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This document proposes a novel channel estimation scheme for a RAKE receiver operating in a time-varying multipath channel. It extends the well-known nonlinear interpolation channel estimator by combining channel estimates from pilot symbols using a Lagrange interpolation filter. This enhances the signal-to-noise ratio and improves channel estimate quality. Simulation results determine the optimal pilot-to-data channel power ratio for best bit error performance.
![Karim OUERTANI, Samir SAOUDI, Mahmoud AMMAR
institut Telecom / Telecom Bretagne, Signal & Communications
Department
Technople de Brest-Iroise, CS 83818 - 29238 Brest Cedex, FRANCE
o
E-mail: karim.ouertani@telecom-bretagne.eu
5. Simulation Results
Summary In this work a novel channel estimation scheme is proposed for a RAKE
receiver operating in a time varying multi-path channel. The approach is an extension
0
of the well known nonlinear interpolation channel estimator, which is based on inter- 10
RAKE CE
polating the channel estimates from pilot symbol sequence. The proposed technique RAKE+Lagrange CE
RAKE PKC
RAKE+Lagrange PKC
manages to combine the obtained samples over one chip duration using a Lagrange 10
1
interpolation 鍖lter, and thereby enhances the signal-to-noise ratio and improves the
quality 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-data 10
2
channel power ratio for the best bit error performance.
BER
3
10
1. Correlation based channel estimation
4
10
5
10
30 25 20 15 10 5 0
SNR(dB)
E鍖ect of imperfect channel estimation - K = 3 users.
In the 鍖gure :
Coherent RAKE block diagram with correlation based channel estimation. PKC refers to the Perfectly Known Channel simulation case.
CE refers to the Channel Estimation simulation case.
Conventional correlation based channel estimation with a RAKE receiver. 10
0
RAKE K=5
The CDMA signal is spread to the chip rate with an SF-long Walsh code. RAKE K=3
RAKE+Lagrange K=5
RAKE+Lagrange K=3
The spread signal is oversampled by an oversampling factor Ns = 4. RAKE+Lagrange K=1
1
10
The signal is transmitted through a multipath Rayleigh fading channel, with a channel
response :
L
BER
2
Gk (i) = gk,l(i)隆(iT k,l) (1) 10
l=1
3
10
2. Channel estimation with Lagrange pre鍖ltering
4
10
rd
The Ns = 4 samples corresponding to one chip are input to a 3 order Lagrange 30 25 20 15
SNR(dB)
10 5 0
interpolation 鍖lter [1],[2] to get an interpolated chip value estimates. BER Vs SNR for conventional channel estimation (RAKE) and proposed
Despreading process is performed with the interpolated chip estimates. channel estimation (RAKE+Lagrange) - K=1, 3 and 5 users.
The Lagrange interpolation 鍖lters are widely used in numerous applications : sampling
rate conversion, digital communications, FIR 鍖lters design, etc.
6. Power Allocation
0
10
SNR = 16dB 0
10
SNR = 12dB 50% of Power Applied to Pilot Symbol
60% of Power Applied to Pilot Symbol
1
1 10
10
BER
BER
2
10
Desired chip value interpolation by a 3rd order Lagrange 鍖lter. 2
10
The 鍖lter coe鍖cients are obtained as follows, 10
3
3
10
4
0 10 20 30 40 50 60 70 80 90 10
30 28 26 24 22 20 18 16 14 12 10
% of Power Applied to Pilot Symbol SNR(dB)
N dk
hd(p) = f or p = 0, 1, 2, ..., Ns (2) BER vs percentage of power applied to BER performance with optimum
k=0 p k pilot channel. pilot power allocation.
N is the 鍖lter order, N = 3. The amount of power applied to the pilot signal was varried from 1 % to 90 %.
d is the delay to be fractionally The optimum power allocation between the pilot channel and the data channel was
approximated, D = 4 . Tc investigated under the assumption of constant total transmit power.
The lowest bit error rate is obtained for 60 % of the signal power applied to the pilot
Structure of the interpolation scheme from the oversampled received signal frame : channel.
chip 0 chip n chip SF1
Pilot 7. References
[1] T. I. Laakso, V. Valimaki, M. Karjalainen, and U. K. Laine. Splitting the Unit
r(n) r(n+1) r(n+2) r(n+3) Delay, in IEEE Signal Processing Magazine, pages: 30-60, January 1996.
h(0) h(1) h(2) h(3) [2] E. Simona Lohan, M. Renfors Performance Analysis of the RAKE Receiver in
the Presence of Multipath Delay Estimation Errors and Rician Fading Chan-
nels, in European transactions on telecommunications, vol. 14, pages: 435-447, July
2003.
[3] M. Meyr, M. Moeneclaey, and S. A. Fechtel. Digital Communication Receivers
: synchronization, channel estimation, and signal processing, Wiley series in
r(n+d) telecommunications and signal processing, Jhon Wiley & sons, 1998.
A 3rd order Lagrange interpolation 鍖lter.](https://image.slidesharecdn.com/posterkobe-121030160935-phpapp02/85/Poster-kobe-1-320.jpg)
Poster kobe
- 1. Karim OUERTANI, Samir SAOUDI, Mahmoud AMMAR institut Telecom / Telecom Bretagne, Signal & Communications Department Technople de Brest-Iroise, CS 83818 - 29238 Brest Cedex, FRANCE o E-mail: karim.ouertani@telecom-bretagne.eu 5. Simulation Results Summary In this work a novel channel estimation scheme is proposed for a RAKE receiver operating in a time varying multi-path channel. The approach is an extension 0 of the well known nonlinear interpolation channel estimator, which is based on inter- 10 RAKE CE polating the channel estimates from pilot symbol sequence. The proposed technique RAKE+Lagrange CE RAKE PKC RAKE+Lagrange PKC manages to combine the obtained samples over one chip duration using a Lagrange 10 1 interpolation 鍖lter, and thereby enhances the signal-to-noise ratio and improves the quality 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-data 10 2 channel power ratio for the best bit error performance. BER 3 10 1. Correlation based channel estimation 4 10 5 10 30 25 20 15 10 5 0 SNR(dB) E鍖ect of imperfect channel estimation - K = 3 users. In the 鍖gure : Coherent RAKE block diagram with correlation based channel estimation. PKC refers to the Perfectly Known Channel simulation case. CE refers to the Channel Estimation simulation case. Conventional correlation based channel estimation with a RAKE receiver. 10 0 RAKE K=5 The CDMA signal is spread to the chip rate with an SF-long Walsh code. RAKE K=3 RAKE+Lagrange K=5 RAKE+Lagrange K=3 The spread signal is oversampled by an oversampling factor Ns = 4. RAKE+Lagrange K=1 1 10 The signal is transmitted through a multipath Rayleigh fading channel, with a channel response : L BER 2 Gk (i) = gk,l(i)隆(iT k,l) (1) 10 l=1 3 10 2. Channel estimation with Lagrange pre鍖ltering 4 10 rd The Ns = 4 samples corresponding to one chip are input to a 3 order Lagrange 30 25 20 15 SNR(dB) 10 5 0 interpolation 鍖lter [1],[2] to get an interpolated chip value estimates. BER Vs SNR for conventional channel estimation (RAKE) and proposed Despreading process is performed with the interpolated chip estimates. channel estimation (RAKE+Lagrange) - K=1, 3 and 5 users. The Lagrange interpolation 鍖lters are widely used in numerous applications : sampling rate conversion, digital communications, FIR 鍖lters design, etc. 6. Power Allocation 0 10 SNR = 16dB 0 10 SNR = 12dB 50% of Power Applied to Pilot Symbol 60% of Power Applied to Pilot Symbol 1 1 10 10 BER BER 2 10 Desired chip value interpolation by a 3rd order Lagrange 鍖lter. 2 10 The 鍖lter coe鍖cients are obtained as follows, 10 3 3 10 4 0 10 20 30 40 50 60 70 80 90 10 30 28 26 24 22 20 18 16 14 12 10 % of Power Applied to Pilot Symbol SNR(dB) N dk hd(p) = f or p = 0, 1, 2, ..., Ns (2) BER vs percentage of power applied to BER performance with optimum k=0 p k pilot channel. pilot power allocation. N is the 鍖lter order, N = 3. The amount of power applied to the pilot signal was varried from 1 % to 90 %. d is the delay to be fractionally The optimum power allocation between the pilot channel and the data channel was approximated, D = 4 . Tc investigated under the assumption of constant total transmit power. The lowest bit error rate is obtained for 60 % of the signal power applied to the pilot Structure of the interpolation scheme from the oversampled received signal frame : channel. chip 0 chip n chip SF1 Pilot 7. References [1] T. I. Laakso, V. Valimaki, M. Karjalainen, and U. K. Laine. Splitting the Unit r(n) r(n+1) r(n+2) r(n+3) Delay, in IEEE Signal Processing Magazine, pages: 30-60, January 1996. h(0) h(1) h(2) h(3) [2] E. Simona Lohan, M. Renfors Performance Analysis of the RAKE Receiver in the Presence of Multipath Delay Estimation Errors and Rician Fading Chan- nels, in European transactions on telecommunications, vol. 14, pages: 435-447, July 2003. [3] M. Meyr, M. Moeneclaey, and S. A. Fechtel. Digital Communication Receivers : synchronization, channel estimation, and signal processing, Wiley series in r(n+d) telecommunications and signal processing, Jhon Wiley & sons, 1998. A 3rd order Lagrange interpolation 鍖lter.