Selected Topics in DSP for Wireless

Jean-Paul M.G. LinnartzNat.Lab., Philips Research

DSP aspects

• Source Coding (Speech coding)• Synchronization• Detection and matched filtering• Diversity and rake receivers• Multi-user detection• Equalization or subcarrier retrieval• Error Correction• Security & cryptographic algorithms

Outline

The Matched Filter PrincipleDiversity

– Diversity Techniques: The choice of the domain– Diversity Techniques: The signal processing – Performance– Space time coding

Code Division Multiple Access– Direct Sequence Basics– Rake receiver

The Matched Filter Principle

The optimum receiver for any signal – in Additive white Gaussian Noise– over a Linear Time-Invariant Channel

is ‘a matched filter’:Integrate

Locally stored reference copy of transmit signal

Channel Noise

Transmit Signal

The Matched Filter Principle

Integrate

Locally stored reference copy of transmit signal for “1”

Channel Noise

Transmit Signal, either S0(t) for “0”

or S1(t) for “1”

Integrate

Locally stored reference copy of transmit signal for “0”

S1(t)

S0(t)

Select largest

Fundamentals of Diversity Reception

What is diversity?• Diversity is a technique to combine several copies of the same

message received over different channels.

Why diversity?• To improve link performance

Methods for obtaining multiple replicas

• Antenna Diversity• Site Diversity • Frequency Diversity• Time Diversity• Polarization Diversity• Angle Diversity

Antenna (or micro) diversity.

- at the mobile– Covariance of received signal amplitude

J02(2πfDτ) = J0

2(2πd/λ).– antenna spacing of λ/2 is enough

- at the base station– All signal come from approximately the same direction– received signals are highly correlated– Larger antenna separation needed– Relevant parameter:

• distance between scattering objects antenna (typically, a is 10 .. 100 meters), and

• distance between mobile and base station.

Site (or macro) diversity

• Receiving antennas are located at different sites. – Example: at the different corners of hexagonal cell.

• Advantage: multipath fading, shadowing, path loss and interference all become "independent"

Angle diversity

• Waves from different angles of arrival are combined optimally, rather than with random phase

• Directional antennas receive only a fraction of all scattered energy.

Frequency diversity

• Each message is transmitted at different carrier frequencies simultaneously

• Frequency separation >> coherence bandwidth

Time diversity

• Each message is transmitted more than once.• Useful for moving terminals• Similar concept: Slow frequency hopping (SFH): • blocks of bits are transmitted at different carrier

frequencies.

Selection Methods

• Selection Diversity• Equal Gain Combining• Maximum Ratio Combining

• Advanced filtering – if interference is present– wiener filtering (MMSE), smart antenna’s, adaptive beam

steering, space-time coding

• Post-detection combining: – Signals in all branches are detected separately– Baseband signals are combined.

Pure selection diversity

Select only the strongest signal• In practice: select the highest signal + interference +

noise power. • Use delay and hysteresis to avoid ping-pong effects

(excessive switching back and forth)

Simple implementation: Threshold Diversity• Switch when current power drops below a threshold• This avoids the necessity of separate receivers for

each diversity branch.

Exercise: Selection Diversity

• The fade margin of a Rayleigh-fading signal is .• A receiver can choose the strongest signal from L

antennas, each receiving an independent signal power.

What is the probability that the signal is x dB or more below the threshold?

Solution: Diversity

Diversity rule: Select strongest signal.

Outage probability for selection diversity: Pr(max(p) < pthr) = Pr(all(p) < pthr) = i Pr(pi < pthr)

For L-branch selection diversity in Rayleigh fading:

Pr max( ) / exp /p p - L 1 1

Outage Probability Versus Fade Margin

•Performance improves very slowly with increased transmit power•Diversity Improves performance by orders of magnitude•Slope of the curve is proportional to order of diversity•Only if fading is independent for all antennas

Better signal combining methods exist: Equal gain, Maximum ratio, Interference Rejection Combining

Performance of Diversity

In a fading channel, diversity helps to improve the slope of the BER curve.

Explain why coding can play the same role.Diversity can be used to combat noise and fading, but

also to separate different user signals.

Diversity Combining Methods

Each branch is • co-phased with the other branches • weighted by factor ai where ai depends on

amplitude i

Selection diversity – ai = 1 if ρi, > ρj, for all j i and 0 otherwise.

Equal Gain Combining: ai =1 for all i. Maximum Ratio Combining: ai = ρi.

Maximum ratio combining

• Weigh signals proportional to their amplitude.

MRC: ai = constant ri

• This is the same as matched filter• After some math:

SNR at the output is the sum of the SNRs at all the input branches

Comparison

Technique: Circuit Complexity: C/N improvement factor:Threshold simple, cheap 1 + γT/Γ exp(-γT/Γ) for L = 2

single receiver optimum for γT/Γ: 1 + e 1.38Selection L receivers 1 + 1/2 + .. + 1/L

EGC L receivers 1 + (L - 1) π/4co-phasing

MRC L receivers Lco-phasingchannel estimator

Space-Time Coding (MIMO)

Multiple Input Multiple Output concept:

In a rich multipath environment, a system with N transmit antennas and M receive antennas can handle min(N,M) simultaneous communication streams.

Direct Sequence CDMA

Direct Sequence

User data stream is multiplied by a fast code sequence

Example: – User bits 101 (+ - +)– Code 1110100 (+ + + - + - -); spead factor = 7

EXORUser Bits

Code Sequence

1 -1 -1-111 1 -1 1 11-1-1 -1 1 -1 -1-111 1

User bit-1 = 1 User bit0 = -1 User bit+1 = 1

User separation in Direct Sequence

Different users have different (orthogonal ?) codes.

Integrate

Code 1

Code 1: c1(t)

User Data 1

User Data 2

Code 2: c2(t)t ci(t) cj(t) = M if i = j = “0” if i = j

Multipath Separation in DS

Different delayed signals are orthogonal

Integrate

Code 1

Code 1: c1(t)

User Data 1

t ci(t) ci(t) = M

t ci(t) ci(t+T) = “0” if T 0

Delay T

Popular Codes: m-sequences

Linear Feedback Shift Register Codes:• Maximal length: M = 2L - 1. Why?• Every bit combination occurs once

(except 0L)• Autocorrelation is 2L - 1 or -1

• Maximum length occurs for specific polynomia only

1

0)()()(

M

mkmcmckR

correlation:

R(k) M

k

D DD

= EXORaddition mod 2

Popular Codes: Walsh-Hadamard

Basic Code (1,1) and (1,-1)

– Recursive method to get a code twice as long

– Length of code is 2l

– Perfectly orthogonal– Poor auto correlation properties– Poor spectral spreading. E.g. all “1” code.

1 11 -1R2 = [ ]

R2i=[ ]

R4=[ ]

Ri Ri

Ri -Ri

1 1 1 11 -1 1 -11 1 -1 -11 -1 -1 1

One column is the code for one user

Cellular CDMA

IS-95: proposed by QualcommW-CDMA: future UMTS standard

Advantages of CDMA• Soft handoff• Soft capacity• Multipath tolerance: lower fade margins needed• No need for frequency planning

Cellular CDMA

Problems• Self Interference

– Dispersion causes shifted versions of the codes signal to interfere

• Near-far effect and power control– CDMA performance is optimized if all signals are received

with the same power – Frequent update needed – Performance is sensitive to imperfections of only a dB– Convergence problems may occur

Synchronous DS: Downlink

In the ‘forward’ or downlink (base-to-mobile): all signals originate at the base station and travel over the same path.

One can easily exploit orthogonality of user signals. It is fairly simple to reduce mutual interference from users within the same cell, by assigning orthogonal Walsh-Hadamard codes.

BS

MS 2MS 1

IS-95 Forward link (‘Down’)

• Logical channels for pilot, paging, sync and traffic. • Chip rate 1.2288 Mchip/s = 128 times 9600 bit/sec • Codes:

– Length 64 Walsh-Hadamard (for orthogonality users)– maximum length code sequence (for effective spreading and

multipath resistance

• Transmit bandwidth 1.25 MHz • Convolutional coding with rate 1/2

IS-95 BS Transmitter

PNIPNQ

Com

bining, weighting and

quadrature modulation

Pilot: DC-signal

W0

W0

WjUserdata

Long code

Blockinterleaver

Convol.Encoder

Sync data

EXOR (addition mod 2)

Asynchronous DS: uplink

In the ‘reverse’ or uplink (mobile-to-base), it is technically difficult to ensure that all signals arrive with perfect time alignment at the base station.

Different channels for different signalspower control needed

BS

MS 2MS 1

IS-95 Reverse link (‘Up’)

• Every user uses the same set of short sequences for modulation as in the forward link. Length = 215 (modified 15 bit LFSR).

• Each access channel and each traffic channel gets a different long PN sequence. Used to separate the signals from different users.

• Walsh codes are used solely to provide m-ary orthogonal modulation waveform.

• Rate 1/3 convolutional coding.

Rake receiver

A rake receiver for Direct Sequence SS optimally combines energy from signals over various delayed propagation paths.

DS reception: Matched Filter Concept

The optimum receiver for any signal – in Additive white Gaussian Noise– over a Linear Time-Invariant Channel

is ‘a matched filter’:Integrate

Locally stored reference copy of transmit signal

Channel Noise

Transmit Signal

Matched Filter with Dispersive Channel

What is an optimum receiver?

Channel Noise

Transmit Signal H(f)

Integrate

Locally stored reference copy of transmit signal

H-1(f)

Integrate

Locally stored reference copy of transmit signal

H(f)

H(f)

Rake Receiver

1956: Price & GreenTwo implementations of the

rake receiver:• Delayed reference• Delayed signal

Integrate

H(f)

D DD

Channel estimate

D DD

H*(f)Channel estimate

Ref code sequence

Ref code sequence

BER of Rake

Ignoring ISI, the local-mean BER is

where

with i the local-mean

SNR in branch i.

11

21

0 j

jL

jj

R

BER

j

j

j iii j

LR

1

J. Proakis, “Digital Communications”, McGraw-Hill, Chapter 7.

Wireless

LR = 1LR = 2

LR = 3

BER

Eb/N0

Advanced user separation in DS

More advanced signal separation and multi-user detection receivers exist.

• Matched filters• Successive subtraction• Decorrelating receiver• Minimum Mean-Square Error

(MMSE)

Optimum

MMSE

Decorrelator

Matched F.

Eb/N0S

pect

rum

ef

ficie

ncy

bits

/chi

p

Source: Sergio Verdu

Software radio

Many functions are executed in software anyhowThere are many different radio standards, multi-mode is

the way to go.Can we share functions?Can we realize a steep cost reduction on DSP

platforms?Architectural choices: • what to make in dedicated hardware?• what to do in programmable ‘filters’?• which operations are done by a general purpose

processor?