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Selected Topics in DSP for Wireless
Jean-Paul M.G. Linnartz
Nat.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 Principle
Diversity– 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
EXOR
User 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
m
kmcmckR
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 Qualcomm
W-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 signals
power 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
2
1
0 j
jL
jj
R
BER
j
j
j iii j
LR
1
J. Proakis, “Digital Communications”, McGraw-Hill, Chapter 7.
Wireless
LR = 1
LR = 2LR = 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/N0
Spe
ctru
m
effic
ienc
ybi
ts/c
hip
Source: Sergio Verdu
Software radio
Many functions are executed in software anyhow
There 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?