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Shivkumar KalyanaramanIBM Research - India
1
Point-to-Point Wireless Communication (II):ISI & Equalization,
Diversity (Time/Space/Frequency)
Shivkumar Kalyanaramanshivkumar-k AT in DOT ibm DOT com
http://www.shivkumar.orgGoogle: “shivkumar ibm rpi”
Based upon slides of P. Viswanath/Tse, Sorour Falahati, Takashi Inoue, J. Andrews, Scott Baxter,& textbooks by Tse/Viswanath, A. Goldsmith, J. Andrews et al, & Bernard Sklar.
Ref: Chapter 3 in Tse/Viswanath texbook
Shivkumar KalyanaramanIBM Research - India
2
Multi-dimensional Fading
Time, Frequency, Space
Shivkumar KalyanaramanIBM Research - India
3
Base Station (BS)Mobile Station (MS)
multi-path propagation
Path Delay
Po
we
r
path-2
path-2path-3
path-3
path-1
path-1
Recall: Multipaths: Power-Delay Profile
Channel Impulse Response: Channel amplitude |h| correlated at delays . Each “tap” value @ kTs Rayleigh distributed
(actually the sum of several sub-paths)
Shivkumar KalyanaramanIBM Research - India
4
Inter-Symbol-Interference (ISI) due to Multi-Path Fading
Transmitted signal:
Received Signals:Line-of-sight:
Reflected:
The symbols add up on the channel
Distortion!
Delays
Shivkumar KalyanaramanIBM Research - India
5
Recall: Attenuation, Dispersion Effects: ISI!
Source: Prof. Raj Jain, WUSTL
Inter-symbol interference (ISI)
Shivkumar KalyanaramanIBM Research - India
6
Recall: Eye pattern
Eye pattern:Display on an oscilloscope which sweeps the system response to a baseband signal at the rate 1/T (T symbol duration)
time scale
ampl
itude
sca
le
Noise margin
Sensitivity to timing error
Distortiondue to ISI
Timing jitter
Shivkumar KalyanaramanIBM Research - India
7
Example of eye pattern with ISI:Binary-PAM, SRRC pulse …
AWGN (Eb/N0=10 dB) and ISI)(7.0)()( Tttthc
Shivkumar KalyanaramanIBM Research - India
8
Plan First, compare 1-tap (i.e. flat) Rayleigh-fading channel vs
AWGN. i.e. y = hx + w vs y = x + w Note: all multipaths with random attenuation/phases are
aggregated into 1-tap
Next consider frequency selectivity, i.e. multi-tap, broadband channel, with multi-paths Effect: ISI Equalization techniques for ISI & complexities
Generalize! Consider diversity in time, space, frequency, and develop efficient schemes to achieve diversity gains and coding gains
Shivkumar KalyanaramanIBM Research - India
9
Single-tap, Flat Fading (Rayleigh) vs AWGN
Shivkumar KalyanaramanIBM Research - India
10
BER vs. S/N performance:
ISI/Freq. Selective Channel (worse than just Rayleigh)
Typical BER vs. S/N curves
S/N
BER
Frequency-selective channel (no equalization)
Flat fading channel
Gaussian channel(no fading)
Frequency selective fading <=> irreducible BER floor!!!
Shivkumar KalyanaramanIBM Research - India
11
BER vs. S/N performance:
w/ Equalization
Typical BER vs. S/N curves
S/N
BER
Flat fading channel
Gaussian channel(no fading)
Diversity (e.g. multipath diversity) <=>
Frequency-selective channel(with equalization)
improved performance
Shivkumar KalyanaramanIBM Research - India
12
Diversity Basic Idea
Send same bits over independent fading pathsIndependent fading paths obtained by time, space,
frequency, or polarization diversity Combine paths to mitigate fading effects
Tb
tMultiple paths unlikely to fade simultaneously
Shivkumar KalyanaramanIBM Research - India
13
Diversity Gain: Short Story…
AWGN case: BER vs SNR:
(any modulation scheme, only the constants differ)
Note: γ is received SNR
Rayleigh Fading w/o diversity:
Rayleigh Fading w/ diversity: (MIMO):
Note: “diversity” is a reliability theme, not a capacity/bit-rate one…For capacity: need more degrees-of-freedom (i.e. symbols/s)
& packing of bits/symbol (MQAM).
Shivkumar KalyanaramanIBM Research - India
14
SNR
BER
Frequency-selective channel (no equalization)
Flat fading channel
AWGN channel
(no fading)
Frequency-selective channel (equalization or Rake receiver)
“BER floor”
BER vs. SNR (cont.)
01 4eP
( )eP
means a straight line in log/log scale
0( )
Shivkumar KalyanaramanIBM Research - India
15
Rayleigh Flat Fading Channel
BPSK: Coherent detection.
Conditional on h,
Averaged over h,
at high SNR.
Looks like AWGN, but…
pe needs to be “unconditioned”
To get a much poorer scaling
Shivkumar KalyanaramanIBM Research - India
16
Typical error event is due to: channel (h) being in deep fade!… rather than (additive) noise being large.
Conditional on h,
When the error probability is very small.
When the error probability is large:
Typical Error Event
Shivkumar KalyanaramanIBM Research - India
17
Preview: Diversity Gain: Intuition Typical error (deep fade) event probability: In other words, ||h|| < ||w||/||x||
i.e. ||hx|| < ||w|| (i.e. signal x is attenuated to be of the order of noise w)
Chi-Squared pdf of
Shivkumar KalyanaramanIBM Research - India
18
MQAM doesn’t change the error asymptotics
QPSK does use degrees of freedom better than equivalent 4-PAM
(Read textbook, chap 3, section 3.1)
Shivkumar KalyanaramanIBM Research - India
19
Frequency Selectivity: Multipath fading & ISI
Mitigation: Equalization & Challenges
Shivkumar KalyanaramanIBM Research - India
20
Multipath: Time-Dispersion => Frequency Selectivity
The impulse response of the channel is correlated in the time-domain (sum of “echoes”) Manifests as a power-delay profile, dispersion in channel autocorrelation function A()
Equivalent to “selectivity” or “deep fades” in the frequency domain Delay spread: ~ 50ns (indoor) – 1s (outdoor/cellular). Coherence Bandwidth: Bc = 500kHz (outdoor/cellular) – 20MHz (indoor) Implications: High data rate: symbol smears onto the adjacent ones (ISI).
Multipath effects
~ O(1s)
Shivkumar KalyanaramanIBM Research - India
21
Equalization
Frequencydown-conversion
Receiving filter
Equalizingfilter
Threshold comparison
For bandpass signals Compensation for channel induced ISI
Baseband pulse(possibly distored)
Sample (test statistic)
Baseband pulseReceived waveform
Step 1 – waveform to sample transformation Step 2 – decision making
)(tr)(Tz
im
Demodulate & Sample Detect
Shivkumar KalyanaramanIBM Research - India
22
What is an equalizer?
We’ve used it for music in everyday life! Eg: default settings for various types of music to emphasize bass, treble etc… Essentially we are setting up a (f-domain) filter to cancel out the channel mpath filtering effects
Shivkumar KalyanaramanIBM Research - India
23
Equalization: Channel is a LTI Filter
ISI due to filtering effect of the communications channel (e.g. wireless channels) Channels behave like band-limited filters
)()()( fjcc
cefHfH
Non-constant amplitude
Amplitude distortion
Non-linear phase
Phase distortion
Shivkumar KalyanaramanIBM Research - India
24
Equalizing filters … Baseband system model
Tx filter Channel
)(tn
)(tr Rx. filterDetector
kz
kTt
ka1a
2a 3aT )(
)(
fH
th
t
t
)(
)(
fH
th
r
r
)(
)(
fH
th
c
c
k
k kTta )( Equalizer
)(
)(
fH
th
e
e
)(tz
Equivalent system
)(ˆ tn
)(tzDetector
kz
kTt )(
)(
fH
th
filtered (colored) noise
)()()()( fHfHfHfH rct
1a
2a 3aT
k
k kTta )( )(tx Equalizer
)(
)(
fH
th
e
e
)()()(ˆ thtntn r
ka)(tz
Equivalent model
Shivkumar KalyanaramanIBM Research - India
25
Equalizer Types
Source: Rappaport book, chap 7
Covered later in slideset
Shivkumar KalyanaramanIBM Research - India
26
Linear Equalizer
Equalizer
Heq(f)1
Hc(f)
Channel
Hc(f)
n(t)
• A linear equalizer effectively inverts the channel.
• The linear equalizer is usually implemented as a tapped delay line.
• On a channel with deep spectral nulls, this equalizer enhances the noise. (note: both signal and noise pass thru eq.)
poor performance on frequency-selective fading channels
Shivkumar KalyanaramanIBM Research - India
27
Decision Feedback Equalizer (DFE)
=> doesn’t work well w/ low SNR. Optimal non-linear: MLSE… (complexity grows exponentially w/ delay spread)
• The DFE determines the ISI from the previously detected symbols and subtracts it from the incoming symbols.
• This equalizer does not suffer from noise enhancement because it estimates the channel rather than inverting it.
The DFE has better performance than the linear equalizer in a frequency-selective fading channel. • The DFE is subject to error propagation if decisions are
made incorrectly.
Hc(f)Forward
Filter
n(t)
x(t)
DFE
Feedback Filter
+
-
x(t)^
Shivkumar KalyanaramanIBM Research - India
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Equalization by transversal filtering Transversal filter:
A weighted tap delayed line that reduces the effect of ISI by proper adjustment of the filter taps.
N
Nnn NNkNNnntxctz 2,...,2 ,..., )()(
Nc 1 Nc 1Nc Nc
)(tx
)(tz
Coeff. adjustment
Shivkumar KalyanaramanIBM Research - India
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Transversal equalizing filter … Zero-forcing (ZF) equalizer:
The filter taps are adjusted such that the equalizer output is forced to be zero at N sample points on each side:
Mean Square Error (MSE) equalizer: The filter taps are adjusted such that the MSE of ISI and noise power at
the equalizer output is minimized. (note: noise is whitened before filter)
Nk
kkz
,...,1
0
0
1)(
N
Nnnc
Adjust
2))((min kakTzE N
Nnnc
Adjust
Shivkumar KalyanaramanIBM Research - India
30
Summary: Equalizer Complexity and Adaptation
Nonlinear equalizers (DFE, MLSE) have better performance but higher complexity
Equalizer filters must be FIR Can approximate IIR Filters as FIR filters Truncate or use MMSE criterion
Channel response needed for equalization Training sequence used to learn channel
Tradeoffs in overhead, complexity, and delay
Channel tracked during data transmissionBased on bit decisionsCan’t track large channel fluctuations
Shivkumar KalyanaramanIBM Research - India
31
Diversity Techniques: Time Diversity
Error Coding, HARQ, Interleaving
Shivkumar KalyanaramanIBM Research - India
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Time Diversity Time diversity can be obtained by interleaving and coding
over symbols across different coherent time periods.
Coding alone is not sufficient!
Channel: timediversity/selectivity, but correlated acrosssuccessive symbols
(Repetition) Coding…w/o interleaving: a full codeword lost during fade
Interleaving: of sufficient depth: (> coherence time)At most 1 symbol of codeword lost
Shivkumar KalyanaramanIBM Research - India
33
Forward Error Correction (FEC): Eg: Reed-Solomon RS(N,K)
Data = K
FEC (N-K)
Block Size (N)
RS(N,K) >= K of Nreceived
Lossy Network
Recover K data packets!
Block: of sufficient size: (> coherence time), else need to interleave, or use with hybrid ARQ
Shivkumar KalyanaramanIBM Research - India
34
Hybrid ARQ/FEC ModelPackets • Sequence Numbers
• CRC or Checksum• Proactive FEC
Status Reports • ACKs• NAKs, • SACKs• Bitmaps
• Packets• Reactive FEC
Retransmissions
Timeout
Shivkumar KalyanaramanIBM Research - India
35
Example: GSM
The data of each user are sent over time slots of length 577 μs Time slots of the 8 users together form a frame of length 4.615 ms
Voice: 20 ms frames, rate ½ convolution coded = 456 bits/voice-frame Interleaved across 8 consecutive time slots assigned to that specific user:
0th, 8th, . . ., 448th bits are put into the first time slot, 1st, 9th, . . ., 449th bits are put into the second time slot, etc.
One time slot every 4.615 ms per user, or a delay of ~ 40 ms (ok for voice). The 8 time slots are shared between two 20 ms speech frames.
Shivkumar KalyanaramanIBM Research - India
36
Time-Diversity Example: GSM
Amount of time diversity limited by application’s delay constraints and how fast channel varies.
In GSM, delay constraint is 40ms (voice). To get full diversity of 8, needs v > 30 km/hr at fc = 900Mhz.
Recall: Tc < 5 ms = 1/(4Ds) = c/(8fcv)
Shivkumar KalyanaramanIBM Research - India
37
GSM contd
Walking speed of say 3 km/h => too little time diversity. GSM can go into a frequency hopping mode, Consecutive frames (each w/ time slots of 8 users) can hop
from one 200 kHz sub-channel to another.
Typical delay spread ~ 1μs => the coherence bandwidth (Bc) is 500 kHz.
The total bandwidth of 25 MHz >> Bc
=> consecutive frames can be expected to fade independently.
This provides the same effect as having time diversity.
Shivkumar KalyanaramanIBM Research - India
38
Repetition Coding: Fading Analysis (contd) BPSK Error probability:
Average over ||h||2 i.e. over Chi-squared distribution,
L-degrees of freedom!
Shivkumar KalyanaramanIBM Research - India
39
Key: Deep Fades Become Rarer
Note: this graph plotsreliability (i.e. BER vs SNR)
Repetition code trades off information rate (i.e. poor use of deg-of-freedom)
Deep fade ≡ Error event…
Shivkumar KalyanaramanIBM Research - India
40
Beyond Repetition Coding: Coding gains
Repetition coding gets full diversity, but sends only one symbol every L symbol times. i.e. trades off bit-rate for reliability (better BER)
Does not exploit fully the degrees of freedom in the channel. (analogy: PAM vs QAM)
How to do better?
Shivkumar KalyanaramanIBM Research - India
41
Rotation vs Repetition Coding
Recall repetition coding was like PAMRotation code uses the degrees of freedom better!
Coding gain over the repetition code in terms of a saving in transmit power by a factor of sqrt(5) or 3.5 dB for the same product distance
Shivkumar KalyanaramanIBM Research - India
42
Antenna (Spatial) Diversity
Shivkumar KalyanaramanIBM Research - India
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Antenna Diversity
Receive(SIMO)
Transmit(MISO)
Both(MIMO)
Shivkumar KalyanaramanIBM Research - India
44
Antenna Diversity: Rx
Receive(SIMO)
Transmit(MISO)
Both(MIMO)
Shivkumar KalyanaramanIBM Research - India
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Receive Diversity
Same mathematical structure as repetition coding in time diversity (!), except that there is a further power gain (aka “array gain”).
Optimal reception is via matched filtering/MRC
(a.k.a. receive beamforming).
Shivkumar KalyanaramanIBM Research - India
46
Array Gain vs Diversity Gain Diversity Gain: multiple independent channels between the transmitter and
receiver, and is a product of the statistical richness of those channels
Array gain does not rely on statistical diversity between the different channels and instead achieves its performance enhancement by coherently combining the actual energy received by each of the antennas. Even if the channels are completely correlated, as might happen in a line-
of-sight (LOS) system, the received SNR increases linearly with the number of receive antennas,
Eg: Correlated flat-fading:
Single Antenna SNR:
Adding all receive paths:
Shivkumar KalyanaramanIBM Research - India
47
Receive Diversity: Selection Combining
Recall: Bandpass vs matched filter analogy. Pick max signal, but don’t fully combine signal
power from all taps. Diminishing returns from more taps.
Source: J. Andrews et al, Fundamentals of WIMAX
Shivkumar KalyanaramanIBM Research - India
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Receive Beamforming: Maximal Ratio Combining (MRC)
Weight each branch
SNR:
MRC Idea: Branches with better signal energy should be enhanced, whereas branches with lower SNR’s given lower weights
Source: J. Andrews et al, Fundamentals of WIMAX
Shivkumar KalyanaramanIBM Research - India
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Recall: Maximal Ratio Combining (MRC) or “Beamforming” … is just Matched Filtering in the Spatial Domain!
Generalization of this f-domain picture, for combining multi-tap signal
Weight each branch
SNR:
Source: J. Andrews et al, Fundamentals of WIMAX
Shivkumar KalyanaramanIBM Research - India
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Selection Diversity vs MRC
Source: J. Andrews et al, Fundamentals of WIMAX
Shivkumar KalyanaramanIBM Research - India
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Antenna Diversity: Tx
Receive(SIMO)
Transmit(MISO)
Both(MIMO)
Shivkumar KalyanaramanIBM Research - India
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Transmit Diversity
If transmitter knows the channel, send:
maximizes the received SNR by in-phase addition of signals at the receiver (transmit beamforming), i.e. closed-loop Tx diversity.
Reduce to scalar channel:
same as receive beamforming.
What happens if transmitter does not know the channel?
Shivkumar KalyanaramanIBM Research - India
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Open-Loop Tx Diversity: Space-Time Coding
Alamouti : Orthogonal space-time block code (OSTBC). 2 × 1 Alamouti STBC
Rate 1 code: Data rate is neither increased nor decreased; Two symbols are sent over two time intervals. Goal: harness spatial diversity. Don’t care about ↑ rate
Alamouti Code:
Shivkumar KalyanaramanIBM Research - India
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Alamouti Scheme
Over two symbol times:
Projecting onto the two columns of the H matrix yields:
•double the symbol rate of repetition coding.
•3dB loss of received SNR compared to transmit beamforming (i.e. MRC or matched filtering).
Shivkumar KalyanaramanIBM Research - India
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Space-time Codes Note: Transmitter does NOT know the channel instantaneously (open-loop)
Using the antennas one at a time and sending the same symbol over the different antennas is like repetition coding. Repetition scheme: inefficient utilization of degrees of freedom Over the two symbol times, bits are packed into only one dimension of
the received signal space, namely along the direction [h1, h2]t. More generally, can use any time-diversity code by turning on one
antenna at a time.
Space-time codes are designed specifically for the transmit diversity scenario. Alamouti scheme spreads the information onto two dimensions - along
the orthogonal directions [h1, h2*]t and [h2,−h1* ]t.
Repetition: Alamouti:
Shivkumar KalyanaramanIBM Research - India
56
ST-Coding Design: Details Space-time code as a set of complex codewords {Xi}, where
each Xi is an L by N matrix. L: number of transmit antennas N: block length of the code.
Repetition: Alamouti:
Normalize the codewords so that the average energy per symbol time is 1, hence SNR = 1/N0.
Assume channel constant for N symbol times
Shivkumar KalyanaramanIBM Research - India
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Code Design & Degrees of Freedom
Shivkumar KalyanaramanIBM Research - India
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Antenna Diversity: Tx+Rx = MIMO
Receive(SIMO)
Transmit(MISO)
Both(MIMO)
Shivkumar KalyanaramanIBM Research - India
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MIMO: w/ Repetition or Alamouti Coding
Transmit the same symbol over the two antennas in two consecutive symbol times (at each time, nothing is sent over the other antenna). ½ symbol per degree of freedom (d.f.)
MRC combining w/ repetition:
Alamouti scheme used over the 2 × 2 channel: Sends 2 symbols/2 symbol times (i.e. 1symbol/d.f), Same 4-fold diversity gain as in repetition.
But, the 2x2 MIMO channel has MORE degrees of freedom!
Shivkumar KalyanaramanIBM Research - India
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MIMO: degrees of freedom Degrees of freedom =
dimension of received signal space
1xL: One-dimensional 2x2: Has 2 dimensions hj: vector of channel gains
from Tx antennas. Space gives new degrees of
freedom. A “spatial multiplexing”
scheme like V-BLAST can leverage the additional d.f.
Shivkumar KalyanaramanIBM Research - India
61
Spatial Multiplexing: V-BLAST
Transmit independent uncoded symbols over antennas and over time!
V-BLAST: poorer diversity gain than Alamouti. But exploits spatial degrees of freedom better
Space-only coding: no Tx diversity. Diversity order only 2. Coding gain possible by coding across space & time (increased
degrees of freedom) with spatial multiplexing
Shivkumar KalyanaramanIBM Research - India
62
MIMO Receiver Issues
V-BLAST uses joint ML reception (complex)
Zero-forcing linear receiver loses one order of diversity. Interference nuller,
decorrelator Noise samples
correlated (colored).
Shivkumar KalyanaramanIBM Research - India
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Summary: 2x2 MIMO Schemes
Need closed-loop MIMO to be able to reap both diversity and d.f. gains
Shivkumar KalyanaramanIBM Research - India
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Frequency Diversity: CDMA Rake, OFDM
Ref: Chapter 3 & 4, Tse/Viswanath book,Chap 13, 15: A. Goldsmith book
Shivkumar KalyanaramanIBM Research - India
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Sender Receiver
Code A
A
Code B
B
AB
AB
CBC
A
Code A
AB
C
Time
Freq
uenc
y
BC
B
A
Base-band Spectrum Radio Spectrum
spread spectrum
What is CDMA ?
Shivkumar KalyanaramanIBM Research - India
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Direct Sequence Spread Spectrum
Bit sequence modulated by chip sequence
Spreads bandwidth by large factor (K)
Despread by multiplying by sc(t) again (sc(t)=1)
Mitigates ISI and narrowband interference
s(t) sc(t)
Tb=KTc Tc
S(f)Sc(f)
1/Tb 1/Tc
S(f)*Sc(f)
Shivkumar KalyanaramanIBM Research - India
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Chips & Spreading
Shivkumar KalyanaramanIBM Research - India
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Processing Gain / Spreading Factor
Shivkumar KalyanaramanIBM Research - India
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Processing Gain & Shannon
With 8K vocoders, above 32 users, SNR becomes too low.
Practical CDMA systems restrict the number of users per sector to ensure processing gain remains at usable levels
Shivkumar KalyanaramanIBM Research - India
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ISI and Interference Rejection
Narrowband Interference Rejection
Multipath Rejection (Two Path Model)
S(f) S(f)I(f)S(f)*Sc(f)
Info. Signal Receiver Input Despread Signal
I(f)*Sc(f)
S(f) S(f)S(f)*Sc(f)[(t)+(t-)]
Info. Signal Receiver Input Despread Signal
S’(f)
Shivkumar KalyanaramanIBM Research - India
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Forward Link(Down Link)
Synchronous Chip Timing
A
B
AA
Signal for B Station(after re-spreading)
Less Interference for A station
Synchronous CDMA Systems realized in Point to Multi-point System.e.g., Forward Link (Base Station to Mobile Station) in Mobile Phone.
Synchronous DS-CDMA: Downlink
Shivkumar KalyanaramanIBM Research - India
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In asynchronous CDMA system, orthogonal codes have bad cross-correlation.
Reverse Link(Up Link)
BA
Signal for B Station(after re-spreading)
Big Interference from A station
Asynchronous Chip Timing
Signals from A and B are interfering each other.
A
B
Asynchronous DS-CDMA: Uplink
Shivkumar KalyanaramanIBM Research - India
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Path Delay
Po
we
r path-1
path-2
path-3
With low time-resolution,different signal paths cannot be discriminated.
•••These signals sometimes strengthen,
and sometimes cancel out each other, depending on their phase relation.••• This is “fading”.
•••In this case, signal quality is damaged
when signals cancel out each other.In other words, signal quality is dominated
by the probability for detected power to be weaker than minimum required level.
This probability exists with less than two paths.
Time
Po
we
r
Detected Power
In non-CDMA system, “fading” damages signal quality.
Frequency-Selective Fading in non-CDMA Broadband System
Shivkumar KalyanaramanIBM Research - India
74
Because CDMA naturally 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
Po
we
r path-1
path-2
path-3
CDMAReceiver
CDMAReceiver
•••
Synchron
ization
Add
er
Path Delay
Po
we
r
CODE Awith timing of path-1
path-1
Po
we
r
path-1
path-2
path-3
Path Delay
Po
we
r
CODE Awith timing of path-2
path-2
interference from path-2 and path-3
•••
Fading in CDMA System: Rake Principle
Shivkumar KalyanaramanIBM Research - India
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In CDMA system, multi-path propagation improves the signal quality by use of RAKE receiver.
Time
Po
we
r Detected Power
RAKEreceiver
Less fluctuation of detected power, because of adding all
energy .
Po
we
r
path-1
path-2
path-3
Fading in CDMA System (continued)
Shivkumar KalyanaramanIBM Research - India
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Recall: Maximal Ratio Combining (MRC), “Beamforming” , Rake Receiving: are just Matched Filtering operations!
Generalization of this f-domain picture, for combining multi-tap signal
Weight each branch
SNR:
Source: J. Andrews et al, Fundamentals of WIMAX
Shivkumar KalyanaramanIBM Research - India
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Rake Receiver: Summary Counter-Intuitive: Increase rate and bandwidth PN Code Autocorrelation attenuates ISI Not particularly effective for wideband signals (no spreading
gain)
Shivkumar KalyanaramanIBM Research - India
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Multi-Carrier Modulation and OFDM
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Frequency Diversity & Multicarrier Modulation, i.e. OFDM
Key Idea: Since we avoid ISI if Ts > Tm, just send a large number of narrowband carriers
M subcarriers each with rate R/M, also have Ts’ = Ts*M. Total data rate is unchanged.
subchannel
frequency
ma
gn
itude
carrier
channel
Figure courtesy B. Evans
Shivkumar KalyanaramanIBM Research - India
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Issues w/ Multicarrier Modulation
1. Large bandwidth penalty since the subcarriers can’t have perfectly rectangular pulse shapes and still be time-limited.
2. Very high quality (expensive) low pass filters will be required to maintain the orthogonality of the subcarriers at the receiver.
3. This scheme requires L independent RF units and demodulation paths.
OFDM overcomes these shortcomings!
Ch.2 Ch.3 Ch.4 Ch.5 Ch.6 Ch.7 Ch.8 Ch.9 Ch.10Ch.1
Conventional multicarrier techniques frequency
Shivkumar KalyanaramanIBM Research - India
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OFDM OFDM uses a computational technique known as the Discrete Fourier
Transform (DFT) … which lends itself to a highly efficient implementation commonly
known as the Fast Fourier Transform (FFT). The FFT (and its inverse, the IFFT) are able to create a multitude of
orthogonal subcarriers using just a single radio.
Ch.1
Saving of bandwidth
Ch.3 Ch.5 Ch.7 Ch.9Ch.2 Ch.4 Ch.6 Ch.8 Ch.10
Orthogonal multicarrier techniques
50% bandwidth saving
frequency
Shivkumar KalyanaramanIBM Research - India
82
OFDM Symbols Group L data symbols into a block known as an OFDM symbol.
An OFDM symbol lasts for a duration of T seconds, where T = LTs. Guard period > delay spread
OFDM transmissions allow ISI within an OFDM symbol … but by including a sufficiently large guard band, it is possible to
guarantee that there is no interference between subsequent OFDM symbols.
The next task is to attempt to remove the ISI within each OFDM symbol
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Cyclic Prefix: Eliminate intra-symbol interference! In order for the IFFT/FFT to create an ISI-free channel, the channel must appear to provide a circular
convolution If a cyclic prefix is added to the transmitted signal, then this creates a signal that appears to be x[n]L, and so
y[n] = x[n] * h[n].
The first v samples of ycp interference from preceding OFDM symbol => discarded. The last v samples disperse into the subsequent OFDM symbol => discarded. This leaves exactly L samples for the desired output y, which is precisely what is required to recover the L data symbols embedded in x. (cyclic convolution output!)
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Cyclic Prefix overhead
More sub-carriers (L), the better! DFT/FFT can scale to 1024/2048 with modern DSPs
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OFDM Implementation
1. Break a wideband signal of bandwidth B into L narrowband signals (subcarriers) each of bandwidth B/L. The L subcarriers for a given OFDM symbol are represented by a vector X, which contains the L current symbols.
2. In order to use a single wideband radio instead of L independent narrow band radios, the subcarriers are modulated using an IFFT operation.
3. In order for the IFFT/FFT to decompose the ISI channel into orthogonal subcarriers, a cyclic prefix of length v must be appended after the IFFT operation. The resulting L + v symbols are then sent in serial through the wideband channel.
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Summary: OFDM vs Equalization
CMAC: complex multiply and accumulate operations per received symbol
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OFDM: summary
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Summary: Diversity
Fading makes wireless channels unreliable.
Diversity increases reliability and makes the channel more consistent.
Smart codes yields a coding gain in addition to the diversity gain.
This viewpoint of the adversity of fading will be challenged and enriched in later parts of the course.
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Extra Background Slides: CDMA / OFDMA
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Spreading: Mutually Orthogonal, Walsh Codes
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Properties of Walsh Codes
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The IS-95 Reverse Link
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Cross-Correlation: PN Sequences
Cross-Correlationbetween Code A and Code B = 5/16
Self-Correlationfor each code is 16/16.
one data bit duration
Spreading Code A
1 0 11 1 1 0 0 10 1 0 1 0 0 1
one data bit duration
Spreading Code A
1 0 01 1 1 0 0 10 1 0 1 0 0 1
Spreading Code A
1 0 01 1 1 0 0 10 1 0 1 0 0 1
0 0 00 0 0 0 0 00 0 0 0 0 0 0
Spreading Code B
1 0 01 1 0 0 1 11 0 0 1 0 1 1
0 0 00 0 1 0 1 01 1 0 0 0 1 0
0
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In order to minimize mutual interference in DS-CDMA , the spreading codes
with less cross-correlation should be chosen.
Synchronous DS-CDMA :Orthogonal Codes are appropriate. (Walsh code etc.)
Asynchronous DS-CDMA :• Pseudo-random Noise (PN) codes / Maximum sequence
• Gold codes
Preferable Codes
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Near-Far Problem: Power Control
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Effect of Power Control
AB
Time
De
tect
ed
Po
we
r
from MS B from MS A
closed loop power
control for MS B.
for MS A
.
Effect of Power Control• Power control is capable of compensating the fading fluctuation.
• Received power from all MS are controlled to be equal.
... Near-Far problem is mitigated by the power control.
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CDMA: Issues
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Key: Interference Averaging!
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Voice Activity: Low Duty Cycle & Statistical Multiplexing
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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
Soft Handoff :• In CDMA cellular system, communication does not break even at the moment doing handoff, because switching frequency or time slot is not required.
Soft Handoff
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Spectrum of the modulated data symbols
Rectangular Window of duration T0 (Time domain)
Has a sinc-spectrum with zeros at 1/ T0 (Freq. domain)
Other carriers are put in these zeros
sub-carriers are orthogonal Equivalent to packing
symbols every T0 seconds in time domain
Frequency
Magnitude
T0
Subcarrier orthogonality must be preservedCompromised by timing jitter, frequency offset, and fading.
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Detour: Circular Convolution & DFT/IDFT
Circular convolution:
Detection of X (knowing H):
(note: ISI free! Just a scaling by H)
Circular convolution allows DFT! (discrete, finite => linear algebra!)
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Recall: DFT/Fourier Methods ≡ Eigen Decomposition!
Applying transform techniques is just eigen decomposition! Discrete/Finite case (DFT/FFT):
Circulant matrix C is like convolution. Rows are circularly shifted versions of the first row
C = UΛU* where F is the (complex) fourier matrix, which happens to be both unitary and symmetric, and multiplication w/ F is rapid using the FFT.
Applying U = DFT, i.e. transform to frequency domain, i.e. “rotate” the basis to view C in the frequency basis.
Applying Λ is like applying the complex gains/phase changes to each frequency component (basis vector)
Applying U* inverts back to the time-domain. (IDFT or IFFT)
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OFDM in WiMAX
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Example: Flash OFDM (Flarion, now Qualcomm)
Bandwidth = 1.25 Mz OFDM symbol = 128 samples = 100 s Cyclic prefix = 16 samples = 11 s delay spread 11 % overhead.
• Permutations for frequency diversity for each user (gaps filled by other users)
• Recall: like repetition coding• Efficiency gained across users•(multi-user & frequency diversity)
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OFDMA: Latin Squares & Hopping Patterns
Hopping pattern matrix: (coordinated w/ neighboring BS)
Interference diversity