Non-Linear UWB Receivers With MLSE Post-Detection

Transcription

1 on-linear UWB Receiver With MLSE Pot-Detection Florian roech, homa Zaowki, and Armin Wittneben Communication echnology Laboratory, EH Zurich, 8092 Zurich, Switzerland Abtract A wirele body area network an average throughput of 500 kbp i conidered baed on ultra-wideband UWB) pule poition modulation. For a long battery autonomy ultra low power conumption i eential. In ] a FCC compliant ultra low power UWB communication ytem wa preented. By mean of a % duty cycle at 50 Mbp peak data rate, the power conumption of the ytem i etimated below mw. o increae inter-ymbol interference ISI) robutne a well a for ynchronization, a imple pot-detection maximum-likelihood equence etimator MLSE) ha been preented 2], 3]. In thi work, we extend thi MLSE approach to over-ampled energy detector and non-ideal integration window. Furthermore, we preent optimal MLSE metric baed on partial channel tate information a a performance benchmark. I. IRODUCIO Recently, ultra-wideband UWB) wirele body area network WBA) gained much interet due to a multitude of attractive application, uch a wirele health monitoring or ubiquitou computing. In a WBA, a number of mall node are placed very cloe to the human body. Since WBA node get their power from rechargeable batterie, it i inevitable that they are extremely energy efficient. o meet uch energy requirement, a low duty cycle operation of the node and thu a high peak data rate i eential. An ultra low power UWB communication ytem ha been preented ] complying the Federal Communication Commiion FCC) regulation. With a % duty cycle operation realized by a peak data rate of 50 Mbp an average power conumption below mw can be achieved. Due to low complexity requirement, an orthogonal binary pule poition modulation BPPM) wa conidered combined a imple energy detector ED). Due to the high pule rate of 50 Mbp, even a moderate channel delay pread lead to inter-ymbol interference ISI). hi dratically degrade the performance of the ED, which i very enitive to ISI. For increaed ISI robutne and a power efficient ymbol ynchronization, a imple potdetection maximum likelihood equence etimator MLSE) ha been preented 2], 3]. he MLSae it deciion on the output ample of a non-linear frontend which conit of a quaring device and a low pa LP) filter, which act a low complexity integration unit. In thi work, we extend the ytem to the cae of an over-ampled frontend and etimate the performance increae a a function of over-ampling. Furthermore, a imple but efficient equalization approach i propoed to mitigate ISI effect, introduced by practical low pa filter ]. In optical communication energy detection baed MLSE i well undertood 4]. Alo publication on MSLE in UWB impule radio UWB-IR) can be found 5]. However, linearized ytem are ued and effect of non-linear cro-term or non- Gauian ditribution are neglected. he main contribution of thi work i the application of the MLSE principle to an over-ampled, non-linear output of an analog UWB BPPM frontend, explicitly taking into account the effect of non-linear cro-correlation term, data dependent noie variance, non-gauian ditribution a well a non-ideal integration window. Different ub-optimal low complexity MLSE are invetigated auming Gauian ditributed ample at the output of the non-linear frontend. For the cae of intantaneou and average power delay profile IPDP/APDP) knowledge at the receiver, optimal MLSE metric are derived. hey take into account non-gauian ditribution and erve a benchmark for the ub-optimal receiver tructure. Although the frontend i over-ampled, all MLSE are implemented a imple Viterbi algorithm which work at ymbol rate and only very few tate. A a next tep toward practical receiver realization, the effect of non-ideal LP filter i conidered. It i hown that ISI introduced by LP filter of mall bandwidth can be removed almot entirely by a imple additional equalizer. A a decreaed LP bandwidth reduce ynchronization requirement, thi equalization i a promiing add-on in practical ytem. Overall, the preented cheme i a very attractive candidate for ISI mitigation and ymbol ynchronization in ultra low complexity receiver. he paper i organized a follow. In Section II, the ytem model i introduced. he MLSE metric are evaluated in Section III and V. he equalizer for non-ideal LP filtering i dicued in Section IV. Performance reult are preented in Section VI followed by a hort ummary in Section VII. II. DISCREE SYSEM MODEL According to Fig., a real dicrete time ytem model of a UWB-IR BPPM i conidered. It i aumed that only one pule per bit i tranmitted. hi i reaonable for hort range communication in WBA due to a moderate path lo ]. ime-hopping i omitted a a time-diviion multiple /08/$ IEEE 468

2 Fig.. Dicrete ytem model acce DMA) approach i conidered. he nominal pule period determine a BPPM frame. Each frame contain one tranmit pule. Depending on the BPPM ymbol value, the pule i tranmitted either in the firt or the econd BPPM half-frame of duration /2. he high peak data rate along a moderate delay pread yield ISI. Mapping the -th BPPM ymbol to a binary vector according to b = 0 x = x 2 x 2+ ] = 0 ] ) b = x = x 2 x 2+ ] = 0 ], 2) the receive ignal become rk] = x 2 h k ] +x 2+ h k ] + n k], 3) 2 hk] the dicrete channel impule repone CIR) of the overall ytem including tranmit and receive filter. he channel tap hk] and the noie ample nk] are independently Gauian ditributed. he receive ignal rk] i either fed to the ub-optimal energy detector top) or to the optimal receiver bottom), whoe metric i evaluated directly from the -th receive vector R of length. he output of the ED low pa F f) i ampled at 2 ova /. For notational convenience, the vector R i divided into p =2 ova part of l p = / p ample each, whereby and ova are choen uch that l p i an integer value: R = r,0, r,,..., r, p ]. 4) hi i depicted in Fig., too. he dicrete CIR i plit accordingly into p L part of l p ample: h = h,0, h,,..., h,p ], 5) where L = h / equal the number of conecutive ymbol which are covered by one CIR. hereby, h i the maximal number of channel tap. One part of R i now written a r,n = h i,n+iova x 2+ n ova i + n,n, 6) i=0 where n,n i jointly Gauian E { n,n n,n} = σ 2 I. III. MLSE FOR OVER-SAMPLED EERGY DEECORS In an ideal ED frontend, the impule repone of the filter fk] i realized a rectangular window of length l p. Hence, the frontend plit each BPPM ymbol into p part and generate the obervation vector L = L,0,...,L,p ]. 7) he n-th ample of the -th ymbol at the ED output equal: L,n = Ĉ,n,i,j ˆX,n,i,j + z,n + q,n, 8) and Ĉ,n,i,j = h i,n+i h j,n+jova ova 9) ˆX,n,i,j = x 2+ n ova i x 2+ n ova j, 0) z,n 0, 4σ 2 Ĉ,n,i,j ˆX,n,i,j ) ) q,n χ 2 σ 2, σ 4, 2) 2 ova ova where χ 2 ha 2 ova degree of freedom. he preented MLSE pot-detector have only limited CSI. In detail, three different MLSE are conidered. MLSE-C and MLSE-C2 are baed on intantaneou channel knowledge. MLSE-C know the intantaneou correlation matrix C = Ĉ Ĉ,α,β = h,αh,β. MLSE-C2 know only the diagonal value of C and aume that the cro-correlation are zero, i.e., C 2 = I h,0h,0, h,h,,..., h, ph,p]. MLSE-C3 i baed on average power knowledge. A we aume independently ditributed channel tap C 3 = E{C } = E{C 2 } i diagonal. Conditioned on their CSI, the MLSE aume Gauian ditributed ample at the output of the integrator F f). hi approximation i jutified by the Central Limit theorem due to the large number of ample in the ummation. Furthermore, they aume no correlation between the ample L,n, conditioned on the CSI. hi i correct for MLSE-C and MLSE- C2 a they have intantaneou CSI but not for MLSE-C3. All the ame MLSE-C3 perform well. All conidered MLSE are realized by Viterbi algorithm maximizing: argmax b log p L b,b,...,b L+, C )), 3) 469

3 and )) log p L b,b,...,b L+, C = p n=0 m,n = 0.5log 2σ,nπ 2 ) L,n m,n 2, 4) 2σ 2,n Ĉ,n,i,j ˆX,n,i,j + σ,n 2 = σ 2 Ĉ,n,i,j x,n,i,j + 2 ova σ 2 5) ova σ 4. 6) Increaing the over-ampling rate ova inherently increae the channel etimation effort. IV. EQUALIZIG PRACICAL LOW PASS FILERS By now the integration wa done by an ideal rectangular window of l p = / p ample, i.e., no additional ISI wa introduced by the LP. If the integration i realized by a realitic LP filter, e.g., a firt order LP filter, ignificant ISI can occur. Fortunately, the LP introduce correlation to ignal and noie component exactly the ame way a it i located after the amplifier and the additive noie. For certain type of LP filter, we how that a imple zero-forcing ZF) equalization i optimal in the ene that it entirely remove ISI out any performance lo and demontrate it effectivene in practice. In detail, we conider low pa filter of the form fk] = d w M n] = f d w p k d p ), 7) { 0 n M 0 ele, 8) and the filter coefficient f d. he correlated output of the ED can therefore be decribed by: L n = d f d L n d. 9) hi correlation can be entirely removed uing a imple ZF equalizer in the digital domain out any performance. Although analog filter decribed by 7) are hardly realizable in practice, a realitic LP filter of mall bandwidth can be approximated pretty well by uch a filter characteritic and can be equalized efficiently in the digital domain. Hence, a firt order LP and a imple equalizer lead to an ultra low power implementation of an almot perfectly rectangular integration window. he equalization can alo be integrated directly into the MLSE metric. However, thi i omitted due to notational clarity. V. OPIMAL MLSE RECEIVERS I FAS FADIG In thi ection, we preent two Viterbi algorithm for the cae, where the receiver ha acce to the linear vector R and know the overall IPDP or APDP, repectively. hey are conidered a benchmark for the ub-optimal but much impler over-ampled energy detection MLSE. he metric have been evaluated by plitting up the ymbolwie ML metric preented in 3]. For clarity, we retrict our attention to one lot interference, where the dicrete channel can be plit into a ignal component v and an interfering component g of length /2 each: h = v, g ]. 20) A hown in Fig., the Viterbi ue the metric f R ), which i baed on R from 4), the partial CSI C and the previou bit. hi lead to: argmax b )) log p R b,b, C. 2) In fat fading, the obervation vector R i independent of the pat if b and C are known. herefore, the preented Viterbi algorithm are optimal MLSE. A. Optimal Metric Baed on APDP We plit the APDP λ h into two part λ h = λ v, ] λ g : { ]} λ v = E v,0,,...,v 2,/2 2 22) { ]} λ g = E g,0,,...,g 2,/2 2, 23) and reorder the obervation vector R according to d = r,0,r,/2,r,,r,/2+,...,r,/2,r, ]. 24) With thi, the a-poteriori probability of the obervation d or equivalently R can be decribed by: p d b,b, λ v, ) ) λ g = exp {G}, 2π d G = 2 he determinant i: /2 r 2 k d,2k,2k + r2 k+/2 λ d,2k+,2k+ 25) +2r k r k+/2 d,2k,2k+. 26) d = ) /2 2 Ψ j, 6 j=0 Ψ j = 6σ 4 +6λ v,j λ g,j b b + b )) +6λ g,j σ 2 b + b )) 27) +6λ v,j σ 2 b + b )). 28) 470

4 he diagonal element of the invere equal: d,k,k = 6 λ g, k/2 b )+λ v, k/2 b + σ 2), 29) for k even and d,k,k = 6 λ g, k/2 b + λ v, k/2 b )+σ 2), 30) for k odd. he non-zero off-diagonal element are: d,k,k+ = λ d,k+,k = 6λ g, k/2 b b ), 3) whereby k i even. In cae of fat fading, the cro-correlation term vanih and the metric implifie to: d = λ h,k 32) d,k,k = /λ h,k 33) G = 2 r 2 k λ h,k. 34) Under the aumption of fat fading and independently ditributed Gauian channel tap, thi metric equal the optimal equence detector and i nearly bit error rate ) optimal. B. Optimal Metric Baed on IPDP For evaluation of the IPDP metric, we plit the probability ) p R b,b, C IPDP = /2 p r,k,r,k+/2 b,b,x k,u k ), 35) x and u the amplitude of v and g, repectively. If the IPDP i known to the receiver and the phae, i.e., the polarity of the multi-path change from ymbol to ymbol, preented Viterbi algorithm i optimal. For the ake of clarity, it i aumed that the IPDP tay contant over one burt, leading to following metric: p ) r,k,r,k+/2 b,b,x k,u k = { 4πσ 2 exp 2σ 2 r,k 2 + r,k+/2 2 + x2 k +u 2 k b + b )] ]} coh b σ 2 ) r,k u k + b r,k+/2 u k ]) +b r,k x k + b ) r,k+/2 x k { exp } σ 2 b b ) x k u k ] + coh b σ 2 ) r,k u k + b r,k+/2 u k ]) b r,k x k b ) r,k+/2 x k { }] exp σ 2 b b ) x k u k ]. 36) VI. PERFORMACE o ee the impact of over-ampling and LP filtering, we compare the performance of different MLSy mean of imulation. he i plotted over the ignal-to-noie ratio / 0, where denote the energy per bit and 0 /2 i the noie power pectral denity. We aume uniformly ditributed channel tap, which i a kind of wort cae cenario for a given delay pread. o achieve a data rate of 50 Mbp BPPM, one bit ha to be tranmitted every 20 n. A BPPM frame ha a duration of =20n and a half-frame a duration of 0 n. Hence, ISI occur for CIR a duration of more than τ = 0 n. o invetigate the performance gain achievable by over-ampling, moderate and trong ISI are conidered auming an ideal integration window. In cae of moderate ISI the CIR ha a duration of τ =4n and in cae of trong ISI τ =9n. a) Moderate ISI: In Fig. 2, the performance of the MLSE-C2 intantaneou out cro-term) and MLSE-C3 average) i hown for different over-ampling factor ova. A benchmark, the performance curve of the ignificantly more complex but optimal MLSE-APDP and MLSE-IPDP are given. he performance of the ymbolwie ED i indicated a well and demontrate it high enitivity even to moderate ISI. Already the very limited CSI C 2 or C 3 out overampling lead to ignificant performance improvement. But both MLSE-APDP and MLSE-IPDP how till ignificantly better performance highlighting that there i till pace for improvement. A mall over-ampling factor ova =2bring again a large performance gain for both MLSE-C2 and MLSE- C3. he performance of the MLSE-C3 doe not improve further by increaing the over-ampling factor to ova > 2. hi i due to the fact that the uniform APDP τ =4n can be decribed almot perfectly by 3 integration part of int / ova =5n duration. Depending on the APDP at hand, higher over-ampling can till bring improvement in other cenario. he performance gap between the MLSE-C3 and the MLSE-APDP i due to the non-gauian ditribution and the correlation between firt and econd half-frame conidered in the MLSE-APDP metric. he MLSE-C2 further improve higher over-ampling and for ova =2achieve almot the ame performance a the much more complex MLSE- APDP. b) Strong ISI: For a uniform APDP τ =9n, the MLSE-C3 performance doe not improve ignificantly over-ampling, a the APDP over two PPM lot i almot flat. hi i hown in Fig. 3. he MLSE-C3 doe hardly improve even for an over-ampling of ova = 60. MSLE-C and MLSE-C2 improve teadily increaing ampling rate. Although the over-ampling gain do not eem very large on firt glance, there i till a SR difference of about 4dB between ova = and ova = 20 at a = and much larger gain can be expected for non-uniform APDP. he performance gap of 3dB between MLSE-C2 ova = 20 and the MLSE-IPDP arie 47

5 Fig Fig. 3. C2 ova= C2 ova=2 C2 ova=2 C3 ova= C3 ova=2 C3 ova=60 IPDP APDP / 0 performance in cae of moderate ISI τ =4n) C ova=20 C2 ova= C2 ova=2 C2 ova=4 C2 ova=20 C3 ova= C3 ova=60 IPDP APDP / 0 performance in cae of trong ISI τ =9n) due to the Gauian aumption made for the metric of the MLSE-C2, which looe it appropriatene increaing over-ampling. he conideration of the cro-term in the metric of C doe not improve the performance ignificantly compared to MLSE-C2. hi agree earlier finding for ova =. It wa found that the cro-term bring only mall improvement for ISI below 20 n 2]. he performance of the MLSE-APDP depend much on the amount of information contained in the APDP. If the APDP i the reult of averaging over very different channel, the APDP i very different from the IPDP and contain hardly ueful information. In thi cae, the MLSE-APDP approache the MLSE-ED. However, if the APDP reult from averaging over rather imilar channel, uch a in a low fading cenario, the APDP reemble pretty much the IPDP and contain a lot of ueful information. In thi cae, the MLSE-APDP approache the MLSE-IPDP. UWB i baically an indoor technology, where low fading cenario dominate and the APDP i imilar to the IPDP. Hence, preented gain for MLSE-C and MLSE-C2 baed on intantaneou energy value, how a high potential of thi approach for many UWB LDR application. c) on-ideal Low Pa Filtering: By now the integration unit wa idealized by a rectangular integration window. But to achieve an ultra low power conumption, the integration 0 2 ZF Ideal LP C3 ova=4 LP C3 ova=4 EQ C3 ova=4 Idieal LP C2 ova=4 LP C2 ova=4 EQ C2 ova= / 0 Fig. 4. performance firt order LP filter of 20 MHz bandwidth and ZF equalizer window i preferably realized by a imple firt order low pa filter ]. In order to enable a reaonable integration duration and hence, to relax ynchronization requirement, a mall bandwidth i required. hi introduce ISI. In Section IV, we howed that by a imple ZF equalizer of only a few ample the ISI can be canceled almot entirely. In Fig. 4, thi i hown for moderate ISI τ =4n, an over-ampling factor of ova =4and LP filter bandwidth B =20 MHz. By application of the firt order LP filter the performance degrade ignificantly up to 5dB due to trong ISI. However, the ISI i entirely removed again by the imple ZF equalizer. VII. COCLUSIOS A promiing low complexity MLSE pot-detection approach for ISI mitigation wa invetigated. It potential wa etimated by benchmarking it to optimal MLSE metric derived for APDP and IPDP knowledge. It wa hown that the preented MLSE approach again improve ignificantly, if marginal over-ampling i applied. Furthermore, the lo from Gauian approximation and neglected cro-correlation wa etimated below 3dB. A imple ZF equalizer wa preented which effectively cancel ISI introduced by a realitic LP filter and therefore, make the propoed pot-detection a valuable cheme for future ultra low power tranceiver. REFERECES ] F. roech, C. Steiner,. Zaowki,. Burger, and A. Wittneben, Hardware aware optimization of an ultra low power UWB communication ytem, in IEEE Int. Conf. Ultra-Wideband ICUWB), Singapore City, Singapore, September 24 26, ] F. roech and A. Wittneben, MLSE pot-detection for ISI mitigation and ynchronization in UWB low complexity receiver, in IEEE Veh. ech. Conf., Dublin, Ireland, ]. Zaowki, F. roech, and A. Wittneben, Partial channel tate information and interymbol interference in low complexity UWB PPM detection, in IEEE Int. Conf. Ultra-Wideband ICUWB), Waltham, MA, September 24 27, ] J. R. Barry, Sequence detection and equalization for pule-poition modulation, in Proc. ICC, vol. 3, ew Orlean, LA, May 5, 994, pp ] M. Sahin and H. Arlan, Inter-ymbol interference in high data rate UWB communication uing energy detector receiver, in IEEE Int. Conf. Ultra-Wideband ICU), Zurich, Switzerland, Sept. 5 8,