ReducedRank Adaptive Least Bit ErrorRate Detection in Hybrid DirectSequence TimeHopping Ultrawide Bandwidth Systems.
ABSTRACT In this paper we consider the lowcomplexity detection in hybrid directsequence timehopping ultrawide bandwidth (DSTH UWB) systems. A reducedrank adaptive LBER detector is proposed, which is operated in the least bit errorrate (LBER) principles within a detection subspace obtained with the aid of the principal component analysis (PCA) assisted reducedrank technique. Our reducedrank adaptive LBER detec tor is free from channel estimation and does not require the knowledge about the number of resolvable multipaths as well as that about the multipaths' strength. In this paper the bit errorrate (BER) performance of the hybrid DSTH UWB system is investigated, when communicating over the UWB channels modelled by the SalehValenzuela (SV) channel model. Our study and simulation results show that this reducedrank adaptive LBER detector constitutes a feasible detection scheme for deployment in practical pulsebased UWB systems. estimation. It achieves its nearoptimum detection with the aid of a training sequence at the start of communication and then main tains its nearoptimum detection based on the decisiondirected (DD) principles during the communication (9). The reducedrank adaptive LBER detector does not require the knowledge about the number of resolvable multipaths as well as that about the locations of the strong resolvable multipaths; It only requires the knowledge (which is still not necessary accurate) about the maximum delayspread of the UWB channels. Furthermore, the reducedrank adaptive LBER detector is operated in a reducedrank detection subspace obtained based on the principal component analysis (PCA) (10). The detection subspace usually has a rank that is significantly lower than that of the original observation space. Owing to the abovementioned properties of the reducedrank adaptive LBER detector, we can argue that it is a lowcomplexity detection scheme, which is feasible for practical
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Conference Paper: ReducedRank Detection for Hybrid DirectSequence Time Hopping UWB Systems in Nakagamim Fading Channels.
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ABSTRACT: This paper investigates and compares the performance of hybrid directsequence timehopping (DSTH) ultrawide bandwidth (UWB) systems using fullrank and various reducedrank detections when minimum meansquare error (MMSE) principles are applied, while communicating over Nakagamim fading channels. In addition to the full rank MMSE detection, three classes of reducedrank MMSE techniques are investigated, which are derived based on the principles of principal components (PC), crossspectral metric (CSM) and Taylor polynomial approximation (TPA), respectively. Our study and simulation results show that the reducedrank techniques constitute a family of promising detection techniques for UWB systems, which are capable of achieving similar bit error rate (BER) performance as the fullrank detection, while with a detection complexity that is significantly lower than that of the fullrank detection.Proceedings of the 68th IEEE Vehicular Technology Conference, VTC Fall 2008, 2124 September 2008, Calgary, Alberta, Canada; 01/2008  SourceAvailable from: Jian (Andrew) Zhang
Conference Paper: Role of pulses in ultra wideband systems
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ABSTRACT: UWB pulses are the unique labels of UWB systems. This paper investigates the role of pulse systematically and highlights the central position of the pulse in UWB systems. Four system properties related closely to the pulse are discussed: propagation properties, capacity, interference to existing systems and performance of correlation receivers. The properties of pulses which function directly on every aspect are highlighted. Novel viewpoint is provided for the evaluation of capacity and interference. Suggestions are given on the pulse design, with emphasis on the whole system performance.UltraWideband, 2005. ICU 2005. 2005 IEEE International Conference on; 10/2005 
Conference Paper: Convergence of a decisiondirected adaptive equalizer
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ABSTRACT: An adaptive decision directed equalizer, wherein the estimates of the transmitted data are used for the adaptation of the equalizer parameters, is analyzed. In the paper the stability of the limit equation associated with the stochastic adaptation algorithm is proved. The convergence of the stochastic algorithm then follows by the application of the standard weak convergence theory. The approach of this paper is different from the earlier such analysis in the literature. Thus in the paper we work with the discrete probability distribution of the transmitted symbols, as is the case in practice, rather than assuming a continuous distribution of these for the sake of theoretical convenience.Decision and Control, 1983. The 22nd IEEE Conference on; 01/1984
Page 1
ReducedRank Adaptive Least Bit ErrorRate Detection in
Hybrid DirectSequence TimeHopping Ultrawide Bandwidth
Systems
Qasim Zeeshan Ahmed, LieLiang Yang and Sheng Chen
School of ECS, University of Southampton, SO17 1BJ, UK.
Tel: +44238059 3364, Fax: +44238059 4508
Email: {qza05r,lly,sqc}@ecs.soton.ac.uk; http://wwwmobile.ecs.soton.ac.uk
Abstract—In this paper we consider the lowcomplexity detection in
hybrid directsequence timehopping ultrawide bandwidth (DSTH UWB)
systems. A reducedrank adaptive LBER detector is proposed, which is
operated in the least bit errorrate (LBER) principles within a detection
subspace obtained with the aid of the principal component analysis (PCA)
assisted reducedrank technique. Our reducedrank adaptive LBER detec
tor is free from channel estimation and does not require the knowledge
about the number of resolvable multipaths as well as that about the
multipaths’strength.Inthispaperthebiterrorrate(BER)performanceof
the hybrid DSTH UWB system is investigated, when communicating over
the UWB channels modelled by the SalehValenzuela (SV) channel model.
Our study and simulation results show that this reducedrank adaptive
LBER detector constitutes a feasible detection scheme for deployment in
practical pulsebased UWB systems.
I. INTRODUCTION
Pulsebased UWB communications schemes constitute a range of
promising alternatives that may be deployed for home, personal
area, sensor network, etc. applications, where the communication
devices are required to be lowcomplexity, highreliability and mini
mum power consumption [1]. However, in pulsebased UWB systems
the spreading factor is usually very high. The UWB channels are
usually very sparse [2], resulting in that a huge number of low
power resolvable multipaths need to be processed at the receiver. As
demonstrated in [1,2], in pulsebased UWB communications the huge
number of resolvable multipaths generally consist of a few relatively
strong paths and many other weak paths. Unlike in the conventional
wideband communications where strong paths usually arrive at the
receiver before weak paths, in UWB communications the timeof
arrivals (ToAs) of the strong multipaths are random variables and are
not necessary the multipaths arriving at the receiver at the earliest. Due
to the abovedescribed issues, therefore, in pulsebased UWB systems
it is normally impractical to carry out directly the coherent detection,
which depends on accurate channel estimation demanding extreme
complexity. In fact, it has been recognized that the complexity might
still be extreme, even when the conventional singleuser matched
filter (MF) detector [3] is employed. This is because there are a huge
number of multipath channels need to be estimated and the detection
complexity is at least proportional to the sum of the spreading factor
and the number of resolvable multipaths [4].
In this paper we consider the lowcomplexity detection in hybrid
DSTH UWB systems [5,6], since the hybrid DSTH UWB scheme
is a generalized pulsebased UWB communication scheme, which
includes both the pure DSUWB and the pure THUWB as special
cases [1,5,6]. The detector proposed is an adaptive detector operated
in a reducedrank detection subspace based on the least bit errorrate
(LBER) principles [7,8], which is hence referred to as the reduced
rank adaptive LBER detector. As our forthcoming discourse shown,
the reducedrank adaptive LBER detector does not depend on channel
estimation. It achieves its nearoptimum detection with the aid of
a training sequence at the start of communication and then main
tains its nearoptimum detection based on the decisiondirected (DD)
principles during the communication [9]. The reducedrank adaptive
LBER detector does not require the knowledge about the number
of resolvable multipaths as well as that about the locations of the
strong resolvable multipaths; It only requires the knowledge (which
is still not necessary accurate) about the maximum delayspread of
the UWB channels. Furthermore, the reducedrank adaptive LBER
detector is operated in a reducedrank detection subspace obtained
based on the principal component analysis (PCA) [10]. The detection
subspace usually has a rank that is significantly lower than that of the
original observation space. Owing to the abovementioned properties
of the reducedrank adaptive LBER detector, we can argue that it is
a lowcomplexity detection scheme, which is feasible for practical
implementation.
Note that, in this contribution the LBER algorithm is preferred
instead of the conventional least meansquare (LMS) algorithm [11],
since, first, the LBER algorithm works under the minimum BER
(MBER) principles, which may outperform the LMS algorithm that is
operated in minimum meansquare error (MMSE) sense [8]. Second,
the LBER algorithm has similar complexity as the LMS algorithm [8].
Furthermore, it has been observed [8] that the LBER algorithm may
provide a higher flexibility for system design in comparison with the
LMS algorithm.
II. DESCRIPTION OF THE HYBRID DSTH UWB SYSTEM
The hybrid DSTH UWB scheme considered in this contribution is
the same as that considered in [12], where nonadaptive reducedrank
detection has been investigated.
A. Transmitted Signal
DS
TH
Pulse
Generator
Spreading
TH Pattern
0,··· ,c(k)
b(k)
i
{d(k)
0,··· ,d(k)
Nc−1}
ψ(t − jTc− c(k)
j
Tψ)
{c(k)
Nψ−1}
ψ(t − jTc)
s(k)(t)
Fig. 1. Transmitter schematic block diagram of hybrid DSTH UWB system.
The transmitter schematic block diagram for the considered hybrid
DSTH UWB system is shown in Fig. 1. We assume for simplicity that
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings
9781424434350/09/$25.00 ©2009 IEEE
Page 2
the hybrid DSTH UWB system employs the binary phaseshift keying
(BPSK) baseband modulation. As shown in Fig. 1, a data bit of the kth
user is first modulated by a Nclength DS spreading sequence, which
generates Nc chips. The Nc chips are then transmitted by Nc time
domain pulses within one symbolduration, where the positions of the
Nc timedomain pulses are determined by the TH pattern assigned
to the kth user. Finally, as shown in Fig. 1, the hybrid DSTH UWB
baseband signal transmitted by the kth user can be written as [5]
?
NcTψ
j=0
s(k)(t) =
Eb
∞
?
b(k)
?
j
Nc
?d(k)
j ψ
?
t − jTc− c(k)
j Tψ
?
(1)
where ?x? represents the largest integer less than or equal to x,
ψ(t) is the basic timedomain pulse of width Tψ, which satisfies
?Tψ
basic timedomain pulse’s width. The other parameters in (1) as well
as the other parameters used in this contribution are listed as follows:
• Eb: Energy per bit;
• Nc: Number of chips per bit and DS spreading factor;
• Nψ: Number of timeslots in a chip and TH spreading factor;
• Tband Tc: Bitduration and chipduration, which satisfies Tb =
NcTc;
• Tψ: Timedomain pulse width or width of a timeslot, which
satisfies Tc = NψTψ;
• b(k)
i
• {d(k)
kth user;
• {c(k)
the kth user;
• NcNψ: Total spreading factor of hybrid DSTH UWB system.
Note that, both the pure DSUWB and pure THUWB schemes con
stitute special cases of the hybrid DSTH UWB scheme. Specifically,
if Nc > 1 and Nψ = 1, Tψand Tcare then equal and in this case the
hybrid DSTH UWB system is reduced to the pure DSUWB system.
By contrast, when Nc = 1 and Nψ > 1, the hybrid DSTH UWB
scheme is then reduced to the pure THUWB scheme.
0
ψ2(t)dt = Tψ. Note that, the bandwidth of the hybrid DSTH
UWB system is approximately equal to the reciprocal of Tψ of the
∈ {+1,−1}: The ith data bit transmitted by user k;
j }: Random binary DS spreading sequence assigned to the
j
∈ {0,1,··· ,Nψ−1}}: Random TH sequence assigned to
B. Channel Model
In this contribution the SalehValenzuela (SV) channel model is
considered, which has the channel impulse response (CIR) [13]
h(t) =
V −1
?
v=0
U−1
?
u=0
hu,vδ(t − Tv− Tu,v)
(2)
where V represents the number of clusters and U denotes the number
of resolvable multipaths in a cluster. Hence, the total number of
resolvable multipath components can be as high as L = UV . In (2)
hu,v = hu,vejθu,vrepresents the fading gain of the uth multipath in
thevthcluster,wherehu,vandθu,vareassumedtoobeytheRayleigh
distribution [13] and uniform distribution in [0,2π), respectively. In
(2) Tv denotes the arrival time of the vth cluster and Tu,v the arrival
time of the uth multipath in the vth cluster. In the considered UWB
channel, the average power of a multipath component at a given delay,
say at Tv+Tu,v, is related to the power of the first resolvable multipath
of the first cluster through the relation of [13]
?
where Ωu,v = E?hu,v2?represents the power of the u resolvable
power decay constants.
Ωu,v = Ω0,0exp
−Tv
Γ
?
exp
?
−Tu,v
γ
?
(3)
multipath of the vth cluster, Γ and γ are the respective cluster and ray
According to (2), we can know that the maximum delayspread of
the UWB channels considered is (TV +TU,V) and the total number of
resolvable multipaths is L = ?(TV+TU,V)/Tψ?+1. In order to make
the channel model sufficiently general, in this contribution we assume
that the maximum delay spread (TV + TU,V) spans g ≥ 1 data bits,
implying that (g − 1)NcNψ ≤ (L − 1) < gNcNψ.
C. Receiver Structure
Let us assume that the hybrid DSTH UWB system supports K
uplink users. When the K number of DSTH UWB signals in the form
of (1) are transmitted over UWB channels having the CIR as shown in
(2), the received signal at the basestation (BS) can be expressed as
r(t) =
?
?
Eb
NcTψ
K
?
k=1
V −1
?
j Tψ− T(k)
v=0
U−1
?
u=0
MNc
?
j=0
h(k)
u,vb(k)
?
j
Nc
?d(k)
j
× ψrec
t − jTc− c(k)
v
− T(k)
u,v− τk
?
+ n(t)
(4)
where n(t) represents an additive white Gaussian noise (AWGN) pro
cess, which has zeromean and a singlesided power spectral density
of N0per dimension, τktakes into account the lack of synchronisation
among the user signals as well as the transmission delay, while
ψrec(t) is the received timedomain pulse, which is usually the second
derivative of the transmitted pulse ψ(t) [14].
The receiver schematic block diagram for the hybrid DSTH UWB
using the considered reducedrank adaptive LBER detection is shown
in Fig. 2. At the receiver, the received signal is first filtered by a MF
having an impulse response of ψ∗
sampled at a rate of 1/Tψ. Then, the observation samples are stored
in a buffer, which are projected to a reducedrank detection subspace,
once a reducedrank detection subspace S S SU is obtained. Finally, the
observations in the detection subspace are input to a traversal filter,
which is controlled by the LBER algorithm, in order to generate
estimates to the transmitted data bits.
Let us assume that a block of M data bits per user is transmit
ted. Then, according to Fig. 2, the detector can collect a total of
(MNcNψ + L − 1) number of samples, where (L − 1) is due to
the L number of resolvable multipaths. In more details, the λth sample
can be obtained by sampling the MF’s output at the time instant of
t = T0+ (λ + 1)Tψ, which can be expressed as
rec(−t). The output of the MF is then
yλ=
??EbTψ
Nc
?−1?T0+(λ+1)Tψ
T0+λTψ
r(t)ψ∗
rec(t)dt
(5)
where T0denotes the ToA of the first multipath in the first cluster.
In order to reduce the detection complexity of the hybrid DSTH
UWBsystem,inthiscontributionweconsideronlythebitbybitbased
detection. Let the observation vectory y yiand the noise vectorn n nirelated
to the ith data bit of the first user (reference user) be represented by
y y yi = [yiNcNψ,yiNcNψ+1,··· ,y(i+1)NcNψ+L−2]T
n n ni = [niNcNψ,niNcNψ+1,··· ,n(i+1)NcNψ+L−2]T
(6)
(7)
where the elements of n n ni are Gaussian random variables distributed
with zeromean and a variance of σ2= N0/2Ebper dimension. Then,
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings
Page 3
Training
Sequences
Algorithm
Decision
Directed
Traversal filter
¯ w w wH
1
Buffer
LBER
Matched−filterSampling
ψ∗
rec(−t)
Re(z(1)
i)
nTψ
ˆb(1)
i
r(t)
yλ
y y yi
¯ y y yi
z(1)
i
S S SH
U
Fig. 2. Receiver schematic block diagram for the hybrid DSTH UWB systems using reducedrank adaptive LBER detection.
as shown in [5,12], y y yican be expressed as
y y yi =
K
?
?
?
?
k=1
i−1
?
i?=0
j=max(0,i−g)
C C C(k)
jh h hkb b b(k)
j
??
i
?
ISI from the previous bits of K users
+C C C(1)
?
?
ih h h1b(1)
??
i
?
Desired signal
+n n ni
+
K
k=2
C C C(k)
i h h hkb(k)
???
Multiuser interference
+
K
?
?
k=1
min(M−1,i+g)
j=i+1
i?=M−1
¯C C C(k)
j h h hkb b b(k)
j
???
ISI from the latter bits of K users
(8)
where the matrices and vectors have been defined in detail in [5,
12]. From (8), we observe that the ith data bit conflicts both severe
intersymbol interference (ISI) and multiuser interference (MUI), in
addition to the Gaussian background noise.
When the conventional linear detectors without invoking reduced
rank techniques are considered, the decision variable for b(1)
reference user can be expressed as
i
of the
z(1)
i
= w w wH
1y y yi, i = 0,1,...,M − 1
(9)
where w w w1 is a (NcNψ + L − 1)length weight vector. Since in
UWB communications the spreading factor NcNψ might be very
high and since the number of resolvable multipath L is usually huge
in UWB channels, the vector w w w1, i.e., the filter length might be
very large. Therefore, the complexity of the corresponding detectors
might be extreme, even when lowcomplexity linear detection schemes
are considered. Furthermore, using very long filter for detection in
UWB systems may significantly degrade the performance of the
UWB systems. For example, using a longer traversal filter results in
lower convergence speed and, hence, a longer sequence is required
for training the filter [11]. Consequently, the datarate and spectral
efficiency of the corresponding communications system decreases.
The robustness of an adaptive filter degrades as the filter length
increases, since more channeldependent variables are required to be
estimated[15].Furthermore,whenalongeradaptivefilterisemployed,
the computational complexity is also higher, since more operations are
required for the corresponding detection and estimation. Therefore,
in this paper the reducedrank adaptive LBER detector is proposed,
in order to achieve lowcomplexity detection in hybrid DSTH UWB
systems.
III. REDUCEDRANK ADAPTIVE LBER DETECTION
In reducedrank detection the number of coefficients to be de
termined is reduced through projecting the received signals to a
lower dimensional detection subspace [10]. Specifically, let P P PU be an
((NcNψ+L−1)×U) processing matrix with its U columns forming
a Udimensional subspace, where U < (NcNψ+ L − 1). Then, for a
given received vectory y yi, the Ulength vector in the detection subspace
can be expressed as
¯ y ¯ y ¯ yi = (P P PH
UP P PU)−1P P PH
??
U
??
S S SH
U
y y yi
(10)
where an overbar is used to indicate that the argument is in the
reducedrank detection subspace.
In this contribution, the PCAassisted reducedrank technique [10,
16] is employed for obtaining the processing matrix: Given the rank U
ofthedetectionsubspace,theU numberofeigenvectorscorresponding
to the U largest eigenvalues of the autocorrelation matrix of y y yi are
utilized to form the processing matrix P P PU [16]. In more detail, the
autocorrelation matrix of y y yi can be represented using eigenanalysis
as
R R Ryi= E[y y yiy y yH
i] = Φ Φ ΦΛ Λ ΛΦ Φ ΦH
(11)
where Λ Λ Λ is a diagonal matrix given by
Λ Λ Λ = diag{λ1,λ2,··· ,λNcNψ+L−1}
which contains the eigenvalues of R R Ryi, while Φ Φ Φ is an unitary matrix
consisting of the eigenvectors of R R Ryi, which can be written as
(12)
Φ Φ Φ = [φ φ φ1,φ φ φ2,··· ,φ φ φNcNψ+L−1]
(13)
where φ φ φiis the eigenvector corresponding to the eigenvalue λi.
Let assume that the eigenvalues are arranged in descent order obey
ing λ1 ≥ λ2 ≥ ··· ≥ λNcNψ+L−1. Then, the processing matrix P P PU
in the context of PCAassisted reducedrank technique is constructed
by the first U columns of Φ Φ Φ, ie., we have P P PU = [φ φ φ1,φ φ φ2,··· ,φ φ φU].
Given the observations in the detection subspace as shown in (10),
the linear detection of b(1)
i
can be carried out by forming the decision
variable
z(1)
i
= ¯ w ¯ w ¯ wH
1¯ y ¯ y ¯ yi
(14)
where ¯ w ¯ w ¯ w1 is now an Ulength weight vector. According to the theory
of the PCAbased reducedrank detection [10], the fullrank BER
performance can be achieved, provided that the rank U of the detection
subspace is not lower than the rank of the signal subspace, which
for our hybrid DSTH UWB system is K(g + 1). However, if the
rank of the detection subspace is lower than the signal subspace’s
rank,thereducedrank detection then conflictsMUI.Consequently, the
BER performance of the hybrid DSTH UWB system using the PCA
based reducedrank detection deteriorate, in comparison with the full
rank BER performance. Therefore, in the PCAbased reducedrank
detection it is important to have the knowledge about the signal sub
space’s rank. Note that, in our simulations considered in Section IV,
the signal subspace’s rank was estimated through eigenanalysis of
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings
Page 4
the autocorrelation matrix R R Ryi, which was estimated with the aid of
a block of data bits.
In (14) the weight vector ¯ w ¯ w ¯ w1 can be obtained with the aid of the
samplebysample adaptive LBER algorithm proposed in [7]. In our
reducedrank adaptive LBER detector for the hybrid DSTH UWB
systems, the reducedrank adaptive LBER is operated in two modes,
namely, the training mode and the decisiondirected (DD) mode,
respectively.Whenoperatedinthetrainingmode,theweightvector ¯ w ¯ w ¯ w1
is adjusted with the aid of a training sequence, which is known to the
receiver. Correspondingly, the update equation in the LBER principle
can be expressed as [8]
¯ w ¯ w ¯ w1(n + 1) = ¯ w ¯ w ¯ w1(n) + μsgn(b(1)
?
i(n))
2√2πρn
?
× exp
−?(z(1)
i (n))2
2ρ2
n
¯ y ¯ y ¯ yi(n), n = 1,2,...
(15)
where sgn(x) is a signfunction, μ is the stepsize and ρn is the so
called kernel width [8]. In the adaptive LBER algorithm, the step
size μ and the kernel width ρn are required to be set appropriately,
in order to obtain a high convergence rate as well as a small and steady
BER misadjustment. Furthermore, it has been observed [8] that the
abovementioned two parameters can provide a higher flexibility for
system design in comparison with the adaptive LMS algorithm, which
employs only single adjustable parameter of the stepsize [11].
When the training stage is completed and the normal data trans
mission is started, the reducedrank adaptive LBER detector is then
switched to the DD mode. Under the DD mode, the estimated data bits
by the receiver are fed back to the adaptive LBER filter, which is then
updated in the LBER principle. Specifically, during the DD mode the
update equation can be expressed as
¯ w ¯ w ¯ w1(n + 1) = ¯ w ¯ w ¯ w1(n) + μsgn(ˆb(1)
?
i(n))
2√2πρn
?
× exp
−?(z(1)
i (n))2
2ρ2
n
¯ y ¯ y ¯ yi(n), n = 1,2,...
(16)
where the estimateˆb(1)
i
is given by
ˆb(1)
i
= sgn(?{z(1)
i }), i = 0,1,...,M − 1
(17)
Let us now provide our simulation results in the next section.
IV. SIMULATION RESULTS AND DISCUSSION
In this section the learning and BER performance of the reduced
rank adaptive LBER detector is investigated by simulations. In our
simulations the total spreading factor was assumed to be a constant of
NcNψ = 64, where the DSspreading factor was set to Nc = 16 and
the THspreading factor was hence Nψ = 4. The normalised Doppler
frequencyshift of the UWB channels was fixed to fdTb = 0.0001. In
our simulations the SV channel model used in [13] was considered
and the channel gains were assumed to obey the Rayleigh distribution.
In more detail, the parameters of the SV channel model used in our
simulations are summarized in the following Table.
1/Λ
14.11 ns
Γγ
2.63 ns4.58 ns
TABLE I
PARAMETERS FOR THE SV CHANNEL MODEL USED IN SIMULATIONS.
Fig. 3 shows the ensembleaverage squared errorrate (SER) learn
ing curve of the reducedrank adaptive LBER detector for the hybrid
DSTH UWB system supporting K = 5 users, when different step
size values are considered. Note that, the SER drawn in Fig. 3 is
defined as
?????
tive LBER detector. In our simulations the signaltonoise ratio (SNR)
per bit was set to Eb/N0 = 10dB, the ensembleaverage SER was
obtained from the average over 2000 independent realizations, the
weight vector was initialized to ¯ w w w(0) = 1 1 1 of an allone vector, and
the rank of the detection subspace was chosen as U = 20. It can be
observed from Fig. 3 that the convergence speed of the reducedrank
adaptive LBER detector is depended on the stepsize μ. Explicitly,
there exists an optimum stepsize value, which results in that the
reducedrank adaptive LBER detector converges to the lowest BER.
As shown in Fig. 3, when an inappropriate stepsize is used, the
convergence speed may become lower and the reducedrank adaptive
LBER detector may converge to a relatively higher SER.
SER =
sgn(b(1)
2√2πρn
i(n))
exp
?
−?(z(1)
i (n))2
2ρ2
n
??????
2
(18)
which is proportional to the BER achieved by the reducedrank adap
050100150
Number of training bits
200250300350400 450500
104
2
5
103
2
5
102
2
5
101
Ensembleaverage SER
= 0.5
= 0.125= 1.0
Fig. 3.
hybrid DSTH UWB system supporting K = 5 users, when the detection
subspace has a rank of U = 20. The parameters used in the simulations were
Eb/N0= 10dB, Doppler frequencyshift of fdTb= 0.0001, ρn =√10σn,
g = 1, Nc= 16, Nψ= 4 and L = 15.
Learning curves of the reducedrank adaptive LBER detector for the
Fig. 4 shows the BER versus SNR per bit performance of the hybrid
DSTH UWB system using reducedrank adaptive LBER detection,
when communicating over the UWB channels experiencing correlated
Rayleigh fading. The hybrid DSTH UWB system considered sup
ported K = 5 users and the normalised Dopper frequencyshift was
assumed to be fdTb = 0.0001. Furthermore, we assumed that g = 1,
implying that the desired bit conflicts ISI from one bit transmitted
before the desired bit and also from one bit transmitted after the
desired bit. Note that, given the parameters as shown in the caption
of the figure, it can be shown that the rank of the signal subspace is
K(g + 1) = 10. From the results of Fig. 4, we observe that, when the
rank of the detection subspace is lower than that of the signal subspace,
i.e., when U ≤ 10, the BER performance of the hybrid DSTH UWB
system improves, as the rank of the detection subspace increases. The
best BER performance is attained, when the rank of the detection
subspace reaches the rank of the signal subspace. When the rank of
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings
Page 5
the detection subspace is higher than that of the signal subspace, no
further SNR gain is achievable. Furthermore, when the rank of the
detection subspace is lower than that of the signal subspace, errorfloor
is observed, explaining that the MUI cannot be fully suppressed by the
reducedrank adaptive LBER detector.
036912 1518
Eb/N0(dB)
105
104
103
102
101
1
Bit Error Rate
U = 1
U = 5
U = 7
U = 10
U = 20
Fig. 4. BER performance of the hybrid DSTH UWB systems using reduced
rank adaptive LBER detection, when communicating over the UWB channels
modelled by the SV channel model associated with correlated Rayleigh fading.
The parameters used in the simulations were K = 5, fdTb= 0.0001, μ =
0.5, ρn=√10σn, g = 1, Nc= 16, Nψ= 4 and L = 15. The frame length
was fixed to 1000 bits, where the first 160 bits were used for training.
036
Eb/N0(dB)
9 1215
105
104
103
102
101
1
Bit Error Rate
U = 1
U = 5
U = 10
U = 15
U = 20
Fig. 5. BER performance of the hybrid DSTH UWB systems using reduced
rank adaptive LBER detection, when communicating over the UWB channels
modelled by the SV channel model associated with correlated Rayleigh fading.
The parameters used in the simulations were K = 5, fdTb= 0.0001, μ =
0.5, ρn =√10σn, g = 3, Nc = 16, Nψ = 4 and L = 150. The frame
length was fixed to 1000 bits, where the first 160 bits were used for training.
Fig. 5 shows the BER versus SNR per bit performance of the hybrid
DSTH UWB system using reducedrank adaptive LBER detection,
when communicating over the UWB channels experiencing correlated
Rayleigh fading, which results in severe ISI. In contrast to Fig. 4,
where we assumed that g = 1 and the number of resolvable multipaths
was L = 15, in the context of Fig. 5 we assumed that g = 3 and
L = 150. The other parameters used for Fig. 5 were the same as those
used for Fig. 4. Note that, for the parameters considered in Fig. 5,
the rank of the signal subspace is K(g + 1) = 20. Again, as the
results of Fig. 5 shown, the BER performance improves as the rank
of the detection subspace increases, until it reaches the rank of the
signal subspace. In comparison with Fig. 4, we can see that, for a
given Eb/N0 value, the fullrank BER shown in Fig. 5 is lower than
the corresponding fullrank BER shown in Fig. 4. This is because the
UWB channel considered associated with Fig. 5 has L = 150 number
of resolvable multipaths, which results in a higher diversity gain than
theUWBchannelconsideredassociatedwithFig.4,whichhasL = 15
number of resolvable multipaths.
V. CONCLUSIONS
In conclusions, our study and simulation results show that the
reducedrank adaptive LBER detector constitutes one of the efficient
detectors for the hybrid DSTH UWB systems. The reducedrank
technique can be employed for achieving lowcomplexity detection
in the DSTH UWB systems and for improving their efficiency. The
reducedrank adaptive LBER detector is capable of achieving the full
rank BER performance with the detection subspace having a rank that
is significantly lower than (NcNψ+L−1) of the original observation
space.
REFERENCES
[1] J. H. Reed, An Introduction to Ultra Wideband Communication Systems.
Prentice Hall, 2005.
[2] A. F. Molisch, J. R. Foerster, and M. Pendergrass, “Channel models for
ultrawideband personal area networks,” IEEE Wireless Communications,
vol. 10, pp. 14–21, Dec. 2003.
[3] S. Verdu, Multiuser Detection. Cambridge University Press, 1998.
[4] Q. Li and L. A. Rusch, “Multiuser detection for DSCDMA UWB in the
home environment,” IEEE Journal on Selected Areas in Communications,
vol. 20, pp. 1701–1711, Dec. 2002.
[5] Q. Z. Ahmed and L.L. Yang, “Performance of hybrid directsequence
timehopping ultrawide bandwidth systems in Nakagamim fading chan
nels,” in IEEE 18th International Symposium on Personal, Indoor and
Mobile Radio Communications, 2007. PIMRC 2007., (Athens, Greece),
pp. 1–5, Sept. 2007.
[6] Q. Z. Ahmed and L.L. Yang, “Normalised least meansquare aided
decisiondirected adaptive detection in hybrid directsequence time
hopping UWB systems,” in to appear in IEEE VTCFall, 2008.
[7] S. Chen, A. K. Samingan, B. Mulgrew, and L. Hanzo, “Adaptive
minimumBER linear multiuser detection for DSCDMA signals in mul
tipath channels,” Signal Processing, IEEE Transactions on [see also
Acoustics,Speech,andSignalProcessing,IEEETransactionson],vol.49,
pp. 1240–1247, June 2001.
[8] S. Chen, S. Tan, L. Xu, and L. Hanzo, “Adaptive minimum errorrate
filtering design: A Review,” IEEE Transactions on Signal Processing,
vol. 88, no. 7, pp. 1671–1679, 2008.
[9] R. Kumar, “Convergence of a decisiondirected adaptive equalizer,” in
22nd IEEE Conference on Decision and Control, vol. 22, pp. 1319–1324,
Dec. 1983.
[10] H. L. V. Trees, Optimum Array Processing. Wiley Interscience, 2002.
[11] S. Haykin, Adaptive Filter Theory. Prentice Hall, 4 ed., 2002.
[12] Q. Z. Ahmed and L.L. Yang, “Reducedrank detection for hybrid direct
sequence timehopping UWB systems in Nakagamim fading channels,”
in to appear in IEEE VTCFall, 2008.
[13] J. Karedal, S. Wyne, P. Almers, F. Tufvesson, and A. F. Molisch, “Statis
tical analysis of the UWB channel in an industrial environment,” in IEEE
60th Vehicular Technology Conference, vol. 1, pp. 81–85, Sept. 2004.
[14] J. Zhang, T. Abhayapala, and R. Kennedy, “Role of pulses in ultra wide
band systems,” in IEEE International Conference on UltraWideband,
pp. 565–570, 2005.
[15] M. Honig and M. K. Tsatsanis, “Adaptive techniques for multiuser
CDMA receivers,” IEEE Signal Processing Magazine, vol. 17, pp. 49–
61, May 2000.
[16] G. H. Dunteman, Principal components analysis. Newbury Park, 1989.
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings