CDMA - DS/SS and Related Topics / EPUSP / P. J. E. Jeszensky / 2004

Multiple Access Techniques FDMA: Frequency Division Multiple Access (one carrier for each user for all connection time)

Time

1

2

3

4

Frequency 1

CDMA - DS/SS and Related Topics / EPUSP / P. J. E. Jeszensky / 2004

TDMA: Time Division Multiple Access (one carrier for a group of users in a time division principle)

Time 3 2 1

Frequency 2

CDMA - DS/SS and Related Topics / EPUSP / P. J. E. Jeszensky / 2004

CDMA: Code Division Multiple Access

(one carrier for all users for all time in a code division principle)

Time 1,23 MHz Frequency 3

CDMA - DS/SS and Related Topics / EPUSP / P. J. E. Jeszensky / 2004

CDMA Philosophy

Swedish

Japanese

English

French

Hungarian

Greek 4

CDMA - DS/SS and Related Topics / EPUSP / P. J. E. Jeszensky / 2004

Some General Characteristics DS/SS Block Diagram

t = kT

Data Source

∫(••) dt

Channel

p(t)

Acos(ωct)

cos(ωct)

p(t)

S(dB)

Bworiginal Bwspread

Freq (MHz) 5

CDMA - DS/SS and Related Topics / EPUSP / P. J. E. Jeszensky / 2004

Power Spectral Densities (PSD) of DS/SS Signals

BPSK signal with power P, carrier frequency fo and a data rate Rb=1/Tb

PTb G (f ) = [sinc 2 (f − f 0 )Tb + sinc 2 (f + f 0 )Tb ] 2 6

CDMA - DS/SS and Related Topics / EPUSP / P. J. E. Jeszensky / 2004

Previous BPSK signal spread by a code with a chip rate Rc=1/Tc - Note that spreading maintains unchanged the total power P; - The ratio G = Rc/Rb = Tb/Tc is known as processing gain and determines the interference rejection capability. 7

CDMA - DS/SS and Related Topics / EPUSP / P. J. E. Jeszensky / 2004

Previous signal and a centred tonal jammer with power J at receiver’s input

8

CDMA - DS/SS and Related Topics / EPUSP / P. J. E. Jeszensky / 2004

The composed signal at detector’s input, r(t), can be written as

r ( t ) = s( t ) + j( t ) s( t ) = 2Pd ( t )p( t )co(ω0 t + ϕ) j( t ) = 2J cos ω0 t Admitting a perfect code synchronism (i. e., p(t) has exactly recovered in the synchronism stage ⇒ p2(t) = 1) after de-spreading we have

r ' ( t ) = r ( t )p( t ) = s' ( t ) + j' ( t ) s' ( t ) = 2Pd( t )co(ω0 t + ϕ) j' ( t ) = 2J p( t ) cos ω0 t Therefore the de-spread effect is to return the desirable signal to its original form and to spread the interference (next slide). 9

CDMA - DS/SS and Related Topics / EPUSP / P. J. E. Jeszensky / 2004

R (SNR)D = P × c J R b

Previous signals now at detector’s output This set of PSD figures shows the interference rejection capability and also the low probability of interception (LPI) for DS-SS signals. 10

CDMA - DS/SS and Related Topics / EPUSP / P. J. E. Jeszensky / 2004

DS/SS Signals Synchronism Synchronism is a two step task: acquisition and tracking. The two more usual acquisition methods are: Serial Search and Matched Filter. After the acquisition stage (which guarantees a Tc/2 uncertainty for the delay between received and local codes) the tracking loop is started. The two more usual tracking loops are: DLL-Delay Lock Loop and Tau-Dither. Acquisition and tracking are based on the well known code sequences autocorrelation function (maximal length in the figure) R(.)

- Tc

L

-1

Tc

11

CDMA - DS/SS and Related Topics / EPUSP / P. J. E. Jeszensky / 2004

Acquisition by Serial Search (Sliding Window)

λ ⋅Tc

Received Code

∫

Comparison

Threshold & Decision

0

Code Generator

Search Control

- Each successive search is carried out at Tc/2 intervals (i. e., 2L possible intervals where L is the code length); - The mean acquisition time is given by Ta cq = LλTc where λ is a fraction of full sequence period, i. e.,

0 < λ ≤ L and its

value is a compromise between Tacq and false alarm probability; - Less complexity × Greater acquisition time. 12

CDMA - DS/SS and Related Topics / EPUSP / P. J. E. Jeszensky / 2004

Acquisition by Matched Filters λ ⋅Tc

∫ 0

p[t] λ ⋅Tc

Received Code

∫ 0

Comparison

Decision

p[t-Tc/2] λ ⋅Tc

∫ 0

p[t-(2L-1).Tc/2]

- All 2L possible search positions are checked in a parallel way; - The acquisition time is given by

Ta cq = λTc

- More complexity × Smaller acquisition time. 13

CDMA - DS/SS and Related Topics / EPUSP / P. J. E. Jeszensky / 2004

DLL-Delay Lock Tracking Loop The DLL starts after the acquisition stage which means that | τ | < Tc / 2. to demodulator X

d ( t ) p( t ) cos( ω 0 t + ϕ)

BPF f , 2Rb o

X (2)

e

envelope detector

1

(3)

PN code generator

+

Y

clock ( VCO )

loop filter -

(1) BPF f , 2Rb o

X

(1) p ( t +

Tc + τ) 2

( 2) p ( t −

Tc + τ) 2

envelope detector

e

(3) p ( t + τ)

τ≤

2

The tracking performance is based on the Y signal which acts as the VCO control signal (next figure).

Tc 2

14

CDMA - DS/SS and Related Topics / EPUSP / P. J. E. Jeszensky / 2004

Y

R PN ( τ − Tc / 2) − 3Tc / 2

τ

Tc / 2 − Tc / 2

3Tc / 2

R PN ( τ + Tc / 2)

In the range ±Tc / 2 the Y signal is a linear function of the delay and therefore this signal can be used to drive the VCO whose equilibrium point is Y=0.

15

CDMA - DS/SS and Related Topics / EPUSP / P. J. E. Jeszensky / 2004

Tau-Dither Tracking Loop The Tau-Dither tracking loop is a time sharing version of DLL with only one correlator circuit avoiding therefore any mismatch between correlators. d(t)p(t) cos(ω0 t + ϕ) X

g(t) BPF f , 2Rb o

envelope detector

X

loop filter

(1) Selector

PN generator

clock ( VCO )

(2) g(t)

(1) p (t +

Tc T + τ) ( 2 ) p (t − c + τ) 2 2

τ≤

Tc 2

The dither function g(t) (unitary bipolar square wave signal) selects the local code early or late version and also, in correspondence, the signal of the envelope detector output. See reference [22] for additional details. 16