ECE 442 COMMUNICATION SYSTEM DESIGNLECTURE 4. SPREAD SPECTRUMHusheng Li

Dept. of EECS

The University of Tennessee

THE MOTHER OF CDMA

Hedy Lamarr (1913---2000): a famous actress in Holly Wood. She invented CDMA in 1941

DIRECT-SEQUENCE CDMA

The signal of DS-CDMA:

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˜ x (t) = x(t)c(t)

Information signal

Wideband PN

waveform

PN WAVEFORM C(T)

We consider rectangle pulses (called chips)

The correlation function is given by

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R τ( ) = Λτ

Tc

⎛

⎝ ⎜

⎞

⎠ ⎟

OUTPUT SPECTRUM

The spectrum of the output signal is given by

is called the bandwidth expansion factor (also called processing gain), which ranges from 10 to 10,000.

The wideband noise-like signal would be hard to distinguish from background noise at an authorized receiver.

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G ˜ x = Gx ( f )∗Gc ( f ) ≈ SxGc ( f )

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Wc /Wx

DS-CDMA RECEIVER

PERFORMANCE OF RECEIVER

When there is noise, the bit error rate is given by

When there is a single-tone jammer, the big error rate is given by

is called the jamming margin.

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Pe = Q 2Eb /N( )

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Pe = Q2Pg

J /SR

⎛

⎝ ⎜

⎞

⎠ ⎟

Processing gain

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10log J /SR( )

MULTIPLE ACCESS

Suppose a user shares the spectrum with M-1 other users. The interference is given by

The bit error rate is then given by (noiseless case)

The interference is like background noise.

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z(t) = Am xm (t − tm )cm (t − tm )m =1

M −1

∑ cosθ m

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Pe = Q 3Pg /(M −1)( )

HOMEWORK

Problem 1: Problem 15.1-1

Problem 2: Problem 15.1-2

Problem 3: Compute the bit error rate of DS-CDMA using QPSK in presence of noise (we have obtained the expression for BPSK in Eq. (6), page 726)