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CDMA: Code-Division Multiple Access with DS-SS and RAKE Receiver, Study notes of Electrical and Electronics Engineering

Georgia Institute of Technology - Main Campus Electrical and Electronics Engineering

An in-depth analysis of cdma (code-division multiple access) technology, focusing on direct sequence spread spectrum (ds-ss) and the rake (receiver with adaptive combining of known delayed replicas of the transmitted signal) receiver. Cdma is a multiplexing technique that allows multiple users to share the same bandwidth at the same time. Ds-ss is a popular method for generating noise-like waveforms for cdma systems, using maximal-length shift registers to produce binary sequences. The rake receiver is used to extract the desired user's signal from the received signal, which includes the desired user's waveform, spreading sequence, and interference from other users. The document also discusses the correlation receiver, multi-user interference, and the ber (bit error rate) for bpsk (binary phase shift keying) assuming awgn (additive white gaussian noise).

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CDMA

Instructor: Mary Ann Ingram

ECE 4823

Motivation

BER depends on bit energy—not on the

bandwidth

Large bandwidth signals are

less sensitive to multipath fading

less vulnerable to jamming

can be concealed

can share a common bandwidth without

interfering with each other

Code-Division Multiple Access

Allows multiple users to share same

bandwidth at the same time

Each user’s waveform is like an

independent noise random process

Interference appears as white noise

Matched filter pulls out desired user’s

waveform, suppresses interference

Direct Sequence Spread

Spectrum (DS-SS)

DS-SS is one popular way to make the

noise-like waveforms for CDMA

Maximal-length shift registers make

binary sequences that have noise-like

properties

m-stage shift register produces a sequence

with a period of length 2m-1

DS-SS Baseband Waveform

Binary noise sequence is mapped to a chip

spreading sequence of +/- 1’s

Each user gets a different spreading

sequence Baseband

Waveform

Short code

example

0TS2TS3TS

TS

Information

waveform

0T

S2TS3TS

1

-1

Chips

The spreading sequence comprises

chips (very short pulses) with width TC

There are an integer number of chips

for each data symbol

chip width

data symbol

Discover Study notes of Electrical and Electronics Engineering Georgia Institute of Technology - Main Campus

Partial preview of the text

Download CDMA: Code-Division Multiple Access with DS-SS and RAKE Receiver and more Study notes Electrical and Electronics Engineering in PDF only on Docsity!

CDMA

Instructor: Mary Ann Ingram

ECE 4823

Motivation

BER depends on bit energy—not on the

bandwidth

Large bandwidth signals are

less sensitive to multipath fading

less vulnerable to jamming

can be concealed

can share a common bandwidth without

interfering with each other

Code-Division Multiple Access

Allows multiple users to share same

bandwidth at the same time

Each user’s waveform is like an

independent noise random process

Interference appears as white noise

Matched filter pulls out desired user’s

waveform, suppresses interference

Direct Sequence Spread

Spectrum (DS-SS)

DS-SS is one popular way to make the

noise-like waveforms for CDMA

Maximal-length shift registers make

binary sequences that have noise-like

properties

m-stage shift register produces a sequence

with a period of length 2 m-

DS-SS Baseband Waveform

Binary noise sequence is mapped to a chip

spreading sequence of +/- 1’s

Each user gets a different spreading

sequence

Baseband

Waveform

Short code

example

0 T^ S 2T^ S 3T^ S

T S

Information

waveform

0 T S 2T S 3T S

1

Chips

The spreading sequence comprises

chips (very short pulses) with width TC

There are an integer number of chips

for each data symbol

chip width

data symbol

Codes for Different Users

Their cross-correlation is nearly zero:

user 1

( ) dt

TS ∫ 0 • ≈^0

M-Sequences

“Maximal-length” or m-sequences are a

well-known class of spreading

sequences

Generated with a linear feedback shift

register

A register of length m generates a code

N long, where N=

m

Generating M-Sequences

The p i’s are the coefficients of a primitive

polynomial

ai ai-1 ai-2 ai-3 ai-4 ai-m+1 ai-m

p 1 p 2 p 3 p 4 p (^) 1m-

Autocorrelation of the M-

Sequence

Very much like an impulse

-1/N

Processing Gain

The number of chips per symbol is the

processing gain (PG)

This is also

where B

SS

and B are the bandwidths of

the chips and the data symbols,

respectively. Usually, BSS >> B

B

B PG

SS

=

Signal Model for k -th User

E

S

= symbol energy

m k(t) = information waveform for k-th user

p k(t) = spreading sequence for k-th user

B = bandwidth of m k(t)

B SS = bandwidth of pk(t)

k k c k S

S

k m t p t ft T

E s t = () ()cos 2 π + θ

2 ()

Graceful Degradation

Unlike TDMA,

CDMA BER

increases

gradually as

more users

are added

Stuber 2000

Narrowband Interference

Interference signal is spread and then filtered

T S

Complex envelope of desired signal

0 T S 2T S 3T S 0 T S 2T S 3T S

1

Filter matched to T (^) S-long pulse

T S

Complex envelope of desired signal

0 T S 2T S 3T S 0 T S 2T S 3T S

1

Filter matched to T (^) S-long pulse Interference bandwidth spreads out to BSS , but bandwidth of filter is only B

Baseband Tapped-Delay Line Model

of Received Complex Envelope

s t

k BSS

1

g

L

g

z ( t ) Σ

rt

j ft

j l l

c

l

rt rte

g e

π

φ α

2

( )=Re

Complex tap gains

B SS

1

g

BSS

1

g

L

Complex noise

Statistical Models of Tap Gains

Under the wide-sense stationary uncorrelated

scattering (WSSUS) assumption, the tap

gains are uncorrelated complex RVs

A reasonable model for the tap gain

magnitudes, α l , is Rayleigh with exponentially

decreasing mean square values

L

l

l l

st Ce

E Ce

β

β α

Small β, small delay spread

Correlator (RAKE) Receiver

B SS

1

rt

Conjugate path gains

B SS

1 B SS

1

L

1 L

g * g * 2 g 3 * gL *

B SS

1

~ *^

s t

k

X

{ ( ) dt }

T

Re ∫ 0 • Σ

k

Decision Variable

not needed if modulation is equal energy

The Decision Variable

The RAKE receiver output is

where the self-interference is

and generally non-Gaussian and correlated

,

1

, 1

2

Re

ml m l

L

k

L k

i

iik p k

L

l

k l

Y g g

Y k n

∑ +^ ∑ ∑ +

−

=

−−

=

autocorrelation of spreading sequence

BER

For DS-SS-BPSK, and assuming ideal

speading sequence (impulse autocorrelation),

then

( )

( L ) b

m

L

l lm m l

m m

L

l (^) m

m b m

e e

A

P A

β β

BPSK DS-SS BER Curves

Channel has 4

taps

RAKE has 4

taps

[Stuber, 2001]

β β β

Compare to 4-th Order Spatial

Diversity

[Stuber, 2001]

β β β

small delay spread yields no diversity

β=1 not as good as L=

Sliding Correlator RAKE

Receiver

The received signal is split into M

branches (M could be less than L)

Each branch signal is weighted with the

conjugate of the path gain (like MRC)

Each weighted branch signal is

correlated with a differently delayed

version of the spreading sequence

Sliding Correlator RAKE

Receiver; Example: M=

p (^) k ( ) t

c

g

b

ga g

rt

•Correlators “hunt” for best delays •for M<L, performance won’t be as good

CDMA: Code-Division Multiple Access with DS-SS and RAKE Receiver, Study notes of Electrical and Electronics Engineering

Related documents

Partial preview of the text

Download CDMA: Code-Division Multiple Access with DS-SS and RAKE Receiver and more Study notes Electrical and Electronics Engineering in PDF only on Docsity!

CDMA

Instructor: Mary Ann Ingram

ECE 4823

Motivation

 BER depends on bit energy—not on the

bandwidth

 Large bandwidth signals are

 less sensitive to multipath fading

 less vulnerable to jamming

 can be concealed

 can share a common bandwidth without

interfering with each other

Code-Division Multiple Access

 Allows multiple users to share same

bandwidth at the same time

 Each user’s waveform is like an

independent noise random process

 Interference appears as white noise

 Matched filter pulls out desired user’s

waveform, suppresses interference

Direct Sequence Spread

Spectrum (DS-SS)

 DS-SS is one popular way to make the

noise-like waveforms for CDMA

 Maximal-length shift registers make

binary sequences that have noise-like

properties

 m-stage shift register produces a sequence

with a period of length 2 m-

DS-SS Baseband Waveform

 Binary noise sequence is mapped to a chip

spreading sequence of +/- 1’s

 Each user gets a different spreading

sequence

Baseband

Waveform

Short code

example

0 T^ S 2T^ S 3T^ S

T S

Information

waveform

0 T S 2T S 3T S

Chips

 The spreading sequence comprises

chips (very short pulses) with width TC

 There are an integer number of chips

for each data symbol

Codes for Different Users

 Their cross-correlation is nearly zero:

M-Sequences

 “Maximal-length” or m-sequences are a

well-known class of spreading

sequences

 Generated with a linear feedback shift

register

 A register of length m generates a code

N long, where N=

Generating M-Sequences

 The p i’s are the coefficients of a primitive

polynomial

Autocorrelation of the M-

Sequence

 Very much like an impulse

-1/N

Processing Gain

 The number of chips per symbol is the

processing gain (PG)

 This is also

where B

SS

and B are the bandwidths of

the chips and the data symbols,

respectively. Usually, BSS >> B

SS

 E

BER depends on bit energy—not on the

Large bandwidth signals are

less sensitive to multipath fading

less vulnerable to jamming

can be concealed

can share a common bandwidth without

Allows multiple users to share same

Each user’s waveform is like an

Interference appears as white noise

Matched filter pulls out desired user’s

DS-SS is one popular way to make the

Maximal-length shift registers make

m-stage shift register produces a sequence

Binary noise sequence is mapped to a chip

Each user gets a different spreading

The spreading sequence comprises

There are an integer number of chips

Their cross-correlation is nearly zero:

“Maximal-length” or m-sequences are a

Generated with a linear feedback shift

A register of length m generates a code

The p i’s are the coefficients of a primitive

Very much like an impulse

The number of chips per symbol is the

This is also

E

m k(t) = information waveform for k-th user

p k(t) = spreading sequence for k-th user

B = bandwidth of m k(t)

B SS = bandwidth of pk(t)

Unlike TDMA,

Interference signal is spread and then filtered

Under the wide-sense stationary uncorrelated

A reasonable model for the tap gain

The RAKE receiver output is

For DS-SS-BPSK, and assuming ideal