Adaptive Lattice Filtersfor CDMA Overlay

DSP 2 Project PresentationBy

Rajat Kapur&

AdityaKiran Jagannatham

CDMA Technology

CDMA is a Multiple Access wireless technique.Uses the idea of Spread SpectrumBenefits of CDMA:

1.Capacity increases of 8 to 10 times that of an AMPS analog system

2. Improved call quality,3.Simplified system planning through frequency reuse.4.Enhanced privacy and Bandwidth on demand5. Possibility of fewer cell sites

The Overlay Concept:Motivation: Increasing demand for BW in Mobile Comm.Establishment of PCN in the 1.85-1.99 GHz Band (‘92)Previously occupied by Narrow-band Microwave Signals This situation of “Spectrum Sharing” CDMA Overlay. Initial experiments in Houston, Orlando, San Diego using

Broad-Band CDMA Goals:1. Overlay would not excessively interfere with N-Band2. PCN users can operate efficiently in the overlay environment3. Conform to PCN philosophy (100W in 183m cell radius)

Adaptive Filtering in CDMA Overlay

LMS Filtering employed in N-Band interference rejection (’96)Lattice Filtering suggested as an alternative by J.Wang and V.Prahatheesan (2K)Lattice shown to outperform LMS

Overlay Receiver

BP Filter LatticeFilter Hard

Decision

( ) cos(2 )i oa t f t

fr t r t b

b

T

T

Channel

CDMA ReceiverNband

Filter

P represents Signal Powerf0 is the CDMA Carrier Frequency

bk – kth user binary information

N = Tb/Tc Processing Gain

k = Rayleigh Fading Parameter ( E(k2) = 2 )

k – Random Phase ~ [0,2]

k – Path Delay ~ [0, Tb ] (Rayleigh Flat Fading Channel)

Bc = 2/Tc - CDMA Signal Bandwidth

j(t) = Narrow-Band Interference Signaln(t) = Band-Limited AWGN (PSD ~ N0/2)

1

( ) 2 ( ) cos(2 ) ( ) ( )......(1)K

k k o kk

r t P b t f t j t n t

( ) ( ) cos[2 ( ) ] ( ) sin[2 ( ) ]c o s oj t j t f t j t f t

jc(t), js(t) – Inphase and Quadrature Narrow-Band Components

= frequency offset from CDMA Carrierp = Bj/Bc

q = Tc

Lattice Filter Structure

( , ) ( , 1) ( ) (( 1) , 1)f c f c n c b ce sT n e sT n R sT e s T n

( , ) (( 1) , 1) ( ) ( , 1)b c b c n c f ce sT n e s T n R sT e sT n

Lattice Recursive Equation

Cleaned CDMA Signal( ) ( , ) ( , )f c f c br sT e sT M e sTc M

….which is the final stage lattice output

AnalysisAlmost EXACT analysis !!!Reflection Coefficient Update Equation is given as:

Ta - Update Interval

Ta 2/Bj, 2/Bj ~ Input Correlation Time

- Step Size

Signal Sampled @ Tc (Chip Time)

Input Signal independent at update intervals No need to ASSUME Independence !Central Limit Principle applied

21 1 , 1 , 1 , 1n a b a c n a f a b a cR j T e jT T n R jT e jT n e jT T n

Input at sample time intervals is given as:

01

, 0 2 .cos 2K

f c k c k k c k c k c ck

e s x T P b s x T a s x T f s x T j s x T n s x T

, 0 ,0c f c b cc x y T E e s x T e s y T

Correlation of input samples:

It can be derived….

00 2

sin 2 cos 2

2 sin 4 cos 4

c

c

c

c PK J N B

c T J c p q

c T J c p q

Observation: Correlation at Tc , 2Tc exclusively from N-Band SignalTc Correlation Time of CDMA Signal Hence is analogous to “White Noise”

Analysis Cont’d…

Analysis Cont’d…

Reflection Coefficient at jth iteration…

The Product term indicates dependence on past dataFor a large number of co-channel users ( K ~ 30 or >) , the term…

1

2

1

, 1 , 1 , 1 . , 1 .

1

1 , 1

j

f a b a c f a b a cx

n a j

b a cr

e jT n e jT T n e j x T n e j x T T n

R j T

e j r T T n

3, 0 ,0f a b a cE e j x T e j x T T

Can be simplified as… cc c T

…using CLP

To yield… 2 11

1

11 3 0

1

j

a c c c

gE R j T c T c T c c T

g

10 1c and g

Analysis Cont’d…

Which in the limit yields…

1 1

0

/ .sin 2 cos 21 2 .

/ 2 /b

J S c p qE R

K J S N E N

1

2 0

0c cc T c c T

E Rc

…clearly showing E[R1] depends on step size !!!Observe: If = 0 …

1 0

cc TE R

c

… the optimal Wiener Filter Coefficient •Similarly, it can shown that

2

2 / 0

1cc T c A

E RA

Analysis Cont’d…

Where A is given by…

… pretty complicated !!!

Analysis Cont’d…

SNR Calculation: The Despreader O/P is given as…

( 1)

0

1

2 cos 2

2

b

b

T

f iT

K

il b i kkk i

r t a t f t dt

P T b I N J

bi() - th bit of ith user

J – NBand interference, N – Interference from Noise

I – Co-Channel User Interference

2

2 2 2

11

2 21 2 1 2 1

0 1 0 2 0 0 00

4

/1 ( 1) 1. , .

2 2 3 2

b

J N I

M M M M Mb

m m m m m mm m m m m

PTSNR

J SE KE w E w w Q m m E w E w w

N N N

Analysis Cont’d…

where

0

1 1 2

2 2

,

1

1

M

f m c fm

r t w r t mT e t M

w

w R t R t

w R t

this FINALLY concludes our analysis !!!

†Precise Details can be found in references…

Simulations:System Specs. :K = 30 (No. of Co-Channel Users), = 0.1 (-7 dB

Fading)

p = Bj/Bc = 5% (0.05) Ta = 20 Tc

q = Tc = 0 (=0)

N = Tb/Tc Processing Gain = 750

J/S = 17,20,23 dBb – 32 Kbps, BPSK SignalLink Specs. :f0 : 1.884 GHz (B-M), 1.956 GHz (M-B)

Chip Rate = 24 Mchips/sec Tc = 1/24E6

48 MHz BW for each DS WaveformN-Band Interference - 64 QAM @ 45 Mbps

†Specs. taken from “On the Feasibility of a CDMA Overlay for PCN (’92)

Simulation Results: Convergence behavior of R1…

Results Cont’d: Convergence behavior of R1…

Results Cont’d: LMS Vs Lattice SNR Performance…

†From: Adaptive Lattice Filters for CDMA Overlay (Trans. Comm., 2K)

Sim. Log.:

Simulations done in Base-Band Iterations of the order 750 X 30 X 30 + 750 X 30 X 40Random Binary Sequences used as PN Sequences = 1 for user no attenuation on Direct PathWhite Noise used

Conclusions…CDMA Overlay effective for frequency re-use

Each stage of the Lattice Converges independent of others

Lattice Filter provides faster rate of convergence compared to LMS Filter

Lattice Filter has good capability of Narrow Band

Interference SuppressionReferences…1. “Adaptive Lattice Filters for CDMA Overlay”- Trans. Comm., 2K 2. “Adaptive LMS Filters for Cellular CDMA Overlay”- Select Areas

in Comm., ‘96 3. “On the Feasibility of CDMA Overlay for PCN”- Select Areas in

Comm.,’924. “Cellular CDMA Overlay Systems”- IEE Proc. Comm., ‘96