Detection Algorithms for Physical Network Coding

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1 01 7th Intrnational ICST Confrnc on Communications and Ntworing in China (CINCOM Dtction lgorithms for Physical Ntwor Coding Chngang Pan, Jianjun Liu, Zhnping u China Mobil sarch Institut ijing, China panchngang@chinamobilcom bstract-this papr invstigats multi-usr dtction (MUD as wll as virtual singl-usr dtction (VSUD for dnoisingbasd physical ntwor coding in two-way rlay channls In MUD, th two sourc mssags ar dtctd sparatly and thn mappd into a rlaying mssag In VSUD, th rlaying mssag is obtaind dirctly dtcting th rcivd signal Maximum lilihood (ML algorithm and linar algorithms ar considrd for both singl-antnna cas and multi-antnna cas with and without transmit powr and phas control Suboptimal dtction algorithms with lowr complxity ar also proposd for VSUD Simulation rsults show that ML VSUD can achiv bttr E prformanc than ML MUD Th proposd dtction algorithms can achiv similar E prformanc to ML VSUD Indx Trms two-way rlay channl; physical ntwor coding; virtual singl-usr dtction; I INTODUCTION Wirlss mobil communications hav bn dvloping rapidly [1-5] For a two-way rlay channl, it usually nds thr phass to complt a data xchang using digital ntwor coding (DNC [6] Dnot th two sourc mssags s, rspctivly DNC first dtcts th rcivd signals to obtain th stimatd mssags s sparatly in th first two phass and thn maps thm into a rlaying mssag s s s, whr dnots a bit-wis XO opration owvr, sinc s only rprsnts th logic rlationship of s, full dcoding may b not ndd at rlay With idal phas and powr control, physical-layr ntwor coding (PLNC [7] can dirctly dtrmin th rlaying mssag s dtcting th rcivd signal This is implmntabl bcaus XO opration for binary bits is quivalnt to algbraic addition for bipolar bits Li PLNC, dnois-and-forward schm [8] timatand-forward schms [9] can dirctly map th rcivd signal to a rlaying mssag from a discrt st and can thus rmov th nois Thr, w rfr to ths physical ntwor coding schms as dnoising-basd physical ntwor coding (D-PNC schm D-PNC wors vry wll with strict phas and powr control For two-way multi-input multi-output (MIMO rlay channls, zro-forcing (ZF basd prcoding [10], lattic rduction aidd ZF basd prcoding [11], and gnralizd schur dcomposition-basd prcoding [1] can b prformd at sourcs to achiv th sam arrival phas and rcivd powr at rlay y doing so, rlay can dtrmin s using a singl-usr-li dtction W rfr to it as virtual singl-usr This wor was supportd in part th National Ky Projct undr Grant 010ZX dtction (VSUD Som wor has bn focusd on D-PNC schms in twoway MIMO rlaying without phas and powr control [13-15] This typ of ntwor coding schms put mphasis on signal dtction at rlay Idal dcoding schm is assumd in [14] Maximum-lilihood (ML dtction is considrd in [13] Maximum a postriori probability dtctor is usd in [15], which is quivalnt to ML dtctor thrin sids ths nonlinar algorithms, lowr-complxity linar algorithms, such as ZF and minimum man squar rror (MMSE dtction ar naturally introducd to D-PNC schms Ths algorithms ar traditionally usd for multi-usr dtction (MUD, whr th sourc mssags s can b dtctd sparatly, which mas DNC applicabl If ths algorithms ar mployd for VSUD, th dtction prformanc can b improvd In [13], a modifid ZF dtctor and MMSE dtctor ar proposd, which prfr to dtct s 1 s + s s s rathr than dtct s sparatly Thn s is drivd computing its lilihood ratio from stimatd s 1 In [16], w hav proposd an MMSE-basd linar dtctor which aims to dtct th algbraic product of sourc mssags, i s P ss Th algbraic product of bipolar bits rprsnts th sam logic rlationship as XO opration for binary bits Dtcting s P is simplr than dtcting both s 1 Th stimatd s P is dirctly mappd into s without lilihood ratio computation In this papr, w addrss th dtction algorithms for VSUD W first discuss ML algorithm for VSUD in singl-antnna cas and propos a suboptimal hard dtction algorithm for practical purpos Thn, w discuss ML algorithm and prsnt a linar dtction algorithm for VSUD in multi-antnna cass II SYSTEM MODEL Considr a narrowband bloc fading two-way rlay channl, whr sourc nods and hav singl antnna and rlay nod is quippd with N antnnas Dirct lin btwn and is assumd to b unavailabl and prfct uplin channl stat information (CSI is availabl at PSK is assumd but all th rsults can b straightforward xtndd to QPSK W considr a two-phas D-PNC schm, whr and transmit thir mssags simultanously to, y h P s + h P s + n, (1 j φ jφ whr y is th rcivd signal at, n is th nois at with n CN (0, δ I, h is th channl vctor from sourc to, is th transmittd symbol of sourc with transmit powr P and transmit phas φ, {, } /1/$ IEEE

2 If CSI of h or powr and phas control information is availabl at sourc nods, and can control thir transmit phass φ to achiv cohrnt transmission bfor or aftr signal procss Transmit powr P is dsignd undr th total transmit powr constraint, i P + P PT Without CSI or powr and phas control information at sourc nods, both and hav th sam transmit powr P P PT and th sam transmit phas φ φ 0 Thn, (1 can b rwrittn an quivalnt modl as y h s + h s + n, ( 1 whr n has a normalizd varianc of δ P T Upon obsrving y, can naturally dcod th symbol pair s, s with a maximum lilihood (ML algorithm j, arg min φ jφ yh h ( s, s s s P s P s (3 and thn obtain s s s Of caus, othr algorithms, such as ZF and MMSE can b mployd to dtct ( s, s W rfr to this as MUD Onc dtrmins th stimatd s, it will broadcast s to both and in th scond phas MUD is not optimal bcaus full dcoding is not ndd in two-way rlay channls In th nxt sction, w will dscrib dtction algorithms to dtct s s s dirctly from y W rfr to this as VSUD W considr ML for VSUD, whr s is dtrmind basd on th lilihood ratio of s W also dsign lowr-complxity dtction algorithms for VSUD III DETECTION LGOITMS: SINGLE-NTENN CSE In th cas of singl-antnna at, all th vctor variabls in signal modl (1 and ( dgrad into scalar variabls Transmission without transmit powr and phas control Without transmit powr and phas control, w considr th dtction algorithms basd on signal modl ( To dscrib th ML algorithm for VSUD, w dfin x yhs hs Th variabl x has a chi-squar distribution and its probability x distribution function (PDF is f ( x From this, w can now comput th lilihood ratio of s Pr ( y s 1 L( s y Pr ( y s 1 f ( x s 1, s 1 + f ( x s 1, s 1 f ( x s 1, s 1 + f ( x s 1, s 1 yhh y+ h+ h + (4 y+ hh y h+ h + h+ h ( a+ b ( a+ b ( + hh ( ab ( ab ( + whr a ( h y and b ( h y with ( dnoting th ral part and ( dnoting conjugat Thn w dtct s ( y ( y 1 L s 1 s (5 1 L s < 1 Th rsulting xprssion for L( s y is somwhat complx For practical applications, considring th symmtry of th lilihood ratio function L, w giv a simpl algorithm ( a ( b ( a b ( hh ( ( hh ls sign sign min, s (6 sign Transmission with transmit powr and phas control With transmit powr and phas control, w considr th dtction algorithms basd on signal modl (1 To achiv 1 cohrnt transmission, lt φ h h Transmit powr P ar givn to maximiz th Euclid distanc d, whr d P h + P h P h P h (7 y maximizing d, w hav T j { } P P h h + h, j,,, j (8 From this, (1 can b furthr simplifid to y h s + s + n, (9 whr 1 h h h h + h and n has a normalizd varianc of With such a signal modl in (9, th MUD ML algorithm in (3 is quivalnt to a hard dtction ( y ( y 1 h s (10 1 < h For VSUD, th lilihood ratio of s in (4 is simplifid to 1 h 4( y h 4( y h L( s ( y + (11 y ltting L( s ( y thrshold as 1, w can obtain a hard dtction 8h ( y h ln ( (1 4h From this, a simpl hard dtction algorithm is givn 1 1 y y h h s ( y < y h h IV DETECTION LGOITMS: MULTI-NTENN CSE Transmission without transmit powr and phas control Without transmit powr and phas control, w considr th dtction algorithm basd on signal modl ( In this cas, 64

3 ML algorithm can b applid into MUD using (3 Whn using ML for VSUD, w first comput th lilihood ratio of s W dfin x yhs hs Th variabl x has a chi-squar distribution with frdom of N and its PDF is ( N N 1 x f x x N, (14 whr N dnots th factorial of N From this, w can now comput th lilihood of s N ( N 1 yhh Pr ( y s 1 yh h + N (15a N ( N 1 y+ h+ h y+ h + h N N ( N 1 y+ hh Pr ( y s 1 y+ h h + N (15b N ( N 1 y h+ h y h + h N Thn w dtct s according to its lilihood ratio ( y s ( y s ( y s ( y s 1 Pr 1 Pr 1 1 s (16 1 Pr 1 Pr 1 < 1 VSUD using (16 can achiv bttr prformanc than MUD using (3, as shown latr owvr, th formr complxity is obviously than th latr on Similar to (6, w giv a lowrcomplxity algorithm ( c ( d ( c d ( hh ( ( h h ls sign sign min, s, (17 sign whr c ( h y and ( d h y Transmission with transmit powr and phas control With transmit powr and phas control, w considr th dtction algorithm basd on signal modl (1 Th transmit phass ar givn φ 0 and φ θ, whr θ is th angl of complx hh W first introduc lowr-complxity linar dtction for VSUD Th linar dtction vctor d and transmit powr P ar givn solving th following optimization problm θ θ ( + ( j j max d d P h P h d P h P h st P + P P T, (18 Considring th fact that th optimal d lis in th subspac spannd vctors h and h, w dsign d whrη P ( 1 j β θ βh h h h d, (19 1+ β 1β η1 1 1 hh h h and [ 0,1] ( α P, α ( 0, T β Lt P α PT and Givn β, d is maximizd whn From (0, w obtain α jθ ( αp ( α P d h h 0 (0 T T ( βη + 1β h ( β + ( 1 β η h + ( βη+ 1β h (1 y substituting α into d, diffrntiating d with rspct to β and furthr stting th drivativ to zro, w obtain th ncssary condition for th optimal solution β 1 β β 0 ( + h ( β ( β η h ( βη+ 1β From (, w can obtain a closd-form xprssion for β Unfortunatly, w find that th closd-form xprssion is quit complx Sinc th trm on th lft hand of quation ( is a dcrasing function of β, altrnativly, w can find β local rsarch with th initial valu of β 1 With th givn transmit powr P and linar dtctor d, (1 can b furthr simplifid to (9 with h bing rplacd d Thus, s can b dtctd finally (13 Whn ML is usd for VSUD, th dtction procss at rlay corrsponds to (16 with transmit powr and phas givn abov V PEFOMNCE EVLUTION In this sction, w valuat th prformanc in trms of bit rror ratio (E at th first phas of physical ntwor coding with MUD and VSUD using diffrnt dtction algorithms s s s s for MUD and r, E is dfind as Pr ( ( s s s Pr for VSUD, whr s ar th stimation symbols aftr dtction In th following Mont Carlo simulations, ach simulation runs 100 tims and ach mssag pact contains 51 bits For simplicity, th lmnts in h ar complx Gaussian random variabl with CN (0,1 Fig 1 shows th E prformanc of MUD and VSUD with diffrnt dtction algorithms for singl-antnna cas It can b sn that VSUD with dtction algorithm using (5 actually outprforms MUD with dtction algorithm using (3 Morovr, VSUD with algorithm using (6 achivs th sam prformanc as MUD algorithm using (3 Furthr obsrvation shows that transmit powr and phas control (TPPC can improv th E prformanc undr th total transmit powr constraint, with xpct that th prformanc of MUD is dcrasd with transmit powr and phas control in lowr SN rgion Fig shows th E prformanc of MUD and VSUD with diffrnt dtction algorithm without transmit powr and phas control for two-antnna cas For comparison purpos, w also considr th following thr dtction schms: 1 MUD with MMSE dtctor; VSUD with th dtctor in [13], dnotd MMSE-sum; 3 VSUD with th dtctor in [16], dnotd MMSE-product 65

4 E MUD using (3 without TPPC VSUD using (6 without TPPC VSUD using (5 without TPPC MUD using (10 with TPPC VSUD using (13 with TPPC ML and is suprior to othr dtctors Sinc VSUD using (17 has lowr complxity it is prfrabl than othr dtctors Fig 3 shows th E prformanc of MUD and VSUD with diffrnt dtction algorithm for two-antnna cas With TPPC, VSUD no mattr using (16 or (13 (Not that (16 and (13 should b computd with transmit powr and phas givn in subsction of sction IV can achiv bttr E prformanc than VSUD without TPPC VI CONCLUSION 10 - normalizd transmit powr P T / (d Figur 1 E for diffrnt dtction algorithms for singl-antnna cas E normalizd transmit powr P T / (d MUD with MMSE VSUD with MMSE-sum VSUD with MMSE-product MUD with ML using (3 VSUD using (17 VSUD with ML using (16 Figur E for diffrnt dtction algorithms without transmit powr and phas control for two-antnna cas E VSUD using (16 with TPPC MUD using (3 with TPPC VSUD using (13 with TPPC VSUD using (16 without TPPC 10-4 normalizd transmit powr P T / (d Figur 3 E for diffrnt dtction algorithms with transmit powr and phas control for two-antnna cas It can b sn that VSUD with ML using (16 has th bst E prformanc whil MUD with MMSE dtction has th wors E prformanc VSUD with MMSE-product dtctor has a prformanc clos to VSUD with MMSE-sum dtctor VSUD using (17 achivs th sam prformanc as MUD with ML and can provid similar prformanc to VSUD with In this papr, w invstigatd virtual singl-usr dtction with non-linar and linar algorithms for D-PNC in two-way rlay channls W prsntd lowr-complxity algorithms for both singl-antnna and multipl-antnna cass W find that VSUD with ML algorithm can ma bttr E prformanc than MUD with ML dtction Th prsntd algorithms can achiv similar prformanc to VSUD with ML whil has lowr complxity nc, thy ar practical for implmnt In futur wor, w ar invstigating th analytical rsults for th prsntd VSUD dtction algorithms EFEENCES [1] Y Zhou and ZG Pan, Impact of LPF Mismatch on I/Q Imbalanc in Dirct Convrsion civrs, IEEE Trans Wirlss Commun, vol 10, issu 4, pp , Jun 011 [] Y Zhou and TS Ng, Prformanc analysis on MIMO-OFCDM systms with Multi-cod Transmission, IEEE Transactions on Wirlss Communications, vol 8, issu 9, pp , Spt 009 [3] Y Zhou, J Wang, TS Ng, K iguchi and M Sawahashi, OFCDM: a promising broadband wirlss accss tchniqu, IEEE Communications Magazin, vol 46, pp 39-49, March 008 [4] Y Zhou, J Wang, and M Sawahashi, Downlin transmission of broadband OFCDM systms---part II: Effct of Dopplr Shift, IEEE Trans Commun, vol 54, no 6, pp , Jun 006 [5] Y Zhou, J Wang, and M Sawahashi, Downlin transmission of broadband OFCDM systms---part I: ybrid Dtction, IEEE Trans Commun, vol 53, no 4, pp , pril 005 [6] S Katti, ahul, W u, D Katabi, M Mdard, and J Crowcroft, XOs in th air: practical wirlss ntwor coding, in Proc of CM SIGCOMM 006, Pisa, Italy, Spt 006, pp [7] S Zhang, S C Liw, and P P Lam, ot topic: physical-layr ntwor coding, in Proc of CM Mobicom, Los ngls, C, Spt 006, pp [8] T Koi-ino, P Popovsi, and V Taroh, Optimizd constllations for two-way wirlss rlaying with physical ntwor coding, IEEE Journal on Slctd ras in Commun, vol 7, no5, Jun 009, pp [9] T Cui and J Kliwr, Mmorylss rlay stratgis for two-way rlay channls, IEEE Trans on Commun, vol 57, no 10, Oct 009, pp [10] Yang, K L, and J Chun, Zro-Forcing asd Two-Phas laying, in Proc of IEEE ICC, Glasgow, Scotland, Jun 007 [11] S Kim and J Chun, Ntwor coding with linar MIMO prdtctor using modulo in two-way channl, in Proc of IEEE WCNC, Las Vgas, NV, Mar 008, pp [1] J Yang and J Chun, Gnralizd Schur dcomposition-basd twoway rlaying for wirlss MIMO systms, in Proc of IEEE GLOECOM 08 [13] S Zhang, S C Liw, Physical layr ntwor coding with multipl antnnas, in Proc of IEEE WCNC 10 66

5 [14] I ammrstrom, M Kuhn, C Esli, J Zhao, Wittnbn, G auch, MIMO two-way rlaying with transmit CSI at th rlay, in Proc of IEEE SPWC 07 [15] Z Zhou and Vuctic, n optimizd ntwor coding schm in twoway rlay channls with multipl rlay antnnas, in Proc of IEEE PIMC, 009, pp [16] C Pan, J Gng, G Liu and Q Wang, Linar Dtction and Prcoding for Physical Ntwor Coding in Two-way MIMO rlay channls, accptd IEEE VTC011 fall [17] MinChul Ju and Il-Min Kim, Error Prformanc nalysis of PSK Modulation in Physical-Layr Ntwor-Codd idirctional lay Ntwors, IEEE Trans Commun, vol 58, no 10, Oct 010, pp

THE IMPACT OF A PRIORI INFORMATION ON THE MAP EQUALIZER PERFORMANCE WITH M-PSK MODULATION

5th Europan Signal Procssing Confrnc (EUSIPCO 007), Poznan, Poland, Sptmbr 3-7, 007, copyright by EURASIP THE IMPACT OF A PRIORI INFORMATION ON THE MAP EQUALIZER PERFORMANCE WITH M-PSK MODULATION Chaabouni