Adaptive Time Hopping PPM UWB Multiple
Access Communication Schemes
G. S. Biradar, S. N. Merchant and U. B. Desai
SPANN Laboratory, Department of Electrical Engineering
Indian Institute of Technology Bombay, Mumbai, INDIA-400076
Tel: +91-22-25764478, Fax: +91-22-25720651
E-mail: gsbiradar, merchant, ubdesai @ee.iitb.ac.in
Abstract—Typical Ultra Wide Band (UWB) systems are built to
meet Quality of service (QoS) constraints under multiple access
environment. We propose a UWB physical layer that adapts
its number of time hops to efficiently meet QoS requirements.
The proposed adaptive UWB uses side information to know the
current QoS and adjusts its number of time hops accordingly.
The system employs adaptive Time Hopping Pulse Position
Modulation (TH-PPM). The bit error rate (BER) performance
is evaluated under additive white Gaussian noise with multiple
access communication.
The paper is organized as follows. In Section II, the system
model and construction of the time hopping PPM UWB signals
is described. In Section III error probability of M-ary PPM
over AWGN channel is presented. In Section IV multiple
access interference and error probability analysis is presented.
In Section V adaptive TH-UWB explained. Simulation results
and performance is given in Section VI. Finally Section VII
provides conclusion.
I. I NTRODUCTION
An Ultra wide band [1] is a new technology that has
the potential to revolutionize wireless communication by
delivering high data rates with very low power densities.
Unlike conventional communication systems UWB systems
operate at base band, and thus involve no intermediate
frequency and carrier synchronization. UWB uses impulse
signal technology to generate UWB communication signals
that consists of trains of time shifted sub nanosecond
impulses. UWB theoretically promises a very high data rate
by employing a large signal band width. However, due to
possible interference to existing communication systems,
power spectrum density limitations imposed by FCC part
15 rules greatly limits the system capabilities. For multiple
access communication modulation schemes like, Time
hopping PPM, Time hopping PAM, Time hopping BPSK,
DS-CDMA, OFDM may be used.
In [1], [2], [3] a time hopping multiple access scheme
for UWB system with PPM was considered, which mainly
concentrates on improving bit error rate performance by using
repetitive coding with M-ary PPM modulation. Reference [4]
proposed adaptive M-ary PPM modulation for optimization
interms of data rate and energy to meet QoS requirements.
In this paper, we propose a new scheme adaptive TH-UWB,
which adapts its number of hops depending on the required
bit error rate (BER) in multiple access communication under
additive white Gaussian noise (AWGN). The exact probability
of error is derived for single user and multiple user under
synchronous transmitter case. Simulation is carried out for
both synchronous and asynchronous cases. Second derivative
of Gaussian pulse is considered for multiple access analysis.
II. S IGNAL AND SYSTEM MODEL
The time hopping M-ary PPM system model for th user
in given by
(1)
where
is the signal amplitude,
represents the
second derivative of Gaussian pulse with pulse width ,
is the frame time, frame is divided into
time slots with
,
also
duration . The pulse shift pattern
called the time hopping sequence for th source and it is
pseudo random with period , this additional shift avoids
catastrophic collisions due to multiple access interference
(MAI). The sequence is the data stream generated by the
th source after channel coding and is the additional time
, a repetition code is
shift utilized by M-ary PPM. If
introduced, that is,
pulses are used to transmit the same
information.
For M-ary PPM, signal amplitude
be written as
so that (1) can
(2)
The received signal can be modeled as:
(3)
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Considering
, the demodulated signal
is given by
(11)
The average probability of a correct decision is given by [8]
(12)
Fig. 1. System model of TH-MA M-ary PPM UWB system
where,
(13)
(4)
Finally, the probability of a symbol error for an M-ary PPM
is
is AWGN noise with power spectral density
where
,
is the propagation delay for the th user,
is
the received pulse waveform. PPM receiver uses bank of M
correlation receivers followed by a detector. Even though the
number of users are more than one still an M-ary correlation
receiver is typically used for simplicity.
III. E RROR PROBABILITY OF M- ARY PPM OVER AWGN
CHANNEL
The vector representation of an M-ary PPM for single user
case is defined as an P dimensional vector with nonzero value
in th dimension.
(5)
(14)
IV. M ULTIPLE ACCESS INTERFERENCE AND ERROR
PROBABILITY
MAI is the factor limiting the performance and capacity
of the system when more than one user is active. MAI can
be modeled as a zero mean Gaussian random variable if
number of users are large [6]. Assuming M-ary PPM signal are
) the MAI and error probability analysis
orthogonal (i.e
given in section III for single user system can be extended to
multiple access system.
A. Multiple access interference and error probability
As given in (3) the received signal is modeled as
where
is the average signal energy.
The received signal can be expressed as
(6)
As illustrated in Fig. 1 optimal receiver for M-ary orthogonal
PPM signals consists of a parallel bank of M cross correlators.
, denote the th basis signal vector, which
Let
shown
is the vector representation of the basis function
in fig. 1, defined as
(7)
where the non zero value 1 is in the th dimension. Assumwas sent, the optimum detector makes a decision on
ing
in favor of the signal corresponding to the cross correlator
with the minimum Euclidian distance.
(8)
where
(15)
to evaluate the MAI , we make the following assumptions:
(a)
for
where
is the
is assumed to be
number of active users, and the noise
independent.
(b) The time hopping sequence
and time delay
are
assumed to be independent and identically distributed (iid)
.
over the time interval
(c) Perfect synchronization is assumed at the receiver that is
is known at the receiver.
Assuming that
and desired user corresponds to
.
The M-ary correlation receiver for user 1 consists of M
cross correlators with basis function
(16)
(9)
(10)
At sample time
is
, the output of each filter
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1259
where, is pulse shaping parameter, The autocorrelation of
double differentiated Gaussian pulse is then
(17)
Assuming PPM signal
be written as
is transmitted by user 1, (17) can
(24)
(18)
where MAI component
considering
is
(25)
(26)
(19)
and AWGN component N is
by defining spread factor
as,
(26) can be written
(27)
(20)
is the AWGN component. By defining the autocorrelation
as
function of
Note that
increases with
,
and the number of
users
, but decreases with the spread ratio
Using standard techniques [8] the average probability of
error for a single user under multiple access interference for
binary PPM is given by
(21)
(28)
(19) can be written as
(22)
where
is the time difference between user 1 and user .
can be modeled
Under the assumptions listed above,
.
as a random variables uniformly distributed over
The MAI is modeled as a Gaussian random process for the
multiuser environment[7]. With the Gaussian approximation
we require the mean and variance of (18) to characterize the
output of the cross correlators.
The AWGN component has zero mean and variance
, the mean and variance of MAI are pulse waveform
specific. The calculations are carried out considering double
differentiated Gaussian pulse as the transmitted pulse and all
PPM signals are equally likely apriori, The double differentiated Gaussian pulse is defined as
V. A DAPTIVE TH-UWB
Under the multiple access environment traditional communication with fixed modulation scheme is inadequate to
efficiently meet QoS requirements. In (27) it is shown that
i.e,
MAI can be reduced by increasing the spread factor
number of time hops. Hence to meet QoS requirements we
propose dynamically changing number of time hops.
In adaptive TH-UWB the first step is to examine the current
QoS, the second step is to check the required QoS, the third
step is to adapt number of hops accordingly. In this paper QoS
is BER. We propose two adaptation schemes:
Receiver
Transmitter
BER
BER
Transport layer
Transport layer
MAI
MAC Layer
Adaptive
Block
MAI
AWGN
MAC Layer
Adaptive
Block
Nh
Nh
Physical Layer
+
Physical Layer
MAI
(23)
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Fig. 2. Block diagram of adaptive UWB system
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0
10
Nou4Ns2Nh1
Nou4Ns2Nh2
Nou4Ns2Nh4
Nou4Ns2Nh8
Nou4Ns2Nh16
Required QoS
Current QoS
Find number of active
UWBs
Increase number of
time hops
−1
Set number of time hops
= X times number of
active UWBs
BER
10
Yes
Current QoS <
Reqired QoS
(ii)
(i)
−2
10
Fig. 3. Proposed adaptive schemes
−3
10
(i) UWB trans-receiver transmits bits at regular intervals and
listens to itself to calculate the BER. Depending on this
information number of hops are varied to meet required BER.
(ii) All active UWB devices regularly send “Hello” messages
so that number of active UWB devices in the area is known
to each other. Depending on this information number of hops
are varied to meet the required BER.
The disadvantage of proposed adaptive scheme is reduction in
data rate as the number of hops increased.
VI. S IMULATIONS AND RESULTS
Simulations were carried out for both synchronous and
asynchronous users. Bit error rate results are presented as
a function of
and number of users. The parameters
considered for simulations are binary PPM with sampling frequency of 50 MHz, chip time of 1 nanosecond, Gaussian pulse
of width 0.5 nanosecond and of 0.5 nanosecond. Pseudo
random time hopping code of length 50000 is generated and
assigned to each user.
Binary data is generated using uniform random number
generator for each user and modulated using UWB pulse.
AWGN noise is generated and added to modulated signal.
Simulations are carried out for different number of hops
bits is
( ) and repetitive coding ( ). Data of length
transmitted and BER performance tested. Receiver uses a
correlation type detector and it is assumed that time hopping
sequence of user of interest is known.
0
2
4
6
8
10
Eb/No (dB)
12
14
16
18
20
Fig. 5. BER plot for Nou=4, Ns=2, Nh=1,2,4,8 and 16 ’Synchronous case’
Fig. 4 shows BER plot for the cases of 4 synchronous users
with
and variable
and .
It is observed that increase in number of hops reduces BER.
Fig. 5 shows an improvement of (3dB) by using repetitive
), but at the cost of reduced data rate.
coding (
Figures 6 and 7 show BER plot for the case of 4 asynchronous users. In this case, since the probability of two or
more users transmitting simultaneously is low it results in less
interference and consequently, BER performance improves.
Fig. 8 shows plot of number of users versus BER for
for
of 10 dB and 15 dB for
and respectively.
gives 3 dB improvement over
for a given
.
Fig. 9 shows BER plot as a function of number of users
and number of hops for SNR of 10 dB and 15 dB. It can be
observed that BER increases with increase in number of users
gives much
and decrease in number of hops. Again
.
better performance than
Therefore using these plots the system can adapt different
hopping length for the required BER under multiple access
condition. Adaptive scheme (i) calculates BER at regular inter-
0
0
10
10
Nou4Ns1Nh1
Nou4Ns1Nh2
Nou4Ns1Nh4
Nou4Ns1Nh8
Nou4Ns1Nh16
Nou4Ns1Nh1
Nou4Ns1Nh2
Nou4Ns1Nh4
Nou4Ns1Nh8
Nou4Ns1Nh16
−1
BER
BER
10
−1
10
−2
10
−2
10
−3
0
2
4
6
8
10
Eb/No (dB)
12
14
16
18
20
Fig. 4. BER plot for Nou=4, Ns=1, Nh=1,2,4,8 and 16 ’Synchronous case’
10
0
2
4
6
8
10
Eb/No (dB)
12
14
16
18
20
Fig. 6. BER plot for Nou=4, Ns=1, Nh=1,2,4,8 and 16 ’Asynchronous case’
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1261
0
10
VII. C ONCLUSIONS
Nou4Ns2Nh1
Nou4Ns2Nh2
Nou4Ns2Nh4
Nou4Ns2Nh8
Nou4Ns2Nh16
In this paper we propose an adaptive TH-PPM for UWB
to maintain the required BER performance under AWGN
and multiple access environment. It is shown that significant
improvement is achieved as the number of hops are increased,
Based on the exhaustive simulation results we conclude that
which is 12 times the number of users is
the value of
with
of 10 dB
sufficient to maintain a BER of
and
=2.
−1
BER
10
−2
10
−3
10
R EFERENCES
−4
10
0
2
4
6
8
10
Eb/No (dB)
12
14
16
18
20
Fig. 7. BER plot for Nou=4, Ns=2, Nh=1,2,4,8 and 16 ’Asynchronous case’
−2
10
Ns1SNR10dB
Ns1SNR15dB
Ns2SNR10dB
Ns2SNR15dB
−3
BER
10
−4
10
−5
10
1
2
3
4
5
6
Number of users
7
8
9
10
Fig. 8. Plot for Number of users vs BER
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vals and varies its number of time hops to meet required BER.
Adaptive scheme (ii) it has been calculated from exhaustive
simulations that of 12 times the number of active users is
sufficient to maintain a BER of
with
of 10 dB
=2. Simulations can be extended to find for different
and
BER requirements.
ns1snr10
ns2snr10
ns1snr15
ns2snr15
−1
10
−2
BER
10
−3
10
−4
10
−5
10
150
10
100
8
6
50
4
Number of hops
0
2
Number of users
Fig. 9. Plot for Number of users, no of hops vs BER
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