ECE 442 COMMUNICATION SYSTEM DESIGN LECTURE 4. SPREAD SPECTRUM Husheng Li Dept. of EECS The University of Tennessee.

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)