EE360 – Lecture 5 Outline• Announcements:

– Revised lecture 4 slides (minus typos) posted– Paper summary deadlines: 4/27, 5/23– Project deadlines: Abstract 5/11, Progress report 6/6

• MAC Channels• Time Division and GSM• Direct Sequence Spread Spectrum• Frequency Hopping• Tradeoffs• User Capacity

Multiple Access Channels

• Multiple users transmitting to a single receiver• Signals have different path gains (near-far problem)• Channel can be divided using TD, FD, or CD

Time Division Frames

Preamble Information Message Guard Time

Frame (Tf)

Slot 1 Slot 2 Slot 3 Slot N...

Header SynchBits

Control,Signaling CRCInfo. Bits

(Training)GuardTime

• In TDD half the slots are for upstream traffic and half for downstream traffic• Generic structure: not all frames used in all systems, and order may vary

Frame Details

• Preamble contains address and sync information used by base and mobile

• Guard times allow sync of receivers between different frames

• Users are assigned a position in each frame (delay of Tf between bursts)

• Superframes (frames of frames) may have additional control frames

Slot Structure• Header: guard (ramp) time for receiver synch. between slots

• Synch: Used to establish bit synch (also for equalizer training)

• Control: Used for handshaking, control, and supervisory messages

• Info. Bits: Coded or uncoded information bits, may include pilot symbols/sequences for channel measurement and equalizer training.

• Guard Time: Prevents overlap at base of slots arriving from different terminals.

Requirements• Equalizer requirements: adaptive equalizer must compensate for time-varying ISI.

– Minimum N=/Ts symbols for training.– For =20sec and Rb=280 Kbps, N=6 minimum (GSM: N=26)– If Tf~Tc, need to retrain every frame (GSM: Tf=4.615 ms, Tc=1/fD=12.5ms for

fD=80 Hz, retrains every frame).

• Guard time requirements: must compensate for LOS propagation delay (R/c for R the cell radius) and delay spread due to multipath (reverse link only).– No delay spread: Tg>R/c=3.3 sec for R=1Km.– Do not need guard time for LOS propagation delay if base station synchronizes

to received (instead of transmitted) signal.– With delay spread : Tg>R/c+, but typically have a smaller guard time.

GSM Slots

• Multiframe has 26 frames (each frame is 4.615ms), with 24 for data and 2 for control. Each call in progress assigned a control channel.

• Slot time is 577s• 26b equalizer training designed to handle delay spread up

to 20 sec. (equalizer design not part of spec.)• Guard time less than maximum • Flag bits distinguish voice from data• Transmission rate approx. 270 Kb/s

Tail3b

Guard8.25s

Data57b

Flag1b

Equal. Train26b

Flag1b

Data57b

Tail3b

Spread Spectrum MAC• Basic Features

– signal spread by a code– synch. between pairs of users– compensation for near-far problem (in MAC channel)– compression and channel coding

• Spreading Mechanisms– direct sequence multiplication– frequency hopping

Note: spreading is 2nd modulation (after bits encoded into digital waveform, e.g. BPSK). DS spreading codes are inherently digital.

Direct Sequence

• Chip time Tc is N times the symbol time Ts.• Bandwidth of s(t) is N+1 times that of d(t).• Channel introduces noise, ISI, narrowband and multiple access interference.

– Spreading has no effect on AWGN noise– ISI delayed by more than Tc reduced by code autocorrelation– narrowband interference reduced by spreading gain.– MAC interference reduced by code cross correlation.

LinearModulation.(PSK,QAM)

d(t)X

Sci(t)

SS Modulator

s(t)Channel X

Sci(t)

Linear Demod.

SS Demodulator

Synchronized

BPSK Exampled(t)

sci(t)

s(t)

Tb

Tc=Tb/10

Spectral Properties

Original Data Signal

Narrowband Filter

Other SS Users

Demodulator Filtering

ISI

Modulated Data

Data Signal with Spreading

Narrowband Interference

Other SS Users

Receiver Input

ISI

8C32810.117-Cimini-7/98

Code PropertiesAutocorrelation:

Cross Correlation

• Good codes have ()=() and ij()=0 for all .– ()=() removes ISI– ij()=0 removes interference between users– Hard to get these properties simultaneously.

sT

cicis

dttstsT 0

)()(1)(

sT

cjcis

ij dttstsT 0

)()(1)(

ISI Rejection• Transmitted signal: s(t)=d(t)sci(t).• Channel:h(t)=(t)+(t-).• Received signal: s(t)+s(t-)• Received signal after despreading:

• In the demodulator this signal is integrated over a symbol time, so the second term becomes d(t-)().– For ()=(), all ISI is rejected.

)()()()()()()()()()()( 2

tststdtdtststdtstdtstr

cici

cicicici

MAC Interference Rejection• Received signal from all users (no multipath):

• Received signal after despreading

• In the demodulator this signal is integrated over a symbol time, so the second term becomes

– For ij()=0, all MAC interference is rejected.

)()()()()()()(,1

2 tststdtstdtstr cijcj

M

ijjjjciici

)()()()(11

j

M

jcjjjj

M

jj tstdtstr

)()(,1

jij

M

ijjjj td

Walsh-Hadamard Codes

• For N chips/bit, can get N orthogonal codes• Bandwidth expansion factor is roughly N.• Roughly equivalent to TD or FD from a capacity

standpoint• Multipath destroys code orthogonality.• Used in IS-95 MAC

Semi-Orthogonal Codes• Maximal length feedback shift register sequences have good

properties– In a long sequence, equal # of 1s and 0s.

• No DC component– A run of length r chips of the same sign will occur 2-rl times in l chips.

• Transitions at chip rate occur often.– The autocorrelation is small except when is approximately zero

• ISI rejection.– The cross correlation between any two sequences is small (roughly ij=G-

1/2 , where G=Bss/Bs)• Minimizes MAC interference rejection

Frequency Hopping

• Spreading codes used to generate a (slow or fast) “hopping” carrier frequency for d(t).• Channel BW determined by hopping range.

– Need not be continuous.• Channel introduces ISI, narrowband, and MAC interference

– Hopping has no effect on AWGN– No ISI if d(t) narrowband, but channel nulls affect certain hops.– Narrowband interference affects certain hops.– MAC users collide on some hops.

NonlinearModulation.(FSK,MSK)

d(t)

Sci(t)

FH Modulator

s(t)Channel

Nonlinear Demod.

FH Demodulator

VCO

FMMod

VCO

FMDemod

Sci(t)

Spectral Properties

Di(f-fc)

Dj(f-fc)

1 3 2 4

1 2 34

Slow vs. Fast Hopping

• Fast Hopping - hop on every symbol– NB interference, MAC interference, and channel nulls affect just one

symbol.– Correct using coding

• Slow Hopping - hop after several symbols– NB interference, MAC interference, and channel nulls affect many

symbols.– Correct using coding and interleaving if # symbols is small.– Slow hopping used in cellular to average interference from other cells

FH vs. DS• Linear vs. Nonlinear

– DS is a linear modulation (spectrally efficient) while FH is nonlinear

• Wideband interference/jamming– Raises noise spectral density, affects both techniques equally.

• Narrowband interference/jamming– DS: interfering signal spread over spread BW, power reduced by spreading gain in demodulator– FH: interference affects certain hops, compensate by coding (fast hopping) or coding and interleaving (slow

hopping).

• Tone interference– DS: tone is wideband, raises noise floor for duration of the tone. Compensate by coding (tone

duration=symbol time) or coding and interleaving (tone duration>symbol time). Similar affect as NB interference in FH.

– FH: Tone affects certain hops. Compensate by coding or coding and interleaving.

FH vs. DS• ISI Rejection

– DS: ISI reduced by code autocorrelation.– FH: ISI mostly eliminated.

• MAC interference– DS: MAC interference reduced by cross correlation of spreading codes. Each additional user raises noise

floor.• Overall SNR reduced

– FH: MAC interference affects certain hops. Each additional user causes more hops to be affected.• More bits likely to be received in error.

• Overlay systems: high-power NB interferers– Similar impact as with regular interferers– DS: Noise floor raised significantly – FH: Hops colliding with interferers are lost– Can notch out interfering signals

Evolution of a Scientist turned Entrepreneur

• “Spread spectrum communications - myths and realities,” A.J. Viterbi, IEEE Comm. Magazine, May ‘79 (Linkabit 5 years old - A TDMA company).

• “When not to spread spectrum - a sequel,” A.J. Viterbi, IEEE Comm. Magazine, April 1985 (Linkabit sold to M/A-Com in 1982)

• “Wireless digital communications: a view based on three lessons learned,” A.J. Viterbi, IEEE Comm. Magazine, Sept.’91. (Qualcomm CDMA adopted as standard).

Myths and Realities• Myth 1: Redundancy in error correction codes spreads signal bandwidth and thereby

reduces processing gain – Reality: Effective processing gain increased by coding by considering symbol rate and

energy– Reality today: coded modulation more efficient even without symbol argument. But

tradeoffs between coding and spreading an open issue.

• Myth 2: Error correction codes only good against uniform interference– Reality: Not true when coding combined with spread spectrum, since SS averages

interference. – Reality today: Unchanged.

• Myth 3: Interleaving destroys memory which can be used to correct errors, hence interleaving is bad

– Reality: Memory preserved by soft-decisions even with an interleaver – Reality today: Unchanged, but interleavers may require excessive delays for some

applications.

• Myth 4: Direct sequence twice as efficient as frequency hopping– Myth=Reality. Argument is that DS is coherent and that accounts for 3dB

difference. Analysis shows that higher level signaling alphabets does not help FH performance with partial band jammer.

– Reality today: A true efficiency tradeoff of FH versus DS has not been done under more general assumptions. FH typically used to average interference. Appealing when continuous spreading BW not available.

When not to Spread Spectrum - A Sequel

• Conclusion 1: When power is limited, don’t contribute to the noise by having users jam one another.

• Conclusion 2: Network control is a small price to pay for the efficiency afforded by TDMA or FDMA– Power control is a big control requirement.

• Conclusion 3: Interference from adjacent cells affects the efficiency of TDMA or FDMA less severely than in CDMA.

• Conclusion 4: Treating bandwidth as an inexpensive commodity and processing as an expensive commodity is bucking current technology trends.

• Caveat: Application was small earth terminals for commercial satellits.

Three Lessons Learned

• Never discard information prematurely

• Compression can be separated from channel transmission with no loss of optimality

• Gaussian noise is worst case. Optimal signal in presence of Gaussian noise has Gaussian distribution. So self-interference should be designed as Gaussian.

Realities• Never discard information prematurely

– Use soft-decisions and sequence detectors, if complexity okay.• Compression can be separated from channel transmission

– For time-invariant single-user channels only.• Self-interference should be designed as Gaussian

– Based on Viterbi’s argument, this represents a saddle (not optimal) point.

– If the self-interference is not treated as interference, then Gaussian signaling is suboptimal (by Shannon theory).

MAC Capacity• User Capacity

– How many users can be accommodated in the channel given performance specs.

- Assumes identical users and white noise model for interference

• Shannon Capacity Region– Upper bound on rate vector that all users can achieve

simultaneously– No complexity or delay constraints.– Optimal signaling and reception (unless constraints are added)– Asymptotically small error probabilty.– Signals from other users not treated as interference

User Capacity• Applicable to CDMA, since TDMA and FDMA have fixed capacity

(# of channels).

• S/(N+I(M)) determined based on the total number of users M and the system model.– Can be deterministic or random (fading).– Interference I(M) modeled as AWGN

• Based on the modulation, coding, channel model, etc., we find the probability of bit error Pe=f[S/(N+I(M))]

• For a given performance Pe we invert the above expression to get the maximum possible M.– Often set N=0 to simplify inversion, implies an interference-

limited system.

Probability of Error• Coherent BPSK: for m users, and a spreading gain G:

• m is typically random. For L total users each with probability p of active transmission and voice activity factor :

2/1

320

G

m

bE

NQPe

mkmmkkLpkp

kL

QPG

m

bE

NL

k

k

me

)1()1(2/1

320

0 0

Note that Pe is concave in m

Pe Approximation

• By concavity of Pe and Jensen’s inequality:

.,2/1

~32

0 LpMQePePG

M

bE

N

Use RHS as approximation for Pe

``Spread spectrum for mobile communications”, Pickholtz, Milstein, Schilling

Effective Energy/Symbol

– M is average number of active users.– r is the code rate– K is the out-of-cell interference ratio (equals zero for a purely MAC

channel) – is the voice activity factor– N is the number of chips per symbol– Factor of 2/3 assumes rectangular pulses, will decrease for other shapes.– Assumes no ISI, flat-fading, or diversity gain.

)1(

320

0

KMNr

EN

NE

seff

s

Required Es/N0• Target Pe

• Invert target Pe to get required Es/N0

• Example: DPSK

targete

reqdo

se P

NEP

1target

e

reqdo

s PNE

targetln5. ereqdy

e PeP

Often cannot get reqd in closed form: Must usenumerical techniques or obtain from BER curve.

User Capacity• Total number of users the MAC channel can support:

• A rougher approximation

reqd

s

NEGM

0

1

Channel coding and interference mitigation increase user capacity

reqd

ssreqd

s

NEaK

GEN

NE

aKGM

0

0

1

0

1)1(2

3)1(2

31

SS vs. Narrowband

• BPSK at a BER of 10-4 requires Es/N07.4dB• Consider a two-user (M=2) DSSS system:

reqds NEGM ]//[1 0

G24568

S/I (dB) 3 6 7 7.8 9

Two-user DSSS system requires spreading gain of 5-6 to getdesired BER, TD system could fit 5-6 users in this bandwidth

Argument for DSSS based on frequency reuse and soft capacity

7.4