Karim OUERTANI, Samir SAOUDI, Mahmoud AMMARinstitut Telecom / Telecom Bretagne, Signal & Communications

DepartmentTechnopole de Brest-Iroise, CS 83818 - 29238 Brest Cedex, FRANCE

E-mail: karim.ouertani@telecom-bretagne.eu

Summary— In this work a novel channel estimation scheme is proposed for a RAKEreceiver operating in a time varying multi-path channel. The approach is an extensionof the well known nonlinear interpolation channel estimator, which is based on inter-polating the channel estimates from pilot symbol sequence. The proposed techniquemanages to combine the obtained samples over one chip duration using a Lagrangeinterpolation filter, and thereby enhances the signal-to-noise ratio and improves thequality of channel estimates. We also investigate optimal power assignment for the pi-lot and data channels. Simulation results allowed us to pinpoint optimum pilot-to-datachannel power ratio for the best bit error performance.

Coherent RAKE block diagram with correlation based channel estimation.

•Conventional correlation based channel estimation with a RAKE receiver.

•The CDMA signal is spread to the chip rate with an SF-long Walsh code.

•The spread signal is oversampled by an oversampling factor Ns = 4.

•The signal is transmitted through a multipath Rayleigh fading channel, with a channelresponse :

Gk(i) =L∑

l=1

gk,l(i)δ(iT − τk,l) (1)

1. Correlation based channel estimation

•The Ns = 4 samples corresponding to one chip are input to a 3rd order Lagrangeinterpolation filter [1],[2] to get an interpolated chip value estimates.

•Despreading process is performed with the interpolated chip estimates.

•The Lagrange interpolation filters are widely used in numerous applications : samplingrate conversion, digital communications, FIR filters design, etc.

Desired chip value interpolation by a 3rd order Lagrange filter.

•The filter coefficients are obtained as follows,

hd(p) =N∏

k=0

d − k

p − kfor p = 0, 1, 2, ..., Ns (2)

•N is the filter order, N = 3.

•d is the delay to be fractionallyapproximated, D = Tc

4 .

•Structure of the interpolation scheme from the oversampled received signal frame :

chip 0 chip SF−1chip n

Pilot

r(n) r(n+1) r(n+2) r(n+3)

h(3)h(2)h(0) h(1)

r(n+d)

A 3rd order Lagrange interpolation filter.

2. Channel estimation with Lagrange prefiltering

−30 −25 −20 −15 −10 −5 010

−5

10−4

10−3

10−2

10−1

100

SNR(dB)

BE

R

RAKE CERAKE+Lagrange CERAKE PKCRAKE+Lagrange PKC

Effect of imperfect channel estimation - K = 3 users.

In the figure :

• ”PKC” refers to the Perfectly Known Channel simulation case.

• ”CE” refers to the Channel Estimation simulation case.

−30 −25 −20 −15 −10 −5 010

−4

10−3

10−2

10−1

100

SNR(dB)

BE

R

RAKE K=5RAKE K=3RAKE+Lagrange K=5RAKE+Lagrange K=3RAKE+Lagrange K=1

BER Vs SNR for conventional channel estimation (’RAKE’) and proposedchannel estimation (’RAKE+Lagrange’) - K=1, 3 and 5 users.

5. Simulation Results

0 10 20 30 40 50 60 70 80 90

10−3

10−2

10−1

100

% of Power Applied to Pilot Symbol

BE

R

SNR = −16dBSNR = −12dB

BER vs percentage of power applied topilot channel.

−30 −28 −26 −24 −22 −20 −18 −16 −14 −12 −1010

−4

10−3

10−2

10−1

100

SNR(dB)

BE

R

50% of Power Applied to Pilot Symbol 60% of Power Applied to Pilot Symbol

BER performance with optimumpilot power allocation.

•The amount of power applied to the pilot signal was varried from 1 % to 90 %.

•The optimum power allocation between the pilot channel and the data channel wasinvestigated under the assumption of constant total transmit power.

•The lowest bit error rate is obtained for 60 % of the signal power applied to the pilotchannel.

6. Power Allocation

[1] T. I. Laakso, V. Valimaki, M. Karjalainen, and U. K. Laine. Splitting the UnitDelay, in IEEE Signal Processing Magazine, pages: 30-60, January 1996.

[2] E. Simona Lohan, M. Renfors Performance Analysis of the RAKE Receiver inthe Presence of Multipath Delay Estimation Errors and Rician Fading Chan-nels, in European transactions on telecommunications, vol. 14, pages: 435-447, July2003.

[3]M. Meyr, M. Moeneclaey, and S. A. Fechtel. Digital Communication Receivers: synchronization, channel estimation, and signal processing, Wiley series intelecommunications and signal processing, Jhon Wiley & sons, 1998.

7. References