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Reduced-Rank Adaptive Least Bit Error-Rate Detection in

Hybrid Direct-Sequence Time-Hopping Ultrawide Bandwidth

Systems

Qasim Zeeshan Ahmed, Lie-Liang Yang and Sheng Chen

School of ECS, University of Southampton, SO17 1BJ, UK.

Tel: +44-23-8059 3364, Fax: +44-23-8059 4508

Email: {qza05r,lly,sqc}@ecs.soton.ac.uk; http://www-mobile.ecs.soton.ac.uk

Abstract—In this paper we consider the low-complexity detection in

hybrid direct-sequence time-hopping ultrawide bandwidth (DS-TH UWB)

systems. A reduced-rank adaptive LBER detector is proposed, which is

operated in the least bit error-rate (LBER) principles within a detection

subspace obtained with the aid of the principal component analysis (PCA)-

assisted reduced-rank technique. Our reduced-rank 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.Inthispaperthebiterror-rate(BER)performanceof

the hybrid DS-TH UWB system is investigated, when communicating over

the UWB channels modelled by the Saleh-Valenzuela (S-V) channel model.

Our study and simulation results show that this reduced-rank adaptive

LBER detector constitutes a feasible detection scheme for deployment in

practical pulse-based UWB systems.

I. INTRODUCTION

Pulse-based 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 low-complexity, high-reliability and mini-

mum power consumption [1]. However, in pulse-based 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 pulse-based 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 time-of-

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 above-described issues, therefore, in pulse-based 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 single-user 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 low-complexity detection in hybrid

DS-TH UWB systems [5,6], since the hybrid DS-TH UWB scheme

is a generalized pulse-based UWB communication scheme, which

includes both the pure DS-UWB and the pure TH-UWB as special

cases [1,5,6]. The detector proposed is an adaptive detector operated

in a reduced-rank detection subspace based on the least bit error-rate

(LBER) principles [7,8], which is hence referred to as the reduced-

rank adaptive LBER detector. As our forthcoming discourse shown,

the reduced-rank adaptive LBER detector does not depend on channel

estimation. It achieves its near-optimum detection with the aid of

a training sequence at the start of communication and then main-

tains its near-optimum detection based on the decision-directed (DD)

principles during the communication [9]. The reduced-rank 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 delay-spread of

the UWB channels. Furthermore, the reduced-rank adaptive LBER

detector is operated in a reduced-rank 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 above-mentioned properties

of the reduced-rank adaptive LBER detector, we can argue that it is

a low-complexity detection scheme, which is feasible for practical

implementation.

Note that, in this contribution the LBER algorithm is preferred

instead of the conventional least mean-square (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 mean-square 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 DS-TH UWB SYSTEM

The hybrid DS-TH UWB scheme considered in this contribution is

the same as that considered in [12], where non-adaptive reduced-rank

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 DS-TH UWB system.

The transmitter schematic block diagram for the considered hybrid

DS-TH 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

978-1-4244-3435-0/09/$25.00 ©2009 IEEE

Page 2

the hybrid DS-TH UWB system employs the binary phase-shift keying

(BPSK) baseband modulation. As shown in Fig. 1, a data bit of the kth

user is first modulated by a Nc-length DS spreading sequence, which

generates Nc chips. The Nc chips are then transmitted by Nc time-

domain pulses within one symbol-duration, where the positions of the

Nc time-domain pulses are determined by the TH pattern assigned

to the kth user. Finally, as shown in Fig. 1, the hybrid DS-TH 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 time-domain pulse of width Tψ, which satisfies

?Tψ

basic time-domain 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 time-slots in a chip and TH spreading factor;

• Tband Tc: Bit-duration and chip-duration, which satisfies Tb =

NcTc;

• Tψ: Time-domain pulse width or width of a time-slot, which

satisfies Tc = NψTψ;

• b(k)

i

• {d(k)

kth user;

• {c(k)

the kth user;

• NcNψ: Total spreading factor of hybrid DS-TH UWB system.

Note that, both the pure DS-UWB and pure TH-UWB schemes con-

stitute special cases of the hybrid DS-TH UWB scheme. Specifically,

if Nc > 1 and Nψ = 1, Tψand Tcare then equal and in this case the

hybrid DS-TH UWB system is reduced to the pure DS-UWB system.

By contrast, when Nc = 1 and Nψ > 1, the hybrid DS-TH UWB

scheme is then reduced to the pure TH-UWB scheme.

0

ψ2(t)dt = Tψ. Note that, the bandwidth of the hybrid DS-TH

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 Saleh-Valenzuela (S-V) 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,v|ejθu,vrepresents the fading gain of the uth multipath in

thevthcluster,where|hu,v|andθu,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,v|2?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 delay-spread 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 DS-TH UWB system supports K

uplink users. When the K number of DS-TH UWB signals in the form

of (1) are transmitted over UWB channels having the CIR as shown in

(2), the received signal at the base-station (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 zero-mean and a single-sided 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 time-domain pulse, which is usually the second

derivative of the transmitted pulse ψ(t) [14].

The receiver schematic block diagram for the hybrid DS-TH UWB

using the considered reduced-rank 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 reduced-rank detection subspace,

once a reduced-rank 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 DS-TH

UWBsystem,inthiscontributionweconsideronlythebit-by-bitbased

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 zero-mean and a variance of σ2= N0/2Ebper dimension. Then,

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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 DS-TH UWB systems using reduced-rank 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

inter-symbol 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 low-complexity 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 data-rate and spectral

efficiency of the corresponding communications system decreases.

The robustness of an adaptive filter degrades as the filter length

increases, since more channel-dependent 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 reduced-rank adaptive LBER detector is proposed,

in order to achieve low-complexity detection in hybrid DS-TH UWB

systems.

III. REDUCED-RANK ADAPTIVE LBER DETECTION

In reduced-rank 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 U-dimensional subspace, where U < (NcNψ+ L − 1). Then, for a

given received vectory y yi, the U-length 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 over-bar is used to indicate that the argument is in the

reduced-rank detection subspace.

In this contribution, the PCA-assisted reduced-rank 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

auto-correlation matrix of y y yi can be represented using eigen-analysis

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 PCA-assisted reduced-rank 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 U-length weight vector. According to the theory

of the PCA-based reduced-rank detection [10], the full-rank 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 DS-TH UWB system is K(g + 1). However, if the

rank of the detection subspace is lower than the signal subspace’s

rank,thereduced-rank detection then conflictsMUI.Consequently, the

BER performance of the hybrid DS-TH UWB system using the PCA-

based reduced-rank detection deteriorate, in comparison with the full-

rank BER performance. Therefore, in the PCA-based reduced-rank

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 eigen-analysis of

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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

sample-by-sample adaptive LBER algorithm proposed in [7]. In our

reduced-rank adaptive LBER detector for the hybrid DS-TH UWB

systems, the reduced-rank adaptive LBER is operated in two modes,

namely, the training mode and the decision-directed (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 sign-function, μ is the step-size 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

above-mentioned 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 step-size [11].

When the training stage is completed and the normal data trans-

mission is started, the reduced-rank 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 DS-spreading factor was set to Nc = 16 and

the TH-spreading factor was hence Nψ = 4. The normalised Doppler

frequency-shift of the UWB channels was fixed to fdTb = 0.0001. In

our simulations the S-V 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 S-V 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 S-V CHANNEL MODEL USED IN SIMULATIONS.

Fig. 3 shows the ensemble-average squared error-rate (SER) learn-

ing curve of the reduced-rank adaptive LBER detector for the hybrid

DS-TH 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 signal-to-noise ratio (SNR)

per bit was set to Eb/N0 = 10dB, the ensemble-average 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 all-one 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 reduced-rank

adaptive LBER detector is depended on the step-size μ. Explicitly,

there exists an optimum step-size value, which results in that the

reduced-rank adaptive LBER detector converges to the lowest BER.

As shown in Fig. 3, when an inappropriate step-size is used, the

convergence speed may become lower and the reduced-rank 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 reduced-rank adap-

050100150

Number of training bits

200250300350400 450500

10-4

2

5

10-3

2

5

10-2

2

5

10-1

Ensemble-average SER

= 0.5

= 0.125= 1.0

Fig. 3.

hybrid DS-TH 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 frequency-shift of fdTb= 0.0001, ρn =√10σn,

g = 1, Nc= 16, Nψ= 4 and L = 15.

Learning curves of the reduced-rank adaptive LBER detector for the

Fig. 4 shows the BER versus SNR per bit performance of the hybrid

DS-TH UWB system using reduced-rank adaptive LBER detection,

when communicating over the UWB channels experiencing correlated

Rayleigh fading. The hybrid DS-TH UWB system considered sup-

ported K = 5 users and the normalised Dopper frequency-shift 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 DS-TH 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, error-floor

is observed, explaining that the MUI cannot be fully suppressed by the

reduced-rank adaptive LBER detector.

036912 1518

Eb/N0(dB)

10-5

10-4

10-3

10-2

10-1

1

Bit Error Rate

U = 1

U = 5

U = 7

U = 10

U = 20

Fig. 4. BER performance of the hybrid DS-TH UWB systems using reduced-

rank adaptive LBER detection, when communicating over the UWB channels

modelled by the S-V 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

10-5

10-4

10-3

10-2

10-1

1

Bit Error Rate

U = 1

U = 5

U = 10

U = 15

U = 20

Fig. 5. BER performance of the hybrid DS-TH UWB systems using reduced-

rank adaptive LBER detection, when communicating over the UWB channels

modelled by the S-V 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

DS-TH UWB system using reduced-rank 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 full-rank BER shown in Fig. 5 is lower than

the corresponding full-rank 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

reduced-rank adaptive LBER detector constitutes one of the efficient

detectors for the hybrid DS-TH UWB systems. The reduced-rank

technique can be employed for achieving low-complexity detection

in the DS-TH UWB systems and for improving their efficiency. The

reduced-rank 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.

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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