spread-spectrum modulation and cdmayiminzhang.com/ece8700/ece8700_2014_d_cdma.pdf · ece 8700...

ECE 8700 Communication System Engineering

Yimin Zhang, Villanova University 1

Spread-Spectrum Modulationand CDMA

Yimin Zhang, Ph.D.

Department of Electrical & Computer Engineering

Villanova University

http://yiminzhang.com/ECE8700



Summary of Multiple Access

FDMA

TDMA

CDMA

pow

er

pow

er

pow

er

CDMA is a multiple spread spectrum system.



Outlines

Spread-spectrum modulation

Direct sequence

SNR enhancement

Error probability

Frequency hopping


Pseudo-noise (PN) sequence

Code division multiple access (CDMA)



Why Spread-Spectrum

Several key advantages:

Resistant to interference (jamming)

Resistant to multipath interference

Low probability of interception

Multiple-access communications

Spectrum overlay

First introduced for military communications

Later known as the technique that supports CDMA



Generations of Mobile Systems

1st Generation (1G): Analog Transmission AMPS TACS (ETACS) NMT

2nd Generation (2G): Digital Transmission GSM CT2, CT3 (Cordless Telephone) DECT CDMA

3rd Generation (3G): Unification of technologies

FPLMTS (Future Public Land Mobile Telecommunication Systems) UMTS (Universal Mobile Telecom System) cdma2000, WCDMA (Wideband CDMA)



Second Generation Share



American Carriers

http://www.gizmodo.com.au/2010/09/giz-explains-the-difference-between-gsm-and-cdma/

More details explained in CDMA vs. GSM: What's the Difference?http://www.pcmag.com/article2/0,2817,2407896,00.asp



Spread Spectrum

• A technique in which the transmission bandwidth W and message bandwidth R are related as

W >> R

• The spectrum spreading is accomplished through the use of a code that is independent of the data sequence.

• Achieves several desirable objectives (e.g., data encryption, anti-jamming)

• Types of Spread Spectrum Communications– Direct Sequence– Frequency Hopping

• Slow Frequency Hopping - multiple symbols per hop• Fast Frequency Hopping - multiple hops per symbol



Direct-Sequence Spreading-Spectrum




X

=

“symbol”

“Barker” sequence

Result of multiplication

Symbol time ts“1” “0”

Chip time tc

• Due to the multiplication of a symbol with Barker code, the “rate-of-change” increases with a factor 11

• This means that cycle rate increases from 1 MHz to 11 MHz

• In terms of spectrum this means that after RF modulation the signal is spread from 2 MHz bandwidth to 22 MHz bandwidth

2 Mhz 22 Mhz



• At the receiver, the spread signal is multiplied again by a synchronized replica of the same code, and is “de-spread” and recovered.

• The outcome of the process is the original “symbol”.

RFDemodulator

Channeland

SourceDecoding

CodeGenerator

X

Multiplied

Code Bits (Chips)

De-SpreadSignal

f

“Spread” FrequencySpectrum

f

Digital Signal (Bits)






0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0-202

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0-202

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0-202

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0-202

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0-505

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0-505

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0-2 0

02 0

Spread Spectrum Communications

b(k)

c(n)c(n) n(t)

)(ˆ nb

b(k)

c(n)

n(t)

d(n)

d(n) y(t) (t)

y(t)

(t)

dtt )(



Direct Sequence

b1(k) d1 (n)

y1 (t)

Spectrum before spreading

Spectrum after spreading

Spectrum after despreading with c1(n)

desired signal

undesired signal(narrowband or wideband)

bp(k) dp (n)

f f

f

ff



Spreading Codes

Requirements for the codes:

(1) Demonstrate noise-like spectrum - Low interference to other systems (if sharing spectrum)- Resistant to jamming- Secure from interception

(2) Easy to distinguish a signal from its delayed version- Feasible for RAKE diversity- Also useful in distance measurement (e.g., radar, ITS)

(3) Easy to distinguish the signal of one user from those of otherusers- Very important in CDMA

Pseudo-noise (PN) sequence, Walsh, and other derivative codes are important codes to achieve these requirements.



Walsh Function

Different Walsh functions are orthogonal. Walsh function well satisfies the third requirement, but is not good for the other requirements.



0 2 4 6 8 10 12 14 16-2

0

2

0 2 4 6 8 10 12 14 16-2

0

2

0 2 4 6 8 10 12 14 16-2

0

2

0 2 4 6 8 10 12 14 16

0

2

4

-4 -2 0 2 4 6 8 10 12-2

0

2

-4 -2 0 2 4 6 8 10 12-2

0

2

-4 -2 0 2 4 6 8 10 12-2

0

2

-4 -2 0 2 4 6 8 10 12-10123

Walsh Function - Orthogonality

c1(n)

c2(n)

c1(n)* c2(n)

The orthogonality of Walsh functions is only satisfied when no delay is present.



PN Sequence

PN sequence provides low and constant autocorrelation for non-zero lags. It well satisfies the first two requirements, but is not necessarily good for the third requirement.

autocorrelation

N

-1 N



Feedback shift register.

PN Sequence

A pseudo-noise (PN) sequence - a periodic binary sequence with a noise-like waveform - usually generated by a feedback shift register



Maximal-length sequence generator with 3 flip-flops (m 3)

PN Sequence

States

1 0 0

1 1 0

1 1 1

0 1 1

1 0 1

0 1 0

0 0 1

1 0 0

…

Output

0

0

1

1

1

0

1

…

mjkksks jj 1,0),()1( 1 mjkksks jj 1,0),()1( 1



PN Sequence

A feedback shift register is said to be linear when the feedback logic consists entirely of modulo-2 adders.

With a total number of m flip-flops, the number of possible states of the shift register is at most 2m.

The zero state (all the flip-flops are in state 0) is not permitted, as then all the states will remain 0.

Therefore, for a PN sequence generated by a linear feedback shift register with m flip-flops, the maximum length is 2m–1.

When a PN sequence has a length of 2m–1, it is called a maximal-length-sequence, or simply m-sequence. (m-sequence is not unique.)



M-Sequence: Properties (1)

Balanced Property: In each period, the number of 1s is always one more than the number of 0s. [m=3: 4 1s, 3 0s; m=5: 16 1s, 15 0s. ]

Run property: Among the 2m–1 runs (subsequence of identical symbols) of 1s and of 0s (2m–2 runs for each of them) in each period, 1/2 the runs of each kind are of length 1 1/4 are of length 2 1/8 are of length 3 …(related to spectrum)

m=3 (2m–1= 7): 0 0 1 1 1 0 1

m=5 (2m–1=31): 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 0 0 1

(m=5: 16 runs)1s 0s

Length 1 4 4Length 2 2 2Length 3 1 1Length 4 0 1Length 5 1 0

(m=3: 4 runs)1s 0s

Length 1 1 1Length 2 0 1Length 3 1 0




Correlation Property:

The period of the waveform is

where

Autocorrelation function

cb NTT

12 mN

period theofremainder for the,1

|||,|11

)()(1)(2/

N

TNTN

tdtctcT

R

cc

T

Tb

cb

b




Correlation Property (con’t):

Difference between the autocorrelation function of a PN sequence and a binary random sequence? Periodic DC component of (-1/N).

Power spectral density: Discrete spectra (delta function)

[increasingly similar when N is large] Similar envelop Different DC component

0

222 sinc1)(1)(

nn c

c NTnf

Nn

NNf

NfS



M-Sequence



M-Sequence: Examples

M=5

[5, 2]This one is simpler in terms of hardware implementations.

[5, 4, 2, 1]




The spectrum of m(t) is the convolution of the spectra of b(t)and c(t). Thus, the bandwidth of m(t) is close to that of c(t).

Code c(t) expands the bandwidth and is referred to as the spreading code.

Spread spectrum communication is resistant to additive interference.

Transmitter Channel

)()()( tbtctm )()()()()()( titbtctitmtr




Receiver requires perfect synchronization (PN sequence lines up exactly with that in the transmitter).

After despreading, the desired signal becomes narrowband, whereas interference signal becomes wideband.

Proper low-pass filtering can significantly reduce the interference power.

Receiver)()()()()()()()()()( 2 titctbtitctbtctrtctz

=1



Direct Sequence / BPSK



Direct Sequence / BPSK

Equivalent model for analysisBecause the system is linear



Spread Spectrum : Anti-Jamming Performance

)()()( tstctx

tfTEts cb

b 2cos2

)(

)()()()()()( tjtstctjtxty

)()()()()()( tjtctstytctu

tfT

t cb

2cos2)(




Input SNR

Output of the signal component after coherent detection

Output of the interference component after coherent detection

For simplicity, we assume that c(t) is random (not pseudo-random), and c(t) and j(t) are independent.

bcbb

bTTs Edttf

TTEdtttsv bb 2cos22

)()( 200

dttftctjT

dtttctjv cT

b

Tj

bb 2cos)()(2)()()(00

J

TE bbI

/SNR




Only the in-phase part of j, denoted as , has to be considered.

k

N

kk

b

c

kcTk

kT

N

kk

b

cTk

kT

N

kk

b

ckT N

kb

cT

bj

jcTT

dtTtjcT

dttftjcT

dttfctjT

dttftctjT

v

c

c

c

c

b

b

1

0

)1(1

0

)1(1

0

0

1

0

0

2)(2

2cos)(2

2cos)(2

2cos)()(2

JTjETT

jjEccETT

jjccETT

jcTTjc

TTEv

ck

N

kb

c

lk

N

kl

N

lk

b

c

lk

N

kl

N

lk

b

c

l

N

ll

b

ck

N

kk

b

cj

2][

][][

][

]var[

21

0

1

0

1

0

1

0

1

0

1

0

1

0

dttfT c

ck 2cos2

Basic function corres-ponding to a chip period

1

0

2||1 N

kk

bj

TJ

Average power of interference

Only real-part

j

0][ jvE




Output SNR

Input SNR

SNR enhancement

Where the factor 2 is because that, the desired signal uses BPSK modulation (i.e., in-phase only), whereas the interference has both in-phase and quadrature components, if it does not know the signal phase.

The ratio Tb/Tc denotes the process gain (PG) due to spectrum spreading, denoted as PG = Tb/Tc.

c

b

c

bO JT

EJT

E 22/

SNR

J

TE bbI

/SNR

c

b

I

O

TT2

SNRSNR




Example: A direct-sequence spread BPSK system uses a feedback shift register of length 19 for the generation of the PN sequence. Calculate the process gain (PG) of the system.

Solution: m=19period of the m-sequence: N=219-1=524288

(There are 524288 chips in each bit interval)

PG = 10 log10N = 10log10524288=57.2 dB




If the jammer does not have any information about its spreading code and phase, it distribute its energy to all the dimensions.

For BPSK signal with PG=N, it spans one of the 2N-dimensional signal subspace.

Therefore, the jamming signal is reduced by a factor of 2N.

Approximate vj as Gaussian (due to central limit theorem), the probability of error is given by

JTEPc

be erfc

21 JTN c

220 JTN c

220




Probability of Error

Jamming Margin (J/P):

0erfc

21

NEP b

e

PG/

0 JP

TT

JTE

JTE

NE

c

bbb

c

bb

JTN c

220

0/PG

NEPJ

b

min010dBdB log10)gain Processing()margin Jamming(

NEb

Jamming Margin



Frequency Hopping

Slow FH Fast FH

Next, we show some examples of FH/MFSK systems.

Process gain due to FH is

PG = Wc/Rs

(see Wc and Rs at the next page)



Frequency Hopping Example



Frequency Hopping Spread Spectrum System (Transmitter)



Frequency Hopping Spread Spectrum System (Receiver)



Slow Frequency Hopping: Example

# of bits per symbol: K=2

# of MFSK tone: M=2K=4

Length of PN segment per hop: k=3

Total # of frequency hops: 2k=8

Variation of the dehopped frequency with time.

sh RR21

sh RR21



Fast Frequency Hopping: Example

# of bits per symbol: K=2

# of MFSK tone: M=2K=4

Length of PN segment per hop: k=3

Total # of frequency hops: 2k=8

Variation of the dehopped frequency with time.

sh RR 2 sh RR 2ECE 8700 Communication System Engineering


Freq.Freq.

BPFDespreader

Code B

Freq.Freq.

BPFDespreader

Code A

DS-CDMA System Overview (Forward link)

Data B

Code B

BPF

Freq.Freq.•••

Data A

Code A

BPF

Freq.Freq.

MS-A

•••

MS-B

BS

Data A

Data B



Freq.Freq.

BPFDespreader

Code B

Freq.Freq.

BPFDespreader

Code A

DS-CDMA System Overview (Reverse Link)

Data B

Code B

BPF

Freq.Freq.

•••

Data A

Code A

BPF

Freq.Freq.

•••

MS-B

MS-A

BS

Data A

Data B



Multi-path Fading

Base Station (BS)Mobile Station (MS)

multi-path propagation

Path Delay

Pow

er

path-2

path-2path-3

path-3

path-1

path-1



Rake Receiver

Because CDMA has high time-resolution,different path delay of CDMA signals

can be discriminated.•••Therefore, energy from all paths can be summed

by adjusting their phases and path delays.••• This is a principle of RAKE receiver.

Path Delay

Pow

er path-1

path-2

path-3

CDMAReceiver

CDMAReceiver

•••

Synchronization

Adder

Path Delay

Pow

er

CODE Awith timing of path-1

path-1

Pow

er

path-1

path-2

path-3

Path Delay

Pow

er

CODE Awith timing of path-2

path-2

interference from path-2 and path-3

•••



Frequency Reusing

f1

f4

f3

f6

f7

f1

f2

f2

f5

f4

f7

f1

f2

f3

f1

f1

f1

f1

f1

f1

f1

f1

f1

f1

f1

f1

f1

f1

f3

f6

f1

f1

TDMA CDMA



Soft Handoff

Σ

Cell B Cell A

Soft handoff : break (old cell A) after connect (new cell B)

transmitting same signal from both BS A and BS B simultaneously to the MS

In CDMA cellular system, communication does not break even at the moment doing handoff, because switching frequency or time slot is not required.



Power Control in CDMA

• CDMA goal is to maximize the number of simultaneous users

• Capacity is maximized by maintaining the signal to interference ratio at the minimum acceptable

• Power transmitted by mobile station must be therefore controlled – enough to achieve target BER: no less no more

– Open loop (Reverse link based on forward link channel gain)

– Closed loop (Base station send feedback to mobile station)



Outlines


Direct sequence

SNR enhancement

Error probability

Frequency hopping


Pseudo-noise (PN) sequence

Code division multiple access (CDMA)



Homework

Review material: Sections 9.13 – 9.15

No Homework

Final grade will be notified by Friday.

This concludes the course…

It was happy “meeting” you all, and best wishes!

spread-spectrum modulation and cdmayiminzhang.com/ece8700/ece8700_2014_d_cdma.pdf · ece 8700...

Documents