Email: wjangWunlnotes.unl.edu. Abstract-In this paper, we apply .... User asynchronism prevailing in spectral density (PSD) is No/2. Tk representstime shifts to ... For this, the template waveform, v(t), for each pulse of each. II. SYSTEM MODEL.
Self-Encoded TH-PPM UWB System with iterative Detection Youn Seok Kim, Won Mee Jang and Lim Nguyen The Peter Kiewit Institute of Information Science, Technology & Engineering Department of Computer and Electronics Engineering University of Nebraska - Lincoln Omaha, NE 68182 Email: wjangWunlnotes.unl.edu Abstract-In this paper, we apply iterative detection to
typical time hopping (TH) pulse position modulation (PPM)
ultra wideband (UWB) spread spectrum systems. Unlike a typical TH-PPM UWB which employs repetition code, the proposed system uses self-encoded code which is updated by user information itself. To take advantage of self-encoded spread spectrum, we apply iterative detection to the TH-PPM UWB system. By means of simulation, we will investigate the bit error rate (BER) performance of the proposed system in additive white gaussian noise (AWGN) channels and also fading channels. We observe a significant BER performance improvement over conventional TH-PPM UWB systems.
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I. INTRODUCTION
ISBN 89-5519-129-4
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Keywords-UWB, TH-PPM, self-encoded multiple access, iterative detection.
An ultra-wideband device widely accepted by industry, according to the FCC's First Report and Order [1], is any device emitting signals with a fractional bandwidth greater than 0.2 or a bandwidth of at least 500 MHz at all times during transmission. The FCC has restricted the use of UWB systems to the frequencies shown in [2] [3]. The gaussian monocycle pulse, commonly used in UWB impulse radio [4] [5] [6], must be filtered to meet the FCC spectrum requirements. Ultra wideband spread spectrum systems use baseband pulses of very short duration, typically on the order of a nanosecond without a sinusoidal carrier to shift the signal to a high frequency band. These features of UWB systems contribute to maintaining the reliable performance for an indoor wireless channel with multipath interference. In multiple access environments, UWB systems use a time hopping sequence which includes time position information for each pulse in each frame time. That is, every pulse that corresponds to each user has a different time shift position that is determined by each user's time hopping sequence. Therefore, serious collision can be avoided between users so that multiple access interference effects are minimized. A novel spread spectrum communication system has been developed for multimedia communications with a multi-rate data transmission [6] [7] [8]. This approach is based on the unconventional self-encoding principles that we have developed for the modulation and detection of spread spectrum signals [9]. The proposed system does not use pseudo-random
=
T
e N'T T
Fig. 1. Block diagram of self-encoded spread spectrum system.
codes. It is unique in the fact that traditional transmit and receive code generators based on the maximal-length sequences or other predetermined spreading sequences are not needed. Because there is memory within the self-encoded spread spectrum (SESS) modulation, it is natural to consider using the maximum likelihood sequence estimation (MLSE) detection based on the Viterbi algorithm. MLSE detection improves the system performance by estimating the sequence of the received signals. However, the number of states in the Viterbi decoder grows exponentially with the spreading factor. Recently a sub-optimal detector, an iterative detection scheme was developed in [10] which can reduce the complexity to a linear order of the spreading factor. The performance of this iterative detector is very close to that of the MLSE detector. Furthermore the performance of the iterative detection can be improved significantly by using chip-interleaving in fading channels [11]. In this paper, we combine the iterative detection with selfencoded ultra wideband TH-PPM spread spectrum multiple access systems. We show that the BER performance can be improved significantly in AWGN channels as well as in fading
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1
X
-1l
(i) 1
I
1
-1l| -i
-I)(001
-
I
1
-1) -l
1
1
1
:13
1L
1
-
I
L
I
I
1
gaussian monocycle [13]. The pulse is given by
SpreaFsequiFNes
SpreadinOF seqiieiiees
Data bit
1I - I
1
-
p(t)=
[1 -4T
() J exP
-27
2)
(-)J
The autocorrelation function of the p(t) can be written as
R(T) = liM 1 T
D
T
T/2
J
p(t)p(t + T)dt.
(3)
Thus, we can get the closed form of the autocorrelation
-1 L
| A | t Fig. 2.
1
ft unction for the gaussian monocycle p(t) [13]
-1 | 1
channels. Multiuser detection is imperative in self-encoded direct sequence spread spectrum (DS-SS)system in order to apply the iterative detection. However, in self-encoded THPPM UWB, we can employ the iterative detection without multiuser detection. It is because of the reduced multiple access interference in UWB by using an extremely short pulse duration less than 1 ns. User asynchronism prevailing in TH-PPM UWB also lessens the multiple access interference in the system. Therefore, it can be more practical to apply the iterative detection to UWB spread spectrum rather than applying it to a direct sequence spread spectrum owing to the reduced computational complexity by eliminating the multiuser detection. The rest of this paper is organized as follows. The system model is developed in Section II with an implementation of the iterative detection in the TH-PPM UWB system. The simulation results supporting the proposed system are given in Section III, and the conclusion follows in Section IV. II. SYSTEM MODEL
a) Conventional TH-PPM UWB: The system model is based on the asynchronous TH-PPM. Notation and terminology in this chapter are consistent with [12] [13]. The signal form of a typical TH-PPM UWB signal is given by (t, i)
Ns
S
J=iNS
-
),
N.
k=1
(5)
where N,, is the total number of users, Ak is the path loss for user-k, n(t) is additive white gaussian noise whose power spectral density (PSD) is No/2. Tk represents time shifts to account for user asynchronism. Assuming that user- I is active, r(t) A si(t- T) + n(t) The signal waveform in transmitting 1 and -1 is;
1: r(t)- Al P
N-1
? Lw
j=O
1: r(t) =A1
p(t jTf -
-
rTTi c
3 p(t - jTf 0 j
(6)
5) + n(t),
(7)
cNT--1T) + n(t).
(8)
-
-
c
j=
The correlation detection scheme is employed for bit decisions. For this, the template waveform, v(t), for each pulse of each frame time is applied to the correlation operation
v(t) = p(t) - p(t - ).
(9)
Then the decision statistic is fTb
N,-1
r(t) ,3 v(t -jTf - cTc -Tl)dt.
(I0)
j=
(1) If r is greater than 0, the decision for the transmitted data is
where t is time, s(t, i) is the i-th data bit of the k-th user, and p(t) is the signal pulse whose width is Tp. Eb is the energy of each bit. Ns is the number of pulses to transmit one bit information. Tf in Equation (1) is the time duration of each frame. Thus, the bit duration, Tb, is NsTf. cf is the time hopping code for the k-th user. We assume c is random by taking an integer in the range 0 < c'k < Nh. Tc is the chip duration. d$k C {0, 1} is the i-th data bit of the k-th user. Finally, d is the time shift to represent binary data bit. The pulse shape that is employed in this system is a second order
ISBN 89-55 1 9-1 29-4
TP
r(t) = 3 Aksk(t - Tk) + n(t),
0
p(t jTf - cT-d
TP
4) In a multiuser environment of AWGN channels, the input signal at the receiver forms
(i+l)N,-1
s
3
TP
Spreading operation of SESS.
-1. Otherwise, the decision is 1. b) Self-Encoded TH-PPM UWB with Iterative Detection: The iterative detection scheme developed in [10] is based on a unique property of SESS. In this paper, we apply iterative detection to TH-PPM UWB to improve the system performance. As can be seen in Fig. 1, spreading codes are updated according to the previous bit information. What is more, the chip based on the bit information stays in the spreading sequence for the following N-bit duration. For this reason, we can extract additional information of the data bit from the next N bits received. Fig. 2 illustrates more about iterative detection in SESS systems. The left side table displays
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. . . .t~ ~ ~ ~ ~ 10-
Ptle Pulse train iit-egaor
ltelaiwr detection
with d u dllg
correlator
C iipr to ze1
10-
0eXUt8,tOL 1.10
t Xt
11 10- tO\
Col1 C.'kli Leerat
Code delc,wl
or 0
r1) e
vuc Lo&k Friti uiitrol
10
Fig. 3. Receiver block diagram of self-encoded TH-PPM with iterative detection.
D]
bU2 b2
=b3 UN
o & 2
el
&o i
...
... .... ...
eN-il eN-2
* - -
. .
-
...
* - -
eN
e-N+4 eO
10
Eb/No (dB)
15
Fig. 4. Analytical and simulation BER, self-encoded DS-SS, 64 chips/bit, single user, Rayleigh fading, reproduced from [11].
information from the next N incoming bit sequence makes it possible to re-estimate b1. That is, the decision variable r of b1 in the proposed system can be written as N 0 r= E ekek + E bi 6 + (12)
k=-N+1
bN+e1
i=2
< _ correlation output iterative detection output where ek is the chip in the despreading sequence at the receiver. A typical TH-PPM UWB employs the repetition code, where an identical symbol is transmitted in every frame. We apply SESS to TH-PPM UWB by replacing the repetition code with a self-encoded code.While maintaining the basic structure of a typical TH-PPM UWB, the self-encoded code is considered under the assumption that the pulse in each frame corresponds to the chip information. Therefore, the spreading
(11)
sk(t,i) - [NxN]
data output and received spread sequence block where &i is the estimated value of the spread chip at the receiver. After the despreadingoperation,asequenceofNdata bits, b1,,* bN, are detected. However, the unique property of SESS allows iterative detection. Therefore, we can obtain the additional information of a data bit from the next N bits. For example, e i carries the information of bi. Thus, the N chip
ISBN 89-5519-129-4
5
length is equal to Ns in the proposed system, which depends on the number of pulses transmitted per each bit. The TH-PPM UWB signal for the k-th user using the self-encoded code can be written in the form
e-N+2 *-e-N+3
.
I-
0
~
UJWB system
the spreading sequence of a user. The right side table exhibits spread sequences after spreading data bits. Here we assume the length of the spreading sequence, N=4. We can observe that the first bit information stays in the shift register until the fifth bit is spread. The polarity of the chip in the spreading sequence of the next N data bits depends on each corresponding data bit due to the XOR operation performed with the data bit. However, we can recover the original data bit information by applying another XOR operation to the chip with each corresponding data bit. Therefore, at the receiver, it is possible that the first data bit information can be re-estimated using the next N data bits. That is, in addition to the correlation output, we can combine the N-chip energy collected from the following N bits for the data bit detection - called iterative detection. Let bi and en be the data bit and the corresponding chip information after spreading, respectively. Then [bb D
b'l
+ Chip interleaving w/ iterative detection simulation Chip interleaving - ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~wI iterative detection analysis -a--- Iterative detection simulation --BPSK
106
Ti
Chip interleaving simulation
Chip intenleaving analysis _____~~~~~~~~~~~~~~~~~~~~~~~~~
N
(i+ 1) N-1
p(t -Tf-
CjfTc-b isff
),
(13)
where bV C {-1,1} is the k-th user bit during the i-th bit interval and sk C { 1,1 } is the self-encoded code during the j-th frame. The product value b.sk C {-1, 1} is mapped into {O,1} for the PPM implementation. bs is thespread chip value at the transmitter and is detected as en in (12) at the receiver, and the corresponding estimated value, en2 (a pure chip value without an XOR operation with the data bit) in (12) constructs despreading sequences for the next incoming bits.
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10°N
E)
code Ns=2repetition Ns=4 code
Ns=-6repetitioncode Ns=16 repetition
The hopping sequence ck is generated using random sequences as in a typical TH-PPM UWB system. Fig. 3 illustrates a self-encoded TH-PPM UWB system. The structure of the proposed system is similar to the conventional TH-PPM UWB
c d so
iterative detection ___ Ns=l6SEMA
10-
-
system except that the correlation procedure follows the selfcodes instead of simple repetition codes. The receiver l structure remains the sames mexcept that (10) is combined with the despreading sequence as encoded
102
fTb
-1 ~~~~~~~~~~~~N,
ejv(t -jTf cT r(t) ,o < * --r| = j io~~~~~~~~~~~~~~~~~~~~~~C -
W
\ \
10-4
\\ \\
-
''.>
-Tl)dt,
(14)
to provide the correlation output that is followed by the iterative detection. III. SIMULATION RESULT
We employ the same system parameters as in [12] for the
106
10-70
2
4
6
10
8
10
Eb/No (dB)
12
12
14
14
16 l
16
Fig. 5. Simulation BER, self-encoded TH-PPM UWB, 8 users (Nq,=8), N8=2, 4, 16, AWGN.
10° IO Ns=16iterative detectionl ---Ns=16 repetition code 10-1
__\_\Ns=l 6 SEMA
A
10-2
10-5
5
10
_
s
Xn
10-3
15
20
Eb/No (dB)
25
30
35
40
Fig. 6. Simulation BER, self-encoded TH-PPM UWB, 8 users (Ntl = 8), N8=16, Rayleigh fading.
ISBN 89-5519-129-4
following simulations; the frame time, Tf = 50 nsec, PPM delay, 6=0.15 ns, number of chips per frame=8, time normallization factor, Tp = 0.2877 ns and impulse width, Tp = 0.7 ns. Fig. 4 shows the BER performance of a chip-interleaved self-
encoded multiple access system with iterative detection in the direct sequence spread spectrum. The spreading factor of 64 chips/bit has been employed with a single user in flat fading channels. We can see that iterative detection is far superior to matched filter detection. The performance of chip-interleaving is very close to, but a little better than iterative detection. The chip-interleaved iterative detection improves the system performance significantly and the BER difference increases at high signal-to-noise ratio (SNR). Since the self-interference due to detection errors at the receiver is not included in analysis, we observe a BER discrepancy at low SNR. However, the analytical result agrees well with the simulation result at high SNR. The performance of the self-encoded TH-PPM UWB system with the iterative detection is shown in Fig. 5. The BER performance of conventional TH-PPM UWB systems with repetition code is shown for eight users with the number of frames (Ns) equal to 2, 4 and 16 in additive white gaussian noise (AWGN) channels. A larger number of frames provides better performance. We can see that the BER performance of the TH-PPM UWB with repetition codes is the same as the BER of self-encoded multiple access system without iterative detection for Eb/N0 > 6. We observed the same result for other values of N, A significant BER improvement is displayed by using self-encoded code with iterative detection. The BER improvement is larger at high SNR. Fig. 6 shows the simulation BER of the TH-PPM UWB for eight users in flat fading channels. We assume that the fading parameter remains the same during a bit duration. The BER of repetition codes is close to a self-encoded code without iterative detection except the self-interference introduced at loW SNR. The self-interference is alsoh observed the ieaiedtcina o N.Hwvr trtv with eeto 1eav eehna o N.Hwvr h trhedtco improves the system performance of a self-encoded code significantly at modest and high SNR region. We observe that the BER improvement becomes greater at high SNR.
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IV. CONCLUSIONS
[6] L. Nguyen, "Self-encoded spread spectrum and multiple access communications," Proc. of the 2000 IEEE International Symposium
We proposed a self-encoded TH-PPM UWB system with ieaiedetection. simulation BRof the iterative detection. We showed that the thesimulation BER ofthe
2000. Sep. and [7] NJ, W Jang L. Nguyen, "Capacity analysis of m-user self-encoded mul-
channels as well as in fadig channels. Future works nclude
[8] Y Kong, L. Nguyen and W. M. Jang, "Self-encoded spread spectrum
proposed system is improved significantly compared with the conventional TH-PPM UWB with repetition codes in AWGN an extension of our system to frequency selective multipath fading channels and its detailed analysis.
tiple access system in AWGN channels," Proc. of the 2000 IEEE International Symposium on Spread Spectrum Techniques and Applications, Parsippany, NJ, Sep. 2000.
modulation with differential encoding," Proc. of the 7th IEEE International Symposium on Spread Spectrum Techniques
[9]
REFERENCES
[1] FCC, "Revision of part 15 of the commission's rules regarding ultrawideband transmission systems," First Report and Order, ET Docket 98-153, FCCO2-8, adopted/released Feb. 14/Apr. 22, 2002. [2] D. Porcino and W. Hirt, "Ultra-wideband radio technology: Potential and challenges Ahead," IEEE Commun. Magazine, vol. 41, no. 7, Jul. 2003, pp. 66-74. [3] G. R. Aiello and G. D. Rogerson, "Ultra-Wideband, Wireless Systems," IEEE Microwave Magazine, vol. 4, no. 2, June 2003, pp. 36-47. [4] 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, Apr. 2000, pp. 679-689. [5] M. Z. Win and R. A. Scholtz, "Impulse radio: how it works," IEEE Communications Letters, vol 2, no 2, Feb. 1998, pp. 36-38.
ISBN 89-551 9-1 29-4
on Spread Spectrum Techniques and Applications, Parsippany,
[10] [11]
[12] [13]
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and Applications (ISSST 02), Prague, Czec Republic, Sep. 2002. L. Nguyen, "Self-encoded spread spectrum communications," Military Communications Conference Proceedings, IEEE MILCOM 1999, vol. 1, 31 Oct.-3 Nov. 1999, pp. 182-186. Y Kong, "Theoretical derivation for single user SESS with iterative detection in a slowly Rayleigh fading two-way multipath channel," Ph.D dissertation, Dept. Elec. Eng, University of Nebraska, 2005. Y. S. Kim, W. M. Jang, Y Kong and L. Nguyen, "Chip-Interleaved SelfEncoded Multiple Access with Iterative Detection in Fading Channels," submitted to Journal of Communications and Networks. B. Hu and N. C. Beaulieu, "Accurate evaluation of multiple access performance in TH-PPM and TH-BPSK UWB systems," IEEE Trans. Commun., vol. 51, no. 10, Oct. 2004, pp. 1758-1766. B. Hu and N. C. Beaulieu, "Accurate evaluation of multiple access performance in time-hopping UWB systems," 2004 IEEE International Conf. Communications, vol 1, 20-24 June 2004, pp. 300-305.
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