital communication, and wireless communications. Suk Chan Kim was born in Namhae, Korea, on February 10, 1971. He received the B.S. (summa cum laude) degree in electronics engineering from Pusan National University (PNU), Busan, Korea, in February 1993, and the M.S.E. and Ph.D. degrees in electrical engineering from Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea, in February 1995 and 2000, respectively. He was a teaching and research assistant at the Department of Electrical Engineering, KAIST, in 1993-1999, and a post doctoral researcher at the Electronics and Telecommunications Research Institute (ETRI), Princeton University, and Lehigh University, in 2000-2001, respectively. He is now an Associate Professor at the Department of electronics engineering, PNU from March 2002. He is a Member of the Research Institute of Computer, Information and Communication (RICIC), Institute of Electronics Engineers of Korea (IEEK), Korean Institute of Communication Sciences (KICS), and a Senior Member of the Institute of Electrical and Electronics Engineers (IEEE). His research interests include mobile communications, statistical signal processing, and communication networks.
J. H. Hwang et al.: Performance Analysis of PO-THMA UWB System Using Mutually Orthogonal MHP Pulses Seokho Yoon (S’99-M’02) received the B.S.E. (summa cum laude), M.S.E., and Ph.D. degrees in electrical engineering from Korea Advanced Institute of Science and Technology (KAIST) in 1997, 1999, and 2002, respectively. From April 2002 to June 2002, he was with the Department of Electrical Engineering and Computer Sciences, Massachusetts Institute of Technology (MIT), Cambridge, MA, and from July 2002 to February 2003, he was with the Department of Electrical Engineering, Harvard University, Cambridge, MA, as a Postdoctoral Research Fellow. In March 2003, he joined the School of Information and Communication Engineering, Sungkyunkwan University, where he is currently an Assistant Professor. His research interests include spread spectrum systems, mobile communications, detection and estimation theory, and statistical signal processing. Dr. Yoon is a Member of the Institute of Electrical and Electronics Engineers (IEEE), Institute of Electronics Engineers of Korea (IEEK), and Korean Institute of Communication Sciences (KICS). He was the recipient of a Bronze Prize at Samsung Humantech Paper Contest in 2000. Bongsoon Kang (M’76) received the B.S. degree in Electronic Engineering from Yonsei University, Seoul, Korea, in 1985, and the M.S. degree in Electrical Engineering. from University of Pennsylvania, Pennsylvania, USA, in 1987, and the Ph.D. degree in Electrical and Computer Engineering from Drexel University, Philadelphia, USA, in 1990. From Dec. 1989 to Feb. 1999, he had worked as a senior staff researcher at the Samsung Electronics Co., Ltd., Korea. Since March 1999, he has been with the School of Electronic Engineering, Dong-A Univ., Busan, Korea. He is the director of the Multimedia Research Center of the University. His research interests include VLSI algorithm/architecture design, image/video processing, and wireless communication.
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Ju Sung Park received was born in Junju, Korea, on December 19, 1953. He received the B.S degree in electronics engineering from Pusan National University, Busan, Korea, in 1976 and the M.S. degree in electrical engineering from the KAIST, Seoul, Korea, in 1978, and the Ph.D. degree in electrical engineering from University of Florida, Gainsville, in 1989, USA. From March 1978 to March 1991, he was with the ETRI, Taejun, Korea, where he work as a Principal Research Engineer and as the manger and the director of IC design group. While at ETRI he designed several bipolar analog IC’s and was in charge of developing VCR IC’s, CMOS 8 bit microprocessor, and telecommunication chips. In 1991, he joined the Electronics Department of Pusan National University, Pusan, Korea, where he is now a professor of Electrical Engineering. His current research interests are microprocessor and DSP core design, digital audio algorithm implementation by hardware and software co-design.
