Selected Topics in DSP for Wireless

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Selected Topics in DSP for Wireless

• Jean-Paul M.G. Linnartz
• Nat.Lab., Philips Research

2
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

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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

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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
Transmit Signal
S
Locally stored reference copy of transmit signal
Channel Noise
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The Matched Filter Principle
Locally stored reference copy of transmit signal
for 0
Transmit Signal, either S0(t) for 0 or
S1(t) for 1
S0(t)
Select largest
Integrate
S
S
Channel Noise
Integrate
S1(t)
Locally stored reference copy of transmit signal
for 1
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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

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Methods for obtaining multiple replicas

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

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Antenna (or micro) diversity.

• - at the mobile
• Covariance of received signal amplitude
• J02(2pfDt) J02(2pd/?).
• antenna spacing of ?/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.

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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"

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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.

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Frequency diversity

• Each message is transmitted at different carrier
  frequencies simultaneously
• Frequency separation gtgt coherence bandwidth

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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.

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Selection Methods

• Selection Diversity
• Equal Gain Combining
• Maximum Ratio Combining
• Advanced filtering
• if interference is present
• wiener filtering (MMSE), smart antennas,
  adaptive beam steering, space-time coding
• Post-detection combining
• Signals in all branches are detected separately
• Baseband signals are combined.

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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.

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Exercise Selection Diversity

• The fade margin of a Rayleigh-fading signal is h.
• 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?

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Solution Diversity

• Diversity rule
• Select strongest signal.
• Outage probability for selection diversity
• Pr(max(p) lt pthr) Pr(all(p) lt pthr) Pi
  Pr(pi lt pthr)
• For L-branch selection diversity in Rayleigh
  fading

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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
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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.

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Diversity Combining Methods

• Each branch is
• co-phased with the other branches
• weighted by factor ai where ai depends on
  amplitude ri
• Selection diversity
• ai 1 if ?i, gt ?j, for all j ? i and 0
  otherwise.
• Equal Gain Combining ai 1 for all i.
• Maximum Ratio Combining ai ?i.

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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

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Comparison
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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.

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Direct Sequence CDMA
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Direct Sequence

• User data stream is multiplied by a fast code
  sequence
• Example
• User bits 101 ( - )
• Code 1110100 ( - - -) spead factor 7

User bit
1
User bit
-1
User bit
1
-1
0
1
1
-1
-1
-1
1
1
1
-1
1
1
1
-1
-1
-1
1
-1
-1
-1
1
1
1
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User separation in Direct Sequence

• Different users have different (orthogonal ?)
  codes.

Integrate
User Data 1
S
Code 1 c1(t)
Code 1
User Data 2
Code 2 c2(t)
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Multipath Separation in DS

• Different delayed signals are orthogonal

Integrate
User Data 1
S
Code 1 c1(t)
Code 1
Delay T
St ci(t) ci(t) M St ci(t) ci(tT) 0
if T ? 0
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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

correlation
R(k) M
k
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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.

One column is the code for one user
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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

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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

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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 1
MS 2
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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

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IS-95 BS Transmitter
W0
Pilot DC-signal
W0
Combining, weighting and quadrature modulation
Sync data
Wj
User data
Block interleaver
Convol. Encoder
PNI
Long code
PNQ
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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 1
MS 2
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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.

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Rake receiver

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

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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
Transmit Signal
S
Locally stored reference copy of transmit signal
Channel Noise
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Matched Filter with Dispersive Channel

• What is an optimum receiver?

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Rake Receiver

• 1956 Price Green
• Two implementations of the rake receiver
• Delayed reference
• Delayed signal

Integrate
S
Ref code sequence
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BER of Rake

• Ignoring ISI, the local-mean BER is
• where
• with gi the local-mean
• SNR in branch i.

J. Proakis, Digital Communications,
McGraw-Hill, Chapter 7.
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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)

Spectrum efficiency bits/chip
Optimum
MMSE
Decorrelator
Matched F.
Eb/N0
Source Sergio Verdu
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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?