Physical layer network coding for next generation wireless broadband

Physical layer network coding for next generation wireless broadband Alister Burr, University of York agb1@ohm.york.ac.uk Agisilaos Papadogiannis, Chalmers University

Outline • The challenge of next generation wireless networks • Next generation network architectures • MIMO and MIMO cellular • Multi-user and Network MIMO • Physical layer network coding • Conclusions

Wireless networks – some history • Began with Marconi in 1890’s • … • 1st generation • analogue, telephony ~1980 (Japan) • 2nd generation • digital, some data ~1992 • 3rd generation • CDMA, flexible services, up to 384 kbit/s ~2002 • 4th generation • OFDM(A), full Internet access, up to 1 Gbit/s ???

4G • The “next generation” has been discussed ever since 3G standards were finalised a decade ago • however it was not initially clear what form the “fourth generation” might take • However starting from 2002 ITU-R has defined the requirements for IMT-Advanced • which has since then been generally accepted as the definition of 4G • Key requirement is 100 Mbit/s for high mobility and 1 Gbit/s for low mobility • Standards currently under development: • Mobile WiMAX (IEEE 802.16e/m) • 3GPP LTE-Advanced

The dream • To provide full Internet connectivity to everyone, anywhere • which means wirelessly • Next generation wireless research has usually focussed on a ‘headline’ maximum data rate • but of course this will not be the rate most users experience, • and probably is not the most important figure • In densely-populated cities a network for everyone must provide extremely high capacity densities

Required capacity density • Average population density in European cities ranges from 3400 - 5400/km2 • however in commercial district in working hours it will be much higher • say 8000/km2 • Suppose 10% subscribe, and 20% of those require access at busy hour • Expected data rate 5 Mbit/s 8000/km2 10%  20%  5 Mbit/s = 800 Mbit/s/km2

Capacity density of 1G • e.g. AMPS, U.S.A: • ~400 channels in each direction • ~15 km radius cells  700 km2 • re-use ~1:10  0.06 channels/km2, • equivalent to approx 1.8 kbit/s/km2 • in approx 50 MHz

Current and 4G systems • Currently one base station serves about 1km2 • 4G bandwidths proposed are ~ 40 MHz • Best available bandwidth efficiency averages about 2 bits/s/Hz across cell • hence capacity density is 80 Mbit/s/km2 • assumes 100% frequency re-use • We need an order of magnitude more! • 10 more bandwidth unlikely to be available

Increased density • We can also increase number of cells • BUT • need many more cell sites • interference

Cell edge problem • We may be able to increase bandwidth efficiency (bits/s/Hz) • use (e.g) advanced MIMO techniques • BUT mobile close to cell edge suffers interference from adjacent cells • Conventionally we reduce frequency re-use • but this reduces available bandwidth by factor 3 or more

BuNGee • University of York is part of a European project tackling these problems • Beyond Next Generation Mobile Broadband (BuNGee) • Proposes: • new hierarchical network architecture based on wireless backhaul • Advanced MIMO techniques for high bandwidth efficiency • Self-organising network for optimal spectrum use • Goal: 1 Gbit/s/km2

Achieving capacity density • Will probably need a combination of the approaches mentioned: • More spectrum • Improved bandwidth efficiency • especially increased use of MIMO • Increased frequency re-use (100%) • Reduced cell size • requires low base station installation cost, • and a cost-effective backhaul network

Wireless backhaul • Simple comparison with 4G proposals suggests we may need ~10 BSs per km2! • We believe that the only cost-effective way to provide this is by wireless backhaul • However must allow for spectrum used by backhaul links • Hence must minimise backhaul load

BuNGee architecture

Some figures • Assume HBS serves 1 km2 • Assume total 40 MHz available • 20 MHz for MS-ABS (access links); • 20 MHz ABS-HBS (backhaul) • Assume average 2 bits/s/Hz across cell • Then capacity per ABS = 20  2 = 40 Mbit/s • No. ABS per HBS = 1 Gbit/s / 40 Mbit/s = 25 • Area served by ABS = 1 km2/25 = 40 000 m2, or 200m square

ABS MS ABS MS HBS Relay ABS Wireless mesh network • Since cells are very small, • mobile (MS) may be served by more than one ABS • MSs now served by optimum combination of available ABSs • Practically abolishes concept of cells! • Overall network looks more like a wireless mesh network

Wireless relaying • A cell can be extended by adding fixed, or infrastructure relays • very similar architecture to wireless backhaul • with relays replacing ABSs • may allow direct connection of MSs to hub Relay Relay

Hierarchical wireless network • A generalised framework for network architectures involving wireless backhaul and/or relaying • we might allow: • more than one layer of relays • direct connections between nodes on the same level • MSs to connect to different relay levels • Again, similar to mesh network in structure

H11 ENCODER DECODER H21   HnR1 r s MIMO link model • MIMO = Multiple Input, Multiple Output • i.e. multiple antennas at each end of a link • Input and output signal can be modelled as (1  nT) and (1  nR) vectors, s and r; noise (1  nR):n • channel modelled as a matrix H:element Hij gives propagation between transmit antenna j and receive antenna i r = H s + n

n 1 n H s r' s' U VH r n nR nT Eigendecomposition • Multiply by matrices U and V at input and output of channel, where • columns of U,V are transmit and receive eigenvectors of the channel • Then U H VH =  • a diagonal matrix with the square roots of the eigenvalues of HHH on the diagonal, and r’i = is’i + n’i • i.e. we create a set of uncoupled channels, whose power gains are the eigenvalues • Each eigenvector can be treated as a steering vector for antenna array  transmit/receive beam patterns

Beamforming model n • Another way of viewing MIMO: • each input stream corresponds to a beam from the antenna array towards a multipath signal • can create as many such beams as there are antennas • hence can transmit up to n = min(nT, nR) beams • provided there are enough multipaths r' s' U VH

MIMO capacity • Capacity and bandwidth efficiency approximately multiplied by no. of streams, n • Slope of curves proportional to n • called multiplexing gain • Dramatic capacity gain!

U int d s int int Beamformer H int W V ˆ d r x U H matched d s n filter MIMO in interference • MIMO cellular system also subject to interference • Beamformer applies linear weights to maximise SNIR at output • filters signals from different directions to maximise signal to noise-plus-interference ratio

Capacity of MIMO cellular • 4 antenna elements • MIMO system capacity around 3  SISO • and more than 1.5  SIMO (smart antenna) • Beamformer (“prewhitening”) very important • Interference limited

Implications for 4G networks • MIMO can dramatically increase link capacity • and significantly increase cellular capacity • Note that capacity is mainly affected by n = min(nT, nR) • Still severely limited by inter-cell interference • Can we reduce the effect of interference?

Multi-user MIMO systems • It has been known since the 1960s that the optimum means of sharing a channel between several users may be by simultaneous, mutually interfering transmission • as opposed to time-division multiplexing, or other orthogonal multiplexing • Information-theoretic approach: • Multiple Access Channel - MAC (uplink) • Broadcast Channel - BC (downlink)

R2 C2 time-sharing rate Csum C1 R1 2-user SISO MAC • Rate region: set of achievable rates of the two sources • C1 and C2 are capacities of two channels without the other • “Corner points” achieved by successive interference cancellation • “Time sharing” sum rate limited to dashed line • in general achievable sum rate Csumexceeds this

Multi-user MIMO MAC • In a multi-user MIMO multiple access channel (uplink), • sum rate capacity limit is capacity of MIMO channel formed by combining all Tx antennas of all users • For nU users with nT Tx antennas, average Tx power Si and Tx time Ti(each) • where: • denotes capacity of nTnR MIMO channel with SNR S

nT BS nU nR Multi-user MIMO • Conventional TDMA/FDMA is equivalent to time-sharing • divides “headline” rate by no. of channels • MU-MIMO allows several users to share same time slot/channel • Users/BS can act as a single nT nU  nR MIMO system • Usually more BS than terminal antennas • multiplexing gain no longer limited by no. terminal antennas

Symmetric and asymmetric • Modest advantage when nT = nR (symmetric links) • Large advantage when nT nR (asymmetric links) • max. multiplexing gain becomes min(nR, nTnU)

R2 C2 time-sharing rate Csum C1 R1 Broadcast channel • Broadcast channel simply means one transmitter to many receivers • obvious example is radio/TV broadcasting, where same message is intended for all • also applies to cellular downlink, where a different message is intended for each receiver • In latter case can define a capacity region like that for multi-user MIMO • Again time sharing (TDMA/FDMA) is sub-optimal

Dirty paper coding (DPC) • This is an information-theoretic result which applies to a channel subject to interference where the interference is known at the transmitter • r = s + i + n • where s is the information signal, i is the interference, and n is noise • Achievable capacity of this channel is log2(1 + PS/Pn) • i.e. the same capacity as if the interference were not present • note this is not achieved by “pre-cancelling” the interference • On a broadcast downlink, the signal to one user is interference to another, and is known at the transmitter

f(x) x A Precoding in practice • Dirty paper precoding in principle operates by selecting a codebook (set of transmitted codewords) depending on the interference • A more practical scheme following the same principle is Tomlinson-Harashima precoding (THP) • Use modulo function f(x), and transmit: • where d is data, i is interference and k is some integer • At the receiver apply the modulo operation again: • interference is removed • some degradation due to “folding” of noise

Linear beamforming • Or simpler still, we can simply form beams to each user • ensuring also that we null interference to other users • this is a purely linear operation

Network MIMO • So far we have assumed that signals from other cells must be treated as interference • However it is possible for several (in principle, all) base stations to cooperate to transmit to a given mobile • or to receive from that mobile • Then there is in principle no CCI! • since all received signals are exploited as signals • The entire system then operates as a multi-user MIMO system with (on the uplink) nTnU nC transmit and nRnC receive antennas • where nC is the number of cooperating cells • in principle multiplexing gain approaches min(nRnC, nTnU nC)

Practical limitations • There are of course practical limitations to this concept: • Where should the processing be performed? • In a hierarchical network like BuNGee, at the hub • Distributed methods also possible, with processing at cooperating BSs • Computational complexity • Synchronisation • Is it feasible to keep cooperating base stations phase synchronous? (especially for downlink) • Backhaul capacity

Backhaul capacity requirements • On the downlink, if two BSs cooperate to communicate with an MS, that MS’s data should be sent to both • could double backhaul requirements • On the uplink, neither may be able to decode the MS without the signal from the other • hence analogue signal may need to be transmitted over the backhaul in high precision • may increase backhaul requirements by several times • Need to ensure backhaul links are efficiently used b1s1 b2s2 r2 r1 s1 s2 a1r1 + a2r2

Limitations of in-band backhauling • If we use wireless backhaul, we must account for bandwidth occupied • Can we re-use the same spectrum in backhaul and access segments? • in-band backhauling • Duplexing restrictions of ABSs usually prevent same resources being used in the two segments in the same place

Network coding • A network node applies a joint coding function to two (or more) incoming data streams • instead of simply switching between them • In this simple example (the “butterfly network”) the central node applies the XOR function (modulo-2 addition) • then both streams can be recovered at both output nodes • without network coding the central link would have to have twice the capacity to achieve this

SA b SB a R DB DA a  b a  b Two-way relay channel (2WRC) • Allows a relay to support transmissions in two directions at once • Relay broadcasts XOR combination of two incoming streams • Each destination can then reconstruct data intended for it by XOR combination with the data it transmitted

Physical layer network coding (PLNC) • In a wireless network, we do not have discrete, non-interfering paths • except by using TDMA or FDMA • Signals: • are broadcast to all nodes within range • combine additively in signal space • However it is still possible to extract a joint information stream equivalent to XOR combination

a b SA SB a + b DB R DA a  b a  b a b a+b a  b 0 0 -2 0 0 1 0 1 1 0 0 1 1 1 +2 0 PLNC for 2WRC • System operates in two phases • Phase 1: sources transmit simultaneously • Phase 2: relay transmits • Assume both sources transmit BPSK • {+1, -1}  {1, 0} Phase 1 Phase 2 SA, SB SA, SB time

SA b SB a R DB DA a  b a  b SA SB R(A) R(B) time SA SB SA, SB R(AB) R(AB) time time For comparison • Without network coding • Network layer network coding • Physical layer network coding

R S D Relay data compression • Cooperative diversity: relay provides extra diversity if S – D link fades • Phase 1: Source transmits to relay and destination • Phase 2: Relay transmits to destination • Note signal at relay is correlated with Phase 1 signal at destination • since both arise from the same data • This allows distributed compression using Slepian-Wolf coding • reduces the data relay must transmit

Slepian-Wolf coding R1 • If two data sources are correlated, their joint information content is less than the sum of their separate content • Can exploit this to compress the data • even though encoders are separate • White area on graph gives rate region • range of possible compressed rates to allow reconstruction S’1 S1 C1 D R2 S’2 S2 C2 R2 R1

T1 T2 B1 B2 B3 Hub PLNC in network MIMO • Example: • 2 terminals connectedto hub via 3 BS • B2 can use PLNC, to shareits link with the hub betweentwo terminals • It can use distributed compression, since the data is correlated with that via B1 and B3 • Reduces backhaul load

Physical layer network coding for next generation wireless broadband