ece442 communication system design lecture 1. basics of...

Course Information History Communication Channels Modulation Coding MIMO and Diversity Multiple Access

ECE442 Communication System DesignLecture 1. Basics of Communication

Theory

Husheng Li

Dept. of Electrical Engineering and Computer Science

Spring, 2014


Course Introduction

1 This course is more focused on the design and analysis ofpractical communication systems, including both wirelesscommunication systems and optical communicationnetworks.

2 Course ContentsBasics of communication theoryCellular systems: 4G LTEWireless LAN: WiFi (IEEE 802.11n)Optical Networks (Sonet/SDH)


Textbook

Textbook 1: A. Goldsmith, Wireless Communications,Cambridge University Press, 2005.Textbook 2: J. Li, X. Wu and R. Laroia, OFDMA MobileBroadband Communications: A System’s Approach,Cambridge University Press, 2013Textbook 3: B. E. Perahia and R. Stacey, Next GenerationWireless LANs: Throughput, Robustness and Reliability in802.11n, Cambridge University Press, 2013.Textbook 4: R. Ramaswami, K. N. Sivarajan and G. H.Sasaki, Optical Networks: A Practical Perspective, 3rdedition, Morgan Kaufmann, 2010.


Syllabus

1 Homework: four problems each week (25%).2 Midterm exam (25%)3 Final exam (25%)4 Project (25%): three projects


Current Wireless Systems: Cellular Systems

1 A cellular system consists of base station, mobile usersand cells.


Architecture of Cellular Systems

1 MTSO is the interface between wireless network and wirednetworks


The Development of Cellular Systems


Data Rate Evolution


Facts of Cellular Phone Subscribers

2.14 billion in 2005; 2.7 billion in 2006.In several countries, including UK, there are more mobilephones than population.80% of the world population enjoy the coverage of mobilephone service in 2008; this percentage increases to 90%in 2010.


Wireless LANs

Wireless Local Area Networks (LANs) support high speeddata transmissions within a small region.All wireless LAN standards in the US operate in unlicensedfrequency bands, such as 900MHz, 2.4GHz and 5.8GHz.IEEE 802.11 (WiFi) is the 2nd generation of LAN, whichoperates with 83.5MHz of spectrum in the 2.4GHz ISMband.


Other Wireless Communication Systems

Satellite communications.Digital wireless TV broadcast.Blue tooth.Cordless phone.


Wireless Spectrum

The frequency spectrum is divided into many bands.


Optical Networks

Optical fibers may be needed for long haul andmetropolitan networks.


Optical Networks History


Two Features of Wireless Channels

1 Broadcast: The wireless signal can also be received byunintended receivers, thus being interference. This isdifferent from wired communications. Thus, in wirelesscommunications, how to tackle interference is a key issue.

2 Fading: the wireless channel may experience deep fade intime or frequency. Thus, in wireless communications, it isimportant to combat fading for reliable data transmission.Fading can also be utilized for opportunisticcommunication.


Two Types of Fading

Large scale fading: characterize the signal strength overlong transmitter-receiver distance (you may need to move100 meters to see the change of signal strength).Small scale fading: characterize the rapid fluctuation overa small distance (you may need to move only half a meterto see the signal strength changing rapidly).


Channel Gain and Path Loss


Channel Gain and Path Loss

1 Channel power gain is given by

G = 10 log10Pr

Pt(dB),

where transmit power is Pt and receive power is Pr .2 Path loss is defined by

L = 10 log10Pt

E [Pr ](dB),

where the expectation is over all random environment(shadow fading, fast fading). Path loss is fixed for all timeand all environment.


Free-space Path Loss

1 Line-of-sight (LOS): no obstructions between thetransmitter and receiver.

2 Path loss:Pr

pt=

(√Glλ

4πd

)2

,

where Gl is antenna product of transmitter and receiver.3 In free-space,

L ∝ d2.

4 But in real-world environment, wireless signal decaysfaster in distance.


Two-Ray Model

1 When h1,h2 d , the receive power is given by

Pr (dB) = Pr (dB)+10 log10(Gl)+20 log10(h1h2)−40 log10(d).

2 In this case, the signal decays much faster than free-spacecase: L ∝ d4.


Hata Model

1 Hata Model (for urban environment):

L(dB) = 69.55 + 26.16 log10(fc)− 13.82 log10(ht )− a(hr )

+ (44.9− 6.55 log10(ht )) log10(d),

where a(hr ) is a correction factor for the mobile heightbased on the size of coverage area.

2 For suburban and rural propagation, the path loss shouldbe corrected (refer to Goldsmith’s book).

3 Note: Hata model is used for outdoor wirelesscommunications.


Shadow Fading

1 Wireless signal often experience variation caused by blockage(say buildings) in the signal path. The variation may also comefrom changes in reflecting surfaces and scattering objects. Wecall it shadow fading.

2 We usually model the shadow fading channel gain as alog-normal random variable (then the shadow fading channelgain in dB is a Gaussian random variable:

p(ψ) =ξ√

2πσψdBψexp

[−

(10 log10 ψ − µpsidB )2

2σ2ψdB

]


Path Loss and Shadow Fading

1 When the path loss and shadow fading are combined, theratio of received to transmitted power in dB is given by

Pr

PtdB = 10 log10 K − 10γ log10

dd0− ψdB.

2 The outage probability is the probability that the receivedpower at a given distance d the received power is below athreshold:

Pout = P(Pr (d) ≤ Pmin).


Small Scale Fading: Multipath Fading

1 Path loss and shadowing are both large scale, whichmeans that it does not change much if the location ofreceived is not much changed.

2 There also exists small scale fading, which changesradically if the location is slightly changed.


Resolvable Paths

1 Small scale fading results from multiple replicas of signal alongmultiple propagation paths (τl means the delay along the l-thpath).

2 For two paths 1 and 2, if |τ1 − τ2| is much smaller than a signalsymbol interval (approximately equalling to inverse bandwidthB−1), these two paths cannot be distinguished (unresolvable); if|τ1 − τ2| is much larger than a signal symbol interval, these twopaths can be distinguished (resolvable).


Narrowband and Wideband Systems

1 In narrowband system, there are very few resolvable paths.Each resolvable signal components may be thesuperposition of several paths. The destruction orconstruction effect of these paths can change rapidly in thescale of wavelength.

2 In wideband systems, resolvable signal component maycontain only one path, whose amplitude changes slowlywhen the location of transmitter changes.


Rayleigh Fading

1 If there are sufficiently many unresolvable paths and noLOS path, the two components rI(t) and rQ(t) are mutuallyindependent Gaussian variables (recall central limittheorem). Then, it is called Rayleigh fading.

2 The distribution of signal amplitude r is (σ2 is a parameterrelated to the variance)

f (r) =rσ2 exp

(− r2

2σ2

), ∀r ≥ 0

and the signal phase is a uniform random variable in[0,2π]. The amplitude and phase are mutuallyindependent. The signal power is an exponentiallydistributed random variable (why?).

3 Rayleigh fading is bad since there may exist very deepfade (very small receive signal power).


Wideband Channel Model

1 When the signal is not narrowband, we get another form ofdistortion due to the multipath delay spread.


Frequency Flat and Selective Fading Channels

1 When the coherence bandwidth is much larger than thesignal bandwidth, the signals at different frequenciesexperience similar fading, called frequency flat fading.

2 When the coherence bandwidth is much smaller than thesignal bandwidth, the signals at different frequencies mayexperience completely different fading, called frequencyselective fading.

3 Impact on communication systems: in frequency flatfading, dead once deep fade; in frequency selective fading,there are always some frequencies being at good state,thus adding robustness. But troublesome equalization isrequired for frequency selective systems.


Frequency Flat Signal Model

1 The fading channel just scales the received signal:

r(l) = a(l)s(l) + n(l),

where r(l) is complex received signal, a(l) is complexchannel gain, s(l) is transmitted signal, n(l) is noise(assumed to be AWGN) and l is sample index.

2 Fast fading: a(l) changes with l .3 Slow fading: a(l) is almost a constant over a period.


Frequency Selective Signal Model

1 Multipath model (M paths):

r(l) =M∑

m=1

am(l)s(l − τm) + n(l).

2 FIR model (delay spread N = τM ):

r(l) =N∑

m=1

ams(l −m) + n(l)

= a ? s(l) + n(l).

In frequency domain, we have R(l) = A(l)S(l) + N(l),where l is index for frequency point (flat fading on differentfrequencies).

3 Both models are used widely in research. They areequivalent if some coefficients in FIR model are set to 0.


Channel Capacity

Given a communication channel, there exists a maximumtransmission rate C. When the rate r is larger than C, thecommunication cannot be reliable; when r < C, thecommunication is asymptotically free of error.For Gaussian noisy channel with signal-to-noise ratio γ,the capacity is given by

C =12

log(1 + γ). (1)


Two-user Case

Consider two users with transmission rates R1 and R2,power P1 and P2. Assume that the noise power is σ2

n. Thenthe capacity region is given by

R1 ≤12

log(1 + P1/σ2n) (2)

R2 ≤12

log(1 + P2/σ2n) (3)

R1 + R2 ≤12

log(1 + (P1 + P2)/σ2n) (4)

The capacity region is convex.


Purpose of Modulation and De-modulation

1 Modulation: mapping coded bits into base band signal.2 Demodulation: recover the coded bits from received base

band signal.3 Requirement:

High spectral efficiency (use as small bandwidth aspossible)High power efficiency (use as small power as possible)High reliability (demodulation error being as small aspossible)

4 Analysis tool: theory of detection.


Signal and System Model

A signal can usually be written as

si (t) =N∑

j=1

sijφj (t),

where φj (t) is the j-th basis function.


Signal Space and Representation

For linear modulation (amplitude or phase modulation), thesignal space is a two-dimensional vector space. The basevectors are φ1(t) = cos(2πfc t) and φ2(t) = sin(2πfc t).

The representation of signal in the vector space is calledconstellation.


Receiver Structure

We can use integrator to obtain rj =∫ T

0 r(t)φj (t)dt and the vectorr = (r1, ..., rN) is called the sufficient statistics.


Decision Regions

Decision rules are represented by decision regions (decision i ifthe received signal falls r in region Zi ).

Error probability (suppose M equal probably messages)

Pe =1M

M∑m=1

P(r not in Zm|message m).


Maximum Likelihood Receiver

Given a received signal r , define the likelihood of the j-thpossible signal as

L(sj) = p(r |sj).

When the noise is Gaussian, the log-likelihood is given byl(sj) = − 1

N0‖r − si‖2.

The maximum likelihood receiver outputs the messagecorresponding to the signal maximizes the likelihood(log-likelihood).


Matched Filter

We call a filter with impulse response ψ(t) = φ(T − t) thematched filter of signal φ(t).The maximum likelihood receiver can also be implementedusing the matched filter.


Passband Modulation Principles

The modulated signal can be written as

s(t) = a(t) cos[2π(fc + f (t))t + θ(t) + φ0].

In the form of in-phase and quadrature components, wehave

s(t) = sI(t)cos(2πfc t)− sQ(t)sin(2πfc t),

which can also be written as the complex basebandrepresentation: s(t) = R

[u(t)e2πfc t].


Amplitude and Phase Modulation

Information can be carried in (M is the size of constellation)

Amplitude only: MAPM (PAM: pulse amplitude modulation);Phase only: MPSK (PSK: phase shift keying)Both amplitude and phase: MQAM (QAM: quadratureamplitude modulation)

MPAM, MPSK and MQAM are all linear modulations.


M-PAM

Information can be carried in (M is the size of constellation)

Amplitude only: MAPM (PAM: pulse amplitude modulation);Phase only: MPSK (PSK: phase shift keying)Both amplitude and phase: MQAM (QAM: quadratureamplitude modulation)

MPAM, MPSK and MQAM are all linear modulations.


Structure of M-QAM Transmitter


Phase Shift Keying (MPSK)

In MPSK, the information is encoded in the phase:

si(t) = Ag(t)cos[2πfc t +

2π(i − 1)

M

].


Demodulation of MPSK

The decision regions of MPSK are shown above.


Differential Modulation

MPSK and MQAM require coherent demodulation, namelythe original phase needs to be known (by using pilotsymbol).When channel changes very fast, it is difficult to estimatethe original phase (unless you use many pilot symbols, butthis causes too much overhead). Then, we needdifferential modulation.Differential modulation conveys information in the changes.DPSK: if bit 0, keep the same phase; if bit 1, change thephase by π. Example: 00100110→ 00πππ0π.


Demodulation of DPSK

Differential modulation is less sensitive to a random drift inthe carrier phase.If the channel has a nonzero Doppler frequency, the signalphase can decorrelate between symbol times.


Frequency Modulation

The frequency modulation signal is given bysi(t) = A cos(2πfi t + φi). The frequency spacing should be0.5/Ts.


Modulation of FSK


Demodulation of FSK


Symbol Synchronization and Carrier Phase Recovery

One of the most challenging tasks of a digital demodulatoris to acquire accurate symbol timing and carrier phaseinformation.Timing information is needed to delineate the receivedsignal associated with a given symbol.The carrier phase information is needed in all coherentdemodulators for both amplitude/phase and frequencymodulation.


Receiver Structure

We denote by θ the unknown parameter vector (φ, τ),where φ is the unknown phase and τ is the unknowntiming.We can estimate them using likelihood function.


Phase Recovery

The optimal solution for the timing is given by the equation∑k sI(k) ∂∂r zk (τ)=0, which can be realized by the above

structure.


Early-Late Gate Syncrhonizer

A non decision-directed timing estimation can be realizedby the early-late gate synchronizer.


Why Coding

1 Use redundancy to enhance robustness: if the informationbit is impair (by noise, fading, interference etc), it can stillbe recovered from redundant bits.

2 If coded in symbols of different time slots, coding is similarto time diversity, which is called repetition code. Channelcoding can also be done in frequency (e.g. in OFDMsystems).

3 Used in wireless communications, storage systems (harddisk) and so on.


Coding Gain

1 Coding gain is the difference of required energy per bit (Eb)(in dB) for coded and uncoded communication achievingthe same error rate.

2 Coding gain could be negative when Eb/N0 is very low.3 Essential problem of coding: Given energy Eb for the

transmission of each information bit, what is thescheme to achieve the optimal performance?.

4 Performance measure: bit error rate and block error rate.


Coding Gain


Basic Concepts

1 Codeword: some number of channel uses to representsome information bits.

2 Codebook: the ensemble of codewords.3 Codeword length: number of channel uses.4 Encoding: mapping from information bits to codewords.5 Decoding: mapping from received signal to information

bits.


Requirements of A Good Coding Scheme

1 Low bit/block error rate.2 Low-complexity encoder and decoder. (random coding has

optimal performance, but the decoding procedure has tolook up a huge codebook)

3 Reasonable codeword length (otherwise the delay is toolong)

4 No performance floor.


Linear Block Codes

The simplest linear block code is the single-bit parity check.A block code generates a block of n coded bits from kinformation bits. We call it (n, k)-code. The coding rate isgiven by R = k/n.A linear block code means the sum of two codewords isstill a codeword. Or equivalently, the codewords form asubspace.


Hamming Distance

Codeword weight: number of nonzero bits.Hamming distance dij : the number of different coded bits intwo codewords ci and cj (the weight of codeword c1 − c2).


Minimum Distance

1 Minimum distance (also minimum weight of nonzerocodewords):

dmin = mini,j

dij ,

which characterizes how close the codewords are close toeach other (the closer, the worse performance)

2 Singleton bound:

dmin ≤ n − k + 1.

If equality holds, it is code maximum distance separation(MDS) code. A codeword in a MDS code is uniquelydetermined by any k elements (why?).


Capability of Error Detection and Correction

1 Error detection: at most dmin − 1 error bits can be detected(but may not be corrected).

2 Error correction: at most⌊

dmin−12

⌋error bits can be

corrected.


Generating Matrix

1 Information bits: k -dimensional row vector space;codewords: n-dimensional row vector space.

2 Generator matrix: mapping from information bit space tocodeword space, namely a k × n matrix.

3 Systematic code: if the generator matrix contains a k × kidentity submatrix (the information bits appear in klocations of codeword).

4 Encoding of information bit vector u:

c = uG


Parity Check Matrix

1 Parity check matrix H (n − k × n) of generator matrix Gsatisfies:

GHT = 0.

2 If receiving s = c + e (called senseword), where e is errorvector, multiplying H yields

sHT = uGHT + eHT = eHT ,

which is called syndrome of s.3 If syndrome is nonzero, we can claim decoding error. If

establishing a mapping between syndrome and errorvector (from an n− k -vector to an n-vector), we can correctsome error bits.


Cyclic Code

1 Cyclic code: any cyclic shift of any codeword is anothercodeword.

2 Polynomial representation (z is a shift operator)c(z) = g(z)u(z):

message: u(z) =k−1∑i=0

uiz i

generator: g(z) =n−k∑i=0

giz i

codeword: c(z) =n−1∑i=0

ciz i


History of Convolutional Code

1 Convolutional code was first proposed by Elias (1954),developed by Wozencraft (1957) and rediscovered byHagelbarger (1959).

2 Viterbi proposed his celebrated algorithm for harddecoding of convolutional code (essentially the same asBellman’s dynamic programming) in 1967.

3 Soft decision algorithm (BCJR algorithm) was proposed byBahl, Cocke, Jelinek and Raviv in 1974 (essentially thesame as forward-backward algorithm in HMM).

4 Convolutional code is widely used in ... for its high efficientencoding and decoding algorithms.


Diagram Representation

1 Constituent: memory, output operators.2 Constraint length ν: length of memory.3 Rate p/q: q output bits when p information bits are input.


Trellis Representation

1 There are 2ν states. Possible state transitions are labeled.2 For each combination of input information bit and state, the

outputs are labeled in the trellis.


Concatenated Codes


Storm in Coding Theory: Turbo Code

1 Before 1993, practical code only achieved performance several dBs beyondShannon capacity.

2 In ICC1993, Berrou, Glavieux, and Thitimajshima published their incrediblepaper: Near Shannon Limit error-correcting coding and decoding: Turbo-codes.

3 "Their simulation curves claimed unbelievable performance, way beyond whatwas thought possible". "The thing that blew everyone away about turbo codes isnot just that they get so close to Shannon capacity but that they’re so easy." —McEliece

4 "They said we must have made an error in our simulations" — Berrou


Rediscovery of LDPC

1 Gallager devised LDPC in his PhD thesis in 1960. It was still impractical at thattime.

2 People (Mackay, Richardson, Urbanke) rediscovered LDPC in late 1990s.3 LDPC beat turbo code and is now very close to Shannon limit (0.0045dB away,

Chung 2001).4 "A piece of 21st century coding that happened to fall in the 20th century" —

Forney5 "We’re close enough to the Shannon limit that from now on, the improvements

will only be incremental" — Tom Richardson


Turbo Encoder

1 A turbo encoder has several component encoders (e.g.convolutional code) and an interleaver (the magic part!).


Interleaver

1 An interleaver is used to permute the information bitsequence. It brings randomness to the encoder (similar toShannon’s random coding)


Turbo Decoder

1 Decoding is done in an iterative (turbo) way.2 The soft output (e.g. a posteriori probability) of one

decoder is used as the a priori probability of anotherdecoder.

3 Such a turbo principle can be applied in many other fields:turbo equalization, turbo multiuser detection and so on.


Performance


LDPC Codes

1 A low-density parity-check code is a linear code with asparse check matrix (H). It could be represented by Tannergraphs.

2 Parity check matrix:

H =

1 1 1 1 0 00 0 1 1 0 11 0 0 1 1 0


LDPC Decoder

1 Message Passing is also called Belief Propagation.2 Step 1: at each check node, the messages from variables

nodes are passed to neighboring variable nodes.3 Step 2: at each variable node, the messages from check

nodes are passed to neighboring check nodes(incorporating the channel observations).

4 Repeat above two steps.


Error Detection

1 The previous channel codes are focused on errorcorrecting. We call it forward error correcting (FEC).

2 We can use Automatic Repeat reQuest (ARQ), i.e. thereceiver sends back a NACK message to inform thetransmitter to retransmit if there is mistake in the firsttransmission.

3 This requires error detection.


CRC

1 A most popular error detection code is cyclic redundancycheck (CRC), which is based on polynomial code in GF(2).

2 Generator polynomial G(x) (for IEEE802)

G(x) = x32 + x26 + x23 + x22 + x16 + x12 + x11

+ x10 + x8 + x7 + x5 + x4 + x2 + x + 1.

3 The data is also expressed as a polynomial M(x).4 The idea is to append a checksum to the end of the data

such that the polynomial represented by the checksummedframe is divisible by G(x).


Diversity

1 Rayleigh fading and log normal shadowing induce a verylarge power penalty.

2 One approach to combat fading is diversity-combining ofindependently fading signal paths. Diversity-combininguses the fact that independent signal paths have a lowprobability of experiencing deep fades simultaneously.

3 Diversity to mitigate the effect of multipath fading(shadowing fading) is called microdiversity(macrodiversity).


Realization of Independent Fading Paths

1 Space diversity: we can use multiple receive antennas torealize independent fading paths.

2 Polarization: We can use either two transmit antennas ortwo receive antennas with different polarization.

3 Smart antennas: an array of antennas can be steered tothe incoming angle of the strongest multipath component.

4 Frequency diversity: We can transmit the samenarrowband signal at different carrier frequencies.


Receiver Diversity

In receiver diversity, the independent fading paths associatedwith multiple receive antennas are combined to obtain aresultant signal that is then passed through a standarddemodulator.


Performance Metrics

Array gain: it results from coherent combining of multiplereceive signals. Even in the absence of fading, this can stilllead to an increase in average received SNR.Diversity gain: it can mitigate the negative effect of fadingand result in the error probability as

Ps = cγ−M ,

where M is called the diversity order.


Selection Combining

In selection combining (SC), the combiner outputs thesignal on the branch with the highest SNR.For Rayleigh fading, we can prove that the average SNR ofthe combiner output isγΣ = γ

∑Mi=1

1i .


Threshold Combining

In threshold combining, the receiver scans each of thebranches in sequential order and outputs the first signalwith SNR above a certain threshold.Similarly to SC, only one branch output is used at a time.Different from SC, TC monitors the SNR at only onebranch.


Maximal Ratio Combining

In MRC, the output is a weighted sum of all branches bysetting

αi = aie−jθj ,

and the SNR is given by

γΣ =1

N0

(∑Mi=1 ai ri

)2

∑Mi=1 a2

i

When the SNR is high, the diversity order of MRC is M.


Equal Gain Combining

In EGC, the weights are the same and the SNR is given by

γΣ =1

N0M

(M∑

i=1

ri

)2

The performance of EGC is quite close to that of MRC,which typically exhibits less than 1dB of power penalty.


Short History of MIMO

1 Multiple-input multiple-output (MIMO).2 The earliest study on MIMO dates back to 1970s (A.R.

Kaye, D.A. George and W. van van Etten). Jack Winters atBell Laboratories and Jack Salz at Bell Labs publishedpapers on beamforming in the mid 1980s.

3 Paulraj and Kailath proposed the concept of SpatialMultiplexing using MIMO in 1993. Telatar derived thechannel capacity of MIMO channels. Foschini devisedBLAST system. Alamouti, Tarokh and Calderbank et aldeveloped space-time code.

4 MIMO is being used in 3G and 4G cellular systems.


Channel Model of MIMO

1 Suppose that there are nt transmit antennas and nr receive antennas. Weassume that the fading in each path is flat and Rayleigh. Furthermore, weassume that the fading channels in different channels are mutually independent.

2 The channel is represented by a nt × nr channel matrix H, whose elements aremutually independent complex Gaussian random variables.

3 Such an independent fading model can be generalized to more complicatedmodel (e.g. correlated fading). Refer to Tse’s book.


Decouple of MIMO Channels

1 Do singular value decomposition (SVD), then

H = UΣV H ,

where U and V are unitary matrices and Σ is a diagonalmatrix.

2 Input x = Vx . Output y = Hx + n. Multiply y with UH , then

y = UH(Hx + n)

= Σx + n.

Since Σ is diagonal, the correlated channels aredecoupled.


Channel Capacity

1 When no channel state information at the transmitter(CSIT) (but the receiver knows H perfectly), the transmitterputs equal power on each transmit antenna. The channelcapacity is given by

C = log det(

I +P

ntσ2n

HHH)

=

nt∑k=1

log(

1 +Pλk

ntσ2n

),

where λk are eigenvalues of HHH . Explicit expressionfor C can be found in Telatar’s paper.

2 When CSIT is available, water-filling can be done toimprove the capacity.


Numerical Results (1)

1 when nr > nt , increasing nr is useless.



1 when nt > nr , increasing nt is useless.



1 when nr = nt , capacity increases linearly.


Scaling Law

1 Consider equal power case (no CSIT). Fix noise power σ2n.

2 When P is sufficiently large, C ∼ min(nt ,nr ) log(P), whichincreases linearly with nt if nt ≤ nr since more independentparallel channels are used.

3 When P is sufficiently small, C ∼ P.4 MIMO works most efficiently in high power regime. It is

required that nt ≥ nr (otherwise the transmit antennas arewasted).


Degrees of Freedom

1 Degrees of freedom (DOF) means the number of parallelchannels.

2 The DOF of a MIMO system is min(nr ,nt ) since it can bedecomposed into min(nr ,nt ) parallel channels.


Bell Labs Layered Space Time (BLAST) Architectures

1 Proposed by G. J. Foschini to improve the transmissionrate.

2 Data transmission rate is improved from to .3 Two versions: V-BLAST and D-BLAST.


Encoding of V-BLAST

1 The encoding process is simple: demultiplex the data stream into nt streams(layers), encode them with single-user encoder (no joint coding) and transmitindependently.

2 Why called vertical BLAST? Serial data is transferred into a vertical vector.


Decoding of V-BLAST

1 At each receive antenna, the signals from different transmit antennas aresuperimposed (like a MAC channel).

2 At the decoder, the layers (streams) are sorted in descending order of receivedpower.

3 Each layer is estimated by considering the remaining layers as noise. Theestimate is fed back to cancel its interference to remaining layers.

4 Such a process is similar to the successive interference cancelation process inscalar MAC channel, thus achieving good performance.


Encoding of D-BLAST (2 Antenna Case)

1 Each codeword is made up of two blocks x iA and x i

B.2 At the first time slot, antenna 1 does not transmit and

antenna 2 transmits x1A.

3 In the remaining time slots, antenna 1 transmits x iB and

antenna 2 transmits x iA (if applicable).


Decoding of D-BLAST (2 Antenna Case)

1 Step 1: Do MMSE estimation for x1B and decoding

codeword 1.2 Step 2: Cancel x1

B in time slot 2 and do the same thing forcodeword 2.

3 Repeat the MMSE-estimation+Decoding+Cancelingprocedure until all codewords have been decoded.


D-BLAST and V-BLAST

1 Difference between V-BLAST and D-BLAST: in V-BLAST, each data stream usesonly one transmit antenna; in D-BLAST, the data streams are rotated and eachdata stream experiences all transmit antennas.

2 V-BLAST is a simpler version of BLAST. It is more feasible for implementation buttheoretically achieves worse performance.

3 D-BLAST achieves more diversity, but requires more complicated encoder anddecoder. It also suffers from the wastage at the beginning and termination.


Transmit Diversity: Alamouti Scheme

1 Alamouti scheme was found by Alamout in Bell Lab andpublished in JSAC (1998). It achieves full diversity for 2× 2MIMO system even when the channel gains are unknownat the transmitter.

2 DO NOT ALWAYS THINK A SIMPLE SCHEME HAS BEENFOUND BY OTHER PEOPLE!


Alamouti Scheme

1 Let h1 and h2 be the channel gains of two transmitantennas, respectively. Received signal y = (y1, y∗2 )T isgiven by (without noise)

y =

(h1 h2h∗2 −h∗1

)(s1s2

)= HAs.

2 Multiplying HHA HA, we have

zi = (|h1|2 + |h2|2)si , i = 1,2.


Space-time Code

1 Space-time code is the generation of Alamouti scheme inboth space (transmit antennas) and time.

2 In 1999, Tarokh, Jafarkhani, and Calderbank publishedtheir papers on space-time code.


Definition of Beamforming

1 "Beamforming is a signal processing technique used witharrays of transmitting or receiving transducers that controlthe directionality of, or sensitivity to, a radiation pattern."(adapted from wiki)

2 Such a pattern can be used to enhance signal strength orseparate users in different directions (directionalantennas). It has been called smart antennas.


Beamforming of Multiple Receive Antennas

1 Suppose one transmit antenna and nr receive antennas.Spacing of antennas is ∆rλ.

2 Received vector signal is given by

h = a√

nr exp(−j2πdλ

)e(Ω),

where d is distance, e(Ω) is signature waveform andΩ = cos(φ) is directional cosine.


Signature Waveform

1 Signature waveform is given by

e(Ω) =1√

nr(1, exp(−j2π∆r Ω), exp(−j2π2∆r Ω), ..., exp(−j2π(nr − 1)∆r Ω)) ,

where d is distance, e(Ω) is signature waveform and Ω = cos(φ) is directionalcosine.

2 Transmitters in different directions have different signature waveforms in thenr -vector space.

3 For two transmitters in two directions, we can use the null vector (steering vector)of Tx1’s waveform to remove its signal.



1 As nr →∞ (but L is fixed), | cos θ| → sinc(L∆Ω). (Why?Consider it as Fourier transform of a rectangular signal).

2 (Refer to Tse’s book), if |∆Ω| 1L , two directions cannot

be distinguished. 1/L is a measure of resolvability.


Phase Array

1 Receiver puts different weights a1, ...,anr on the receiveantennas.

2 The array response is the Fourier transform of a1, ...,anr .3 The receiver can change the weights to obtain arbitrary

receive pattern.


Applications of Beamforming

1 Multiple receive antennas (SIMO): can be beamforming toseparate users with spatial distinction, which is call spatialdivision multiple access (SDMA).

2 Multiple transmit antennas (MISO): similar analysis toSIMO; can be used to focus the power on the direction tothe receiver, thus increasing the SNR at the receiver anddecreasing the interference to other transmission pairs.


Interference in Multiuser Systems

If two nodes transmit in the same time and the samefrequency band, their signal will collide. Signal becomesinterference.Multiaccess: to separate multiple signals.


Different Multiple Access Schemes

TDMA: Separating in time domainFDMA: Separating in frequency domainCDMA: mixed in both time and frequency domains;separating by codeCSMA: separated in time, but without scheduling


Time Division Multiple Access

The time slots have been allocated before datatransmission.Synchronization, i.e. estimating timing information, is a keyproblem. Two types: decision-directed and non-decisiondirected.


Decision-directed Synchronization

Principle: assume the transmitted signal is known (e.g.pilot symbols);Expected received signal

s(t ; τ) =∑

k

s(k)g(t − kTs − τ).

Likelihood function:

L(τ) = exp[− 1

N0

∫T0

[r(t)− s(t ; τ)]2]


Time Offset Estimation

The time offset τ maximizing the likelihood satisfies

∑k

s(k)d

dτzk (τ) = 0,

wherezk (τ) =

∫T0

r(t)g(t − kTs − τ)dt .


Early-late Gate Synchronizer

Need not know the original signal.Principle: shift the time offset to match the correct one.


Mother of CDMA

Hedy Lamarr (1913-2000): a movie star in 1940s (sixhusbands). She has a star in the Hollywood Walk of Fame.On Aug. 11, 1942, US Patent 2,292,387 was issued toHedy Lamarr and Antheil. This is the early version offrequency hopping communications.


Frequency Hopping CDMA in WWII

Frequency hopping CDMA was widely used in World WarII.In each time slot, the transmit chooses one randomfrequency to transmit, for security.


Commercial CDMA Systems

IS-95 (Interim Standard 95) is the first CDMA based digitalcellular standard, pioneered by Qualcomm.Currently, there are two standards of CDMA sysetms:cdma2000 (3GPP2) and WCDMA (3GPP). Both are basedon direct-sequence CDMA.


Time Structure of DS-CDMA Systems

Each symbol contains N chips in time. N is calledspreading gain, or processing gain. Each chip could be 1or -1.Vector signal: r = xksk , where xk is scalar informationsymbol for user k and sk is an N-vector of the chips, calledspreading code (or signature waveform).


Orthogonal Spreading Code

s1,s2,s3,s4 =

1 1 1 11 1 −1 −11 −1 −1 11 −1 1 −1

Check sT

i sj = 0, if i 6= j .


CDMA Receiver

Received signal:

r =K∑

k=1

xksk + n.

How to detect xk from the superimposed signal?For user k , the scalar output of a correlation detector isgiven by

zk = sTk r = xk + sT

k n.


Difference between coding and CDMA

Compared with uncoded system, channel coding usesmore time and energy to transmit one bit.CDMA system uses the same time and power as a narrowband system to transmit one bit. There is no coding here.


Spectrum Spreading

There are N changes within a symbol period, therefore itrequires approximately N times bandwidth. CDMA is awideband systemBetter resolution of multiple paths.Larger channel capacity (recall Shannon’s formula).


Non-orthogonal Spreading Codes

In most practical CDMA systems, the spreading codes arenot orthogonal.Reason:

An orthogonal CDMA system can contain at most N users.More users will break the orthogonality.When multiple path fading exists, the orthogonality isbroken even if the spreading codes are orthogonal. (WHY?)The orthogonality is broken for asynchronous transmission.(WHY?)


Matched Filter

Matched filter: for user k , we use

zk = sTk r = xk + sT

k n.

Multiple access interference (MAI):

Ik =∑i 6=k

sTi sk .

Signal-to-interference-plus-noise ratio (SINR) is given by

SINR =E[|sk |4

]E[|Ik |2

]+ σ2

n.


SINR

Signal-to-interference-plus-noise ratio (SINR) is given by

SINR =E[|sk |4

]E[|Ik |2

]+ σ2

n.

Asymptotic case: as K ,N →∞

SINR → 1β + σ2

n.

(Suppose all transmit powers are 1.)


Rake Receiver

Working for multipath fading. Each finger corresponds to apath. Achieving diversity.


Near-far Problem

Because of inter-user interference, the user far from thebase station may be killed by a closer user.


Power Control

The user closer to the base station should transmit withless power and the user farer away from the bast stationshould transmit with larger power.Requirement of power control is usually expressed as (R.Yate, 1995)

p ≥ I(p),

where p = (p1, ...,pK ) is the vector of transmit power of Kusers, I(p) represents the vector of effective interference.


SINR

We consider K users and 1 base station. The channel gainfrom user k to base station is denoted by hk and the noisepower at base station m is denoted by σ2

n.The SINR of user k is given by pkµk , where

µk =hk∑

i 6=k Pihi + σ2n.

When the required SINR is γk for user k , the effectiveinterference can be written as

I(p)k =γk

µk.


Power Control Algorithm

The power control is carried out in an iterative way(proposed by R. Yates)1

p(t + 1) = I(p(t))

Theorem: If I(p) is feasible, for any initial powerconfiguration, the power control algorithm converges to aunique fixed point.

1R. Yates, “A framework for uplink power control in cellular radio systems”,IEEE Journal on Selected Areas in Communications, Vol.13, No.7,Sept.1995.


OFDM

OFDM: Orthogonal Frequency Division MultiplexingOFDM was born in 1960s in Bell Labs.Life begins at forty (John Lenon).Now OFDM is the fundamental signaling technique for 4Gcellular systems (UWB, LTE, WiMAX).


Big Picture of OFDM

The data is divided into many streams and transmitted onmany subcarriers (also called tones).


Features of OFDM

No need for equalization (no ISI). Each tone looks like ascalar channel. High speed.Good structure for resource allocation.


Why Use Random Access?

In TDMA, CDMA or OFDMA, the channels (time slots forTDMA, spreading code for CDMA and subcarrier forOFDMA) need to be distributed to the transmitters by acenter.In a general network, there is no center or the users mayemerge or quit, it is different to schedule the transmissionin a stationary way.In random access, there is no fixed channel assignment.The access is probabilistic and the signals are separatedby probability.

Advantage: no channel scheduling;Drawback: possible collision and less efficient; whenthroughput when the number of nodes is large.


Types of Random Access

Aloha: the first technology of random accessCarrier sensing multiple access with collision detection(CSMA-CD): used in EthernetCarrier sensing multiple access with collision avoidance(CSMA-CA): used in WiFi (IEEE 802.11)


History of Aloha Aloha

Proposed by Abramson in 1970 at the University of Hawaii.The idea was to use low-cost ham radio-like systems tocreate a computer network linking the far-flung campusesof the University.It can be categorized into pure and slotted Aloha systems.


Basic Protocol of Pure Aloha

Transmission: when a user has data, it transmitsimmediately. It is possible that some other user istransmitting.Random recession: if the transmission fails (due totransmission collision), the user waits for a random time τand then retransmits. The random time τ satisfies theexponential distribution:

p(τ) = αe−ατ


Basic Protocol of Slotted Aloha

The time is slotted. The transmissions can only begin atthe head of each time slot.The waiting time is discrete, measured by time slots.


Performance Analysis of Pure Aloha

Let Tp be the time required to send a packet. Then, if thereis another packet transmitting within the vulnerable region(2Tp), the transmission will fail.


Performance Analysis of Pure Aloha

Assume that the arrival of packets satisfies a Poissondistribution and averagely λ packets arrive within a unittime. The probability of k packets arrives within time periodt is given by

P(k) =(λt)ke−λt

k !

The probability that there is no packet within a period of2Tp is given by e−2G, where G = λTp. This is also theprobability of successful transmission.The average number of successfully transmitted packets(throughput), S, is given by

S = Ge−2G.

The maximum of S is 0.184 when G = 0.5.


Performance Analysis of Slotted Aloha

For slotted Aloha, the vulnerable time is Tp.Using the same argument, for slotted Aloha, S is given by

S = Ge−G.

The maximum of S is 0.368 when G = 1.


Comparison of Pure and Slotted Aloha

Slotted Aloha achieves better performance.


Carrier Sensing Multiple Access (CSMA)

Principle of CSMA: sense the carrier before transmission;if finding some other transmitter is transmitting, it waits fora random time and then transmit. A transmitter transmitsonly when the channel is detected idle.Two versions:

collision detection (CD): a transmitter is able to detectsignal collision;collision avoidance (CA): use RTS and CTS to clear hiddennode and exposed node (will explain later).


Nonpersistent CSMA/CD

Rule of transmission (from Proakis’ book):If the channel is idle, the user transmits a packet;If the channel is sensed busy, the user schedules thepacket transmission at a later time according to some delaydistribution. At the end of the delay interval, the user againsenses the channel and repeats.


1-persistent CSMA/CD

Rule of transmission (from Proakis’ book):If the channel is idle, the user transmits a packet;If the channel is sensed busy, the user schedules thepacket transmission at a later time according to some delaydistribution. At the end of the delay interval, the usertransmits with probability 1.


p-persistent CSMA/CD

Rule of transmission (from Proakis’ book):If the channel is idle, the user transmits with probability p ordelay by τ seconds with probability 1− p;If at time τ , the channel is still sensed idle, the above isrepeated. if a collision happens, the users rescheduleretransmission of the packets according to some delaydistribution;If at time τ , the channel is still busy, the user waits until itbecomes idle and repeat the above steps.


Comparison of Aloha and CSMA/CD

0.01-persistent CSMA looks the best. (Then, why considerother types of CSMA?)


Hidden Node and Expose Node

Hidden node: A is transmitting. C wants to transmit to Bbut is out of the sensing range for A, then C transmits andcollides with A at B.Expose node: B is transmitting, then C dare not transmit,but D is actually out of the interference range of B.


Collision Avoidance

When A wants to transmit, it sends a request-to-transmit(RTS) to B. Neighboring nodes then know A intends totransmit.When B agrees to receive, it sends a clear-to-transmit(CTS) to A. Neighboring nodes will keep silent.


Interference Limited and Thermal Limited

Thermal limited: noise is too strong and SNR is too small.Example: in a one-to-one communication system, thetransmitter and receiver are too far away from each other;or in a multiuser system that has very little interference.Interference limited: noise is negligible and interferencedominates; it is useless to simply increase transmit power.Example: CDMA system.


Two Approaches

Interference Average: consider interference as noise and allow collision; but theinterference is averaged. (we can also call it interference diversity). Example:symbol rate hopping OFDM

Interference Avoidance: avoid collision. Example: CDMA/CA.

ece442 communication system design lecture 1. basics of...

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