Adaptive Rake Receiver Joined with Chip Equalization for DS-CDMA UWB Systems over ISI Channels

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Procedia

Engineering

www.elsevier.com/locate/procedia

2012 International Workshop on Information and Electronics Engineering (IWIEE)

Adaptive Rake Receiver Joined with Chip Equalization for

DS-CDMA UWB Systems over ISI Channels

Feng Wang

*

Jiangsu Technology and Engineering Center of Meteorological Sensor Network, Nanjing University of Information Science & Technology, Nanjing, 210044, China

Abstract

Since there is much larger channel delay spread, there is serious inter-symbol interference (ISI) when ultra-wideband (UWB) wireless communication systems work at high data speed. The serious ISI affects the performance of UWB systems seriously. In this paper, a scheme to suppress ISI is developed for direct sequence spread-code division multiple access (DS-CDMA) UWB systems with a high data speed and an adaptive joint chip equalization Rake (AJCE-Rake) receiver is proposed. The proposed AJCE-Rake receiver spreads the number of traditional Rake receiver taps to collect multi-path component and equalize the inter-chip interference simultaneously. Then the soft output of AJCE-Rake receiver is despreaded with the user's spreading code. Finally, the decision is made to recover the transmitted symbol. The simulation results verify that ISI is suppressed effectively and the system performance is improved evidently.

Keywords: UWB; ISI; Rake receiver; MMSE; Chip equalization; 1. Introduction

Ultra-wideband (UWB) signals indoor propagation process is characterized by dense multipath propagation. Therefore, the UWB system has a strong anti-multipath fading capability due to use Rake receiver to collect multi-path energy to achieve multipath diversity. Therefore, Rake receiver is very important for UWB system performance. In the absence of inter-symbol interference (ISI), maximum

*

* Corresponding author.

E-mail address: [email protected]

Open access under CC BY-NC-ND license.

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ratio combining (MRC) Rake receiver can get the best performance. However, indoor channel measurement data show that UWB channel delay spread is very great. When transmission data speed is high, there will be serious inter-symbol interference (ISI). Then MRC-Rake receiver performance will be seriously degraded by ISI. So an important research area of UWB Rake receiver is to suppress ISI. Since the decision results of the Rake receiver has been affected by ISI, the equalizer can be utilized to equalize the ISI after the Rake. Ref. [1]-[6] studied performance of the decision feedback equalization Rake (DFE-Rake) receiver. However, this Rake receiver with DFE requires that bit error rate (BER) of Rake receiver must be below a certain value in order to ensure that the equalizer has a good effect. If ISI is very serious, BER of the decision results of the Rake receiver is very high. Then the DFE after the Rake receiver hasn’t good effect of equalizing ISI. When there is the absence of ISI, MRC-Rake receiver can achieve maximizing signal power. When the data rate is relatively high, the received signal contains ISI and the MRC Rake receiver to maximize the signal power can not effectively suppress the ISI [7].

In other words, when there is ISI, the weight coefficients decided according the estimated channel information and the MRC criterion isn’t the best. Thus based on minimum mean-square error (MMSE) criterion Ref. [8]-[10] propose MMSE-Rake receiver, which determines the Rake receiver weight coefficients based on MMSE criterion to improve the performance of the receiver. Since there is serious ISI for high-rate DS-UWB communication systems, there must exist serious inter-chip interference (ICI). The paper studies equalizing ISI and combining multipath components, proposes an adaptive joint chip equalization Rake (AAJCE-Rake) receiver to further improve the performance of the receiver. Its adaptive algorithm is given based on MMSE criterion.

2. Signal and System Model

For single-user DS-UWB system, the transmitter with binary phase-shift keying (BPSK) modulation transmitted the continuous-time signal can be described as

( )

_k

(

_s

)

k

s t

+∞

b Aw t kT

=−∞

=

∑

−

(1)

where

b ∈ −

_k

{ }

1, 1

is the kth BPSK data symbol,

T

_s denotes the symbol period and

A

is the signal amplitude.

w t

( )

denotes the user characteristic spreading waveform, which can be modeled as

1 0

( )

N _j

(

_c

)

j

w t

−

c p t jT

=

∑

−

(2)

where N is spread spectrum factor,

c

_j

∈

{

1 N

, 1

−

N

}

denotes the j-th chip of user spreading code

sequence,

T

_c is chip time, and

p t

( )

denotes the UWB pulse with normalized energy and duration

T

_p (

T

_p

<

T

_c ).

After transmitted signal passes through the dense multipath channel, the received signal is

1 0

( )

L _l

(

_l

)

( )

l

r t

−

h s t

τ

n t

=

∑

−

+

(3)

( )

n t

is the additive white Gaussian noise (AWGN）with zero mean and variance

N

₀

2

.

h

_l and

τ

_l are multipath amplitude and delay respectively.

L

is the number of total multipaths.

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The structure of the AJCE-Rake receiver is shown in Fig. 1. Here is signal processing model of the proposed Rake receiver. The continuous-time signal received by the receiver first passes through the matched filter, and its output is sampled at chip rate. Consider the discrete-time signal model in the pth

chip duration: , 0 M M p p iN k i p p k p iN k i p i M i M i

d

− −

d

− − =− =− ≠

=

∑

+

=

+

∑

+

r

h

n

h

n

(4) w p r ( ) r t xk +

−

ˆ_k b p x p d

Fig. 1 Structure of the AJCE-Rake receiver where

h

_k = [ 1

0, ,0,

L−

K

123 h

0 ,

h

L−1 ]T. For i<0,

h

k i+ =[

h

iN_c+1 ,

h

L−1 , 1

0, ,0

c L iN− −

K

123

]T and for i>0,

k i−

h

=[

h

₀ , ₁ c L iN

h

− + , 1

0, ,0

c L iN− −

K

123

]T.

p kN j

=

+

(

0 ≤ <

j N

),

d

p

=

b c

k j. The first term of Eq. (4) is

the desired signal term, the second one is the ISI, and the last one is AWGN. Equation (4) can be modified as

p

=

+

p

r

Hd n

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where

H

=[

h

_{k M}₋ ,...

h

_p, …

h

_{k M}₊ ], ,

d

=[

d

_{p MN}₋ ,…,

d

_p,…,

d

_{p MN}₊ ]T.

The discrete-time vector of the pth chip is processed to combine multipath components and equalize inter-chip interference simultaneously by the AJCE-Rake receiver. Finally the dispreading and decision are carried out. Suppose that the weight coefficient vector of the AJCE-Rake receiver is

w

. We use MMSE criterion to determine the weight coefficient vector. MMSE criterion can be written as

arg min

( )

MMSE

=

_w

J

MMSE

w

(6) where

(

)

{

2

}

( )

MMSE p p

J

w

=

E d

−

d

%

(7) T p p

d = w r

%

₍₈₎

The optimum weight vector to minimize

J

_MMSE

( )

w

is the Winner solution obtained by deriving

( )

MMSE

J

w

about

w

. Using Eq. (7) and Eq. (8), let the derivative of

J

_MMSE

( )

w

equals zero. Then the norm equation

Rw

_MMSE

=

u

₀ can be obtained, where

R

=

E

{ }

r r

_{p p}T ,

u

₀

=

E

{ }

r

_{p p}

d

. The Winner solution is

w

_MMSE

=

R u

−1 ₀. The soft output of the AJCE-Rake receiver is

x = w r

_p T _p. Collect the outputs of all the chips in symbol duration to form a column vector. Then this vector is despreaded and combined. Finally the combining output is decided:

b

%

_k

=

sign

(

c x

T _k

)

, where

c

=

[

c

₀

, ,

K

c

_N₋₁

]

T is the user spread code vector.

x

_k denotes the column vector, which consists of all chip output in the k-th

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In order to track channel variation, adaptive algorithms such as LMS and RLS can be adopted to update the weight coefficients. This paper takes this RLS algorithm as an example to present the adaptive updating algorithm of the AJCE-Rake receiver:

Initialization: 1

δ

−

=

P

E

=

w 0

Update the weight coefficients: T p p

e d

=

− w r

p T p p

λ

=

+

Pr

g

r Pr

(

_p

)

λ

=

−

P

P gr P

e

= +

w w g

where

P

is the inverse matrix estimate of

R

,

δ

takes very small positive constant.

E

denotes identity matrix and

g

is gain vector.

λ

(

0 < ≤

λ

1

) is forgetting factor.

4. Simulation Results and Analysis

In this section, BER performance of the AJCE-Rake receiver proposed in this paper is simulated in channel models: CM1 and CM4. At the same time the performances of the traditional Rake, DFE-Rake and MMSE-Rake receivers are also simulated for comparison.

The user spread code is

c

= −

[

1,1,1 1,1,1, 1, 1

−

− −

]

and

N =

8

. Chip time

T =

_c

1ns

, symbol time

8ns

s

T =

. Chip rate achieves 1Gc/s and data rate is 125Mb/s. The second order derivate of Gaussian pulse is adopted as UWB pulse, whose time domain expression is

(

)

(

)

2

( )

1 4

_m

exp

2

_m

p t

_{= −}

_⎡

_⎣

π τ

t

_⎤

_⎦

⎡

₋

π τ

t

⎤

⎣

⎦

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whereτm is pulse shape factor and τm=0.2ns in this paper. Pulse duration Tp=0.5ns and duty ratio is 0.5.

The distance between the transmitter and the receiver is 2m in CM1 and 8m in CM4. Fig.2 and Fig.3 give the simulation results of BER performances of these four receivers over these two channels respectively.

0 2 4 6 8 10 12 10-6 10-5 10-4 10-3 10-2 10-1 100

Signal to Noise Ratio, SNR (dB)

Bi t Er ro r R ate , BER Rake DFE-Rake MMSE-Rake AJCE-Rake 0 2 4 6 8 10 12 10-4 10-3 10-2 10-1 100

Signal to Noise Ratio, SNR (dB)

B it E rr or R at e Rake DFE-Rake MMSE-Rake AJCE-Rake

Fig.2 BER performance over CM1 channel Fig.3 BER performance over CM4 channel From Fig.2 and Fig.3, it can be seen that the DFE-Rake receiver performance is slightly better than that of the traditional Rake receiver. These two receivers have a BER floor of about 3×10-1_{due to the severe}

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some extent. However serious ISI makes this effect be severely limited. Using channel state information MMSE-Rake receiver selects some strongest path signals and optimizes the combining weight vector based on the MMSE criterion. Compared with DFE-Rake receiver, it obtains evident performance improvement, which can be seen from Fig.2 and Fig.3. The AJCE-Rake receiver proposed in this paper adopts the Rake receiver structure based chip equalizer, utilizes the MMSE criterion to optimize the weight vector and achieves effectively suppressing ISI by equalizing inter-chip interference. Therefore Fig.2 and Fig.3 verify that AJCE-Rake receiver performs much better than MMSE-Rake over the two typical channels. And when BER=10-5_{, it has SNR gain of about 2dB over CM1 channel, and when}

BER=10-2_{, about 3.3dB over CM4 channel. It also can be seen that compared with MMSE-Rake, higher}

SNR is, more evident performance improvement the AJCE-Rake receiver obtains. As SNR becomes higher, the ISI gradually becomes main factor affecting performance. AJCE-Rake can efficiently suppress ISI so that it gets more and more notable improvement. Meanwhile compared with MMSE-Rake receiver, AJCE-Rake receiver has more evident performance improvement in CM4 than in CM1. The reason is that ISI becomes more serious in CM4 than in CM4 and AJCE-Rake receiver can efficiently suppress ISI.

5. Conclusion

Serious ISI is an important factor constrainting BER performance of DS-CDMA high-speed communication systems. Although the DFE can be used to equalize ISI behind the Rake receiver, error propagation make DFE performance deteriorate sharply so that there is a BER floor. MMSE-Rake receiver optimizes the weight vector of Rake receiver based on MMSE criterion to obtain some performance improvement. But its performance is still constrained to some degree by ISI due to the absence of equalizing ISI. Therefore this paper proposes AJCE-Rake receiver, which spread the taps of Rake receiver to achieve multipath diversity and equalizing inter-chip interference simultaneously. Compared with three other receivers, it has evident BER performance improvement.

References

[1] Bikramaditya Das, Susmita Das. Rake-MMSE time domain equalizer for high data rate UWB communication system.

2009 Annual IEEE India Conference; 2009:1–4.

[2] Susmita Das, Bikramaditya Das. Time domain equalization technique using Rake-MMSE receivers for high data rate UWB communication system. 2009 First International Conference on Networks & Communications, 2009:1249–1253.

[3] Eslami, M., Xiaodai Dong. Rake-MMSE-Equalizer performance for UWB. IEEE Communications Letters; 2005;9(2):502-504.

[4] Zheng, Y. J., Ng, J.H., Yang, L.. A low-complexity blind Rake combining equalizer for UWB communication systems. IEEE International Conference on Ultra-Wideband; 2006:629–633.

[5] Ren-Jr Chen, Chang-Lan Tsai. Design and performance analysis of the receivers for DS-UWB communication systems. IEEE International Conference on Ultra-Wideband; 2006:651–656.

[6] Yu-Hao Chang, Shang-Ho Tsai, Xiaoli Yu, Kuo C.-C.J.. Performance enhancement of channel-phase precoded ultra-wideband (CPP-UWB) systems by Rake receivers. IEEE Global Telecommunications Conference; 2008:1–5.

[7] Gezici S., Mung Chiang, Poor H.V., Kobayashi H.. A genetic algorithm based finger selection scheme for UWB MMSE Rake receivers. IEEE International Conference on Ultra-Wideband, 2005:164–169.

[8] Chen R., Po-Lin Chiu, Hua-Lung Yang. Design and performance analysis of DS-UWB Rake receiver. IEEE International Symposium on Circuits and Systems; 2006:4715–4718.

[9] Boubaker N., Letaief K.B.. MMSE multipath diversity combining for multi-access TH-UWB in the presence of NBI. IEEE Transactions on Wireless Communications; 2006;5(4):712–719.

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3773 Feng Wang / Procedia Engineering 29 (2012) 3768 – 3773

some extent. However serious ISI makes this effect be severely limited. Using channel state information MMSE-Rake receiver selects some strongest path signals and optimizes the combining weight vector based on the MMSE criterion. Compared with DFE-Rake receiver, it obtains evident performance improvement, which can be seen from Fig.2 and Fig.3. The AJCE-Rake receiver proposed in this paper adopts the Rake receiver structure based chip equalizer, utilizes the MMSE criterion to optimize the weight vector and achieves effectively suppressing ISI by equalizing inter-chip interference. Therefore Fig.2 and Fig.3 verify that AJCE-Rake receiver performs much better than MMSE-Rake over the two typical channels. And when BER=10-5_{, it has SNR gain of about 2dB over CM1 channel, and when}

BER=10-2_{, about 3.3dB over CM4 channel. It also can be seen that compared with MMSE-Rake, higher}

SNR is, more evident performance improvement the AJCE-Rake receiver obtains. As SNR becomes higher, the ISI gradually becomes main factor affecting performance. AJCE-Rake can efficiently suppress ISI so that it gets more and more notable improvement. Meanwhile compared with MMSE-Rake receiver, AJCE-Rake receiver has more evident performance improvement in CM4 than in CM1. The reason is that ISI becomes more serious in CM4 than in CM4 and AJCE-Rake receiver can efficiently suppress ISI.

5. Conclusion

Serious ISI is an important factor constrainting BER performance of DS-CDMA high-speed communication systems. Although the DFE can be used to equalize ISI behind the Rake receiver, error propagation make DFE performance deteriorate sharply so that there is a BER floor. MMSE-Rake receiver optimizes the weight vector of Rake receiver based on MMSE criterion to obtain some performance improvement. But its performance is still constrained to some degree by ISI due to the absence of equalizing ISI. Therefore this paper proposes AJCE-Rake receiver, which spread the taps of Rake receiver to achieve multipath diversity and equalizing inter-chip interference simultaneously. Compared with three other receivers, it has evident BER performance improvement.

References

[1] Bikramaditya Das, Susmita Das. Rake-MMSE time domain equalizer for high data rate UWB communication system. 2009 Annual IEEE India Conference; 2009:1–4.