Shivkumar Kalyanaraman IBM Research - India 1 Point-to-Point Wireless Communication (II): ISI &...

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


2

Multi-dimensional Fading

Time, Frequency, Space


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)


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


5

Recall: Attenuation, Dispersion Effects: ISI!

Source: Prof. Raj Jain, WUSTL

Inter-symbol interference (ISI)


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


7

Example of eye pattern with ISI:Binary-PAM, SRRC pulse …

AWGN (Eb/N0=10 dB) and ISI)(7.0)()( Tttthc


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


9

Single-tap, Flat Fading (Rayleigh) vs AWGN


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!!!


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


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


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).


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( )


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


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


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


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)


19

Frequency Selectivity: Multipath fading & ISI

Mitigation: Equalization & Challenges


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)


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


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


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


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


25

Equalizer Types

Source: Rappaport book, chap 7

Covered later in slideset


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


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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)^


28

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


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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


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


31

Diversity Techniques: Time Diversity

Error Coding, HARQ, Interleaving


32

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


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


34

Hybrid ARQ/FEC ModelPackets • Sequence Numbers

• CRC or Checksum• Proactive FEC

Status Reports • ACKs• NAKs, • SACKs• Bitmaps

• Packets• Reactive FEC

Retransmissions

Timeout


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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.


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)


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.


38

Repetition Coding: Fading Analysis (contd) BPSK Error probability:

Average over ||h||2 i.e. over Chi-squared distribution,

L-degrees of freedom!


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…


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?


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


42

Antenna (Spatial) Diversity


43

Antenna Diversity

Receive(SIMO)

Transmit(MISO)

Both(MIMO)


44

Antenna Diversity: Rx

Receive(SIMO)

Transmit(MISO)

Both(MIMO)


45

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).


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:


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


48

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



49

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:



50

Selection Diversity vs MRC



51

Antenna Diversity: Tx

Receive(SIMO)

Transmit(MISO)

Both(MIMO)


52

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?


53

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:


54

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).


55

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:


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


57

Code Design & Degrees of Freedom


58

Antenna Diversity: Tx+Rx = MIMO

Receive(SIMO)

Transmit(MISO)

Both(MIMO)


59

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!


60

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.


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


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).


63

Summary: 2x2 MIMO Schemes

Need closed-loop MIMO to be able to reap both diversity and d.f. gains


64

Frequency Diversity: CDMA Rake, OFDM

Ref: Chapter 3 & 4, Tse/Viswanath book,Chap 13, 15: A. Goldsmith book


65

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 ?


66

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)


67

Chips & Spreading


68

Processing Gain / Spreading Factor


69

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


70

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)


71

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


72

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


73

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


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


75

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)


76

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:



77

Rake Receiver: Summary Counter-Intuitive: Increase rate and bandwidth PN Code Autocorrelation attenuates ISI Not particularly effective for wideband signals (no spreading

gain)


78

Multi-Carrier Modulation and OFDM


79

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


80

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


81

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


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


83

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!)


84

Cyclic Prefix overhead

More sub-carriers (L), the better! DFT/FFT can scale to 1024/2048 with modern DSPs


85

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.


86

Summary: OFDM vs Equalization

CMAC: complex multiply and accumulate operations per received symbol


87


88

OFDM: summary


89

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.


90

Extra Background Slides: CDMA / OFDMA


91

Spreading: Mutually Orthogonal, Walsh Codes


92

Properties of Walsh Codes


93

The IS-95 Reverse Link


94

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


95

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


96

Near-Far Problem: Power Control


97

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.


98

CDMA: Issues


99

Key: Interference Averaging!


100

Voice Activity: Low Duty Cycle & Statistical Multiplexing


101

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


102

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.


103

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!)


104

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)


105

OFDM in WiMAX


106

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)


107

OFDMA: Latin Squares & Hopping Patterns

Hopping pattern matrix: (coordinated w/ neighboring BS)

Interference diversity

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Shivkumar Kalyanaraman IBM Research - India 1 Point-to-Point Wireless Communication (II): ISI &...

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