LMS Adaptive Equalizer Matlab Project S-88.2111 Signal Processing - - PowerPoint PPT Presentation

LMS Adaptive Equalizer Matlab Project

S-88.2111 Signal Processing in Telecommunications 1 Spring 2009, Lecture Period IV Signal Processing Laboratory Helsinki University of Technology

written by Mobien Mohammed

S-88.2111 Signal Processing in Telecommunication I (3 cp)

Outline

• 1. System Model
• 2. Channel Model
• 3. Adaptive Equalizer
• 4. Simulation Model
• 5. Sample Demo System
• 6. Practical Issues

S-88.2111 Signal Processing in Telecommunication I (3 cp)

• 1. System Model

+

• ek

zk qk xk nk rk

∑ ∑

Source Channel Equalizer Slicer Delay

S-88.2111 Signal Processing in Telecommunication I (3 cp)

• FIR type of channel introduces inter-symbol interference (ISI):

where L is the number of channel coefficients

• Model for noise

– Additive White Gaussian Noise (AWGN) with the power σn

2

• 2. Channel Model

) 1 ( 1 2 2 1 1

... ) (

− − − − −

+ + + + =

L L z

c z c z c c z C

S-88.2111 Signal Processing in Telecommunication I (3 cp)

• Adaptive updating of the equalizer using the LMS algorithm

where rk input signal vector (rk=[rk rk-1 … rk-(N-1)]T) hk weight vector ek error signal µ step size

• Mean Square Error (MSE) criterion
• 3. Adaptive Equalizer

k k k k

e r h h μ 2

1

+ =

+

[ ]

2

E

k k

e MSE =

S-88.2111 Signal Processing in Telecommunication I (3 cp)

• Implementation of transmission system in Matlab

– Transmitter – Channel – Equalizer – Decision device

• 4. Simulation Model

S-88.2111 Signal Processing in Telecommunication I (3 cp)

... Simulation Model

%%%------------------------------------------------------------------ %%% Transmitter %%%------------------------------------------------------------------ x=sign(randn(1,K)); % Generate BPSK data. ref_x=[0*ones(1,D),x]; % Generate reference signal. %%%------------------------------------------------------------------ %%% Channel %%%------------------------------------------------------------------ for i=1:I, % Run all the indepedent runs. ['Iteration:',mat2str(i)] % Iteration index. channel_data=filter(cn,1,x); % Distort the signal. n=sqrt(sigma2_n)*randn(1,K); % Generate white noise sequence. channel_output=channel_data+n; % AWGN channel. %%%------------------------------------------------------------------ %%% Equalizer %%%------------------------------------------------------------------ [h,e,q,z]=lms(channel_output,ref_x,my,N); % Linear LMS equalizer. MSE=MSE+abs(e).^2; % Mean Square Error(MSE). end

S-88.2111 Signal Processing in Telecommunication I (3 cp)

• 5. Sample Demo System
• Channel model (W=2.9; L=3; l=0, ..., L-1)

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + = ) 1 ( 2 cos 1 2 1 l W cl π

Parameter Value Number of independent runs I 200 Number of transmitted symbols K 500 Number of filter coefficients N 11 Noise power σn

2

0.001 Step size μ (μmax/3) 0.0276 Channel coefficients [h0 h1 h2] [0.2194 1.0000 0.2194]

• Simulation parameters

S-88.2111 Signal Processing in Telecommunication I (3 cp)

5.1 Mean Square Error (MSE)

Parameters: N = 11, D = 7, μ = 0.0276

S-88.2111 Signal Processing in Telecommunication I (3 cp)

5.2 Impulse responses

S-88.2111 Signal Processing in Telecommunication I (3 cp)

5.3 Frequency responses

S-88.2111 Signal Processing in Telecommunication I (3 cp)

5.3 Time domain responses

S-88.2111 Signal Processing in Telecommunication I (3 cp)

• This project is required for the course
• You may work in teams of 2
• Please register your group with the assistant
• Grading

– Pass/Fail

• Documentation

– Brief report please! – Emphasize on the results rather than the already given background

• Project deadline: May 29, 2009
• 6. Practical issues