Performance Analysis Of Time Hopping And Direct Sequence UWB . - UMD

1y ago
7 Views
1 Downloads
571.02 KB
5 Pages
Last View : 25d ago
Last Download : 2m ago
Upload by : Troy Oden
Transcription

Performance Analysis of Time Hopping and DirectSequence UWB Space-Time SystemsW. Pam Siriwongpairat, Masoud Olfat, and K. J. Ray LiuDepartment of Electrical and Computer Engineering,University of Maryland, College Park, MD 20742, USA. {wipawee, molfat, kjrliu}@eng.umd.eduAbstract— In this paper, we analyze the performance of UltraWideBand (UWB) Multiple-Input Multiple-Output (MIMO) systemsemploying various modulation and multiple access schemes, including Time Hopping (TH) Binary Pulse Position Modulation (BPPM),TH Binary Phase Shift Keying (BPSK), and Direct Sequence (DS)BPSK. We quantify the performance merits of UWB Space-Time(ST) systems regardless of the specific coding technique. We introduce a framework that enables us to compare UWB-MIMO systemswith conventional UWB single-antenna systems in terms of diversityand coding gains. We show that the combination of ST coding andRake architecture is capable of exploiting spatial diversity as well asmultipath diversity, richly inherent in UWB environments. We findthe upper bound on the average Pairwise Error Probability (PEP)under the hypothesis of quasi-static Nakagami-m frequency selectivefading channels. Finally, simulation results are presented to supportthe theoretical analysis.I. I NTRODUCTIONUltra-WideBand (UWB) technology is defined as a transmission scheme that occupies a bandwidth of more than 20% ofits center frequency, or typically more than 500 MHz. TheMultiple-Access (MA) capability of UWB system can be attainedby incorporating the UWB signal with a pseudo-random TimeHopping (TH) or spreading sequence. With its unique propertiesof extensive multipath diversity and support for MA, UWB isa viable candidate for short range communications in densemultipath environments.Multiple-Input Multiple-Output (MIMO) system has been wellknown for its potential of improving system performance undermultipath scenarios. By the use of Space-Time (ST) codingtechniques, MIMO can provide both diversity and coding advantages simultaneously, and hence yield high spectral efficiency andremarkable quality improvement.To exploit the benefits of both UWB and MIMO systems, UWBST coded scheme has been proposed [1]. The authors in [1]suggested an UWB ST coded system based on repetition code,which is a special case of what we present in this work. In thispaper, we consider UWB ST systems with various modulationand MA schemes including TH Binary Pulse Position Modulation(BPPM) [2], TH Binary Phase Shift Keying (BPSK) [3], andDirect Sequence (DS) BPSK [4]. We quantify the performancefigures of UWB ST systems regardless of specific coding scheme.Based on quasi-static Nakagami-m frequency selective fadingchannel model, we characterize the performances of UWB STsystems with the diversity and the coding gains. We utilize theReal Orthogonal Design (ROD) [5] as the engine code for UWBST codes. Our simulation results show that DS-UWB-MIMOtransmission provides superior performance in both single-userand multi-user scenarios.IEEE Communications SocietyGlobecom 2004The rest of the paper is organized as follows. Section IIdescribes the models of UWB ST signals. The structure of UWBMIMO receivers and the analysis of the received UWB ST signalsare presented in Section III. In Section IV, we investigate thesystem performances in terms of the upper bound of the PairwiseError Probability (PEP). The performances of UWB ROD STcodes are evaluated in Section V. Section VI describes numericalresults and finally Section VII concludes the paper.II. UWB ST S IGNAL M ODELSWe consider UWB-MIMO multi-user environment with Nuusers, each equipped with Nt transmit antennas, and a receiverwith Nr receive antennas. At each transmitter, the input binarysymbol sequence (coded or uncoded) is divided into blocks ofNb symbols. Each block is encoded into a ST codeword tobe transmitted over Nt transmit antennas during K time slots.Since K time slots are required to transmit Nb symbols, thecode rate is R Nb /K. Each ST codeword matrix can thenbe expressed as an K Nt matrix Du whose (k, i)th elementis diu (k), diu (k) { 1, 1}, which represents the binary symboltransmitted by the uth user at transmit antenna i over time slotk. The transmitter converts the ST codeword Du into UWB STsignal matrix X̃u (t) whose (k, i)th element is the transmittedUWB signal x̃iu (k; t) corresponding to the symbol diu (k). Thesignal x̃iu (k; t) depends on the particular MA and modulationschemes and will be discussed in the following subsections.A. TH-BPPMThe information of TH-BPPM system is conveyed by thepositions of the pulses. The transmitted signal can be describedas [2] Eu1 diu (k)x̃iu (k; t) w̃ t kTf cu (k)Tc Td , (1)Nt2where w̃(t) is the transmitted monocycle of duration Tw , and Tfis the pulse repetition period with Tf Tw . The monocycle Eu /Ntis normalized to have unit energy, and the factorensures that the total transmitted energy of the uth user is Euduring each frame interval, independent of the number of transmitantennas. Each frame contains Nc subinterval of Tc secondswhere Nc Tc Tf . The TH sequence of the uth user is denotedby {cu (k)}, 0 cu (k) Nc 1. It provides an additionaltime shift of cu (k)Tc seconds to the k th monocycle in orderto allow MA without catastrophic collisions. Td represents themodulation delay which is used to distinguish between pulsescarrying information diu (k) { 1, 1}. Since an interval ofTw Td second is used for one symbol modulation, the hopduration is chosen to satisfy Tc Tw Td .35260-7803-8794-5/04/ 20.00 2004 IEEE

r 0 (t )TH-BPSK scheme exploits the TH sequence concept as doesin the TH-BPPM. However, the information in TH-BPSK systemis carried in the polarities of the pulses. The transmitted UWBTH-BPSK signal is given by [3] Eu iix̃u (k; t) d (k)w̃(t kTf cu (k)Tc ).(2)Nt uSimilar to the TH-BPPM case, each frame contains only onemonocycle with a delay corresponding to the assigned TH sequence, {cu (k)}, 0 cu (k) Nc 1. Since the modulationinterval is Tw , the hop duration is selected such that Tc Tw .The monocycle is normalized to have unit energy, and the totaltransmitted energy per frame of the uth user is Eu .C. DS-BPSKIn DS-BPSK systems, the information is spread by a sequenceof multiple monocycles whose polarities are determined by the 1spreading sequence {cu (nc )}nNcc 0, cu (nc ) { 1, 1}. The transmitted DS-BPSK signal is modelled as [4] N K 1c 1 Eu iidu (k)cu (nc )w̃(t kTf nc Tc ). (3)x̃u (t) Nt Ncn 0k 0cThe frame interval Tf is divided into Nc segments of durationTc . The hop period is chosen to satisfy Tc Tw . Since eachframe contains Nc normalized monocycles, we introduce thefactor 1/Nc to ensure that the sequence of Nc monocycleshas unit energy. With the factor Eu /Nt being included, thetransmitted energy per frame is Eu .III. UWB-MIMO R ECEIVER D ESCRIPTIONSWe consider frequency selective channel model [6] where thechannel of the uth user is modelled as a tapped-delay line with Lutaps. The channels are assumed to be real, mutually independentand quasi-static, i.e., the channels remain constant over a block ofK time slots. The channel impulse response from the ith transmitantenna of the uth user to the j th receive antenna is given byhiju (t) L u 1αuij (l)δ(t τu (l)),0k'RakeReceiver (t )RakeReceiverL 1l ' 0{ y ( l ')}N r 1k'L 1l ' 0k ' 0, , K 1D̂0Fig. 1: UWB-MIMO receiver description.where Γ(·) denotes the Gamma function, m is the fading parameter, and Ωu (l) is the average power. We assume that {τu (l)}and Ωu (l) of the lth path are similar for every transmit-receivelink. For the signal transmitted from the desired user, we assumethat the TH or spreading sequence and Channel State Information(CSI) are known at the receiver.At the receive antenna output, the shape of transmitted monocycle w̃(t) is transformed to its second derivative due to the effectof propagation channel and the variation of antenna characteristicscaused by large bandwidth [7]. Denote the received monocycleas w(t) and define xiu (k; t) similar to the transmitted waveformx̃iu (k; t) by replacing w̃(t) with w(t). The received monocycle isassumed known at the receiver.The autocorrelation function of w(t) is given by γ(s) w(t s)w(t)ds, where γ(0) 1.The received signal at receive antenna j comprises the signal fromthe desired user, MAI and noise, i.e., rj (t) r0j (t) njM U (t) Nu 1 jru (t),nj (t), where njM U (t) u 1ruj (t) Nt 1 K 1u 1 L αuij (l)xiu (k; t τu (l))i 0 k 0 l 0denotes the signal from user u, and nj (t) is real additive whiteGaussian noise process with zero mean and two-sided powerspectral density N0 /2.At the receiver, we employ L-finger (L maxu {Lu }) Rakereceivers, each adopting a reference waveform vk (t) whichthcomprises the delay versions of w(t). The output of the l correlator at receive antenna j is given by jj ykj (l ) vk (l )rj (t)dt yd,k(5) (l ) nT,k (l ), (4)l 0where {αuij (l)} are the multipath gain coefficients, {Lu } denotethe number of resolvable paths, and {τu (l)} represent the pathdelays relative to the delay of the desired user’s first arrivalpath. Without loss of generality, we consider the first user asthe desired user, and assume that τ0 (0) 0. We analyze anasynchronous MA system in which the relative propagation delaysare random variables derived from the uniform distribution. Inorder to simplify the analysis, we assume that the minimumresolvable delay is equal to the pulse width, as in [4]. To avoid theInter-Symbol Interference (ISI), we choose the signal parametersto satisfy Nc Tc maxu {τu (Lu 1)} Tf . The channel fading isassumed to be Nakagami-m distributed with a Probability DensityFunction (PDF) m 2mm 22m 1ijp αu (l) (x) xexp x ,Γ(m) Ωu (l)Ωu (l)IEEE Communications SocietyGlobecom 2004rN r 1{ y ( l ')}Maximum LikelihoodDecoderB. TH-BPSKjj where vk (l ) vk (t τ0 (l )), yd,k (l ) and nT,k (l )jj nM U,k (l ) nk (l ) denote the correlator outputs correspondingto the desired transmitted data and the MAI plus thermal noise,respectively. Assuming no ISI, only the desired user’s signalthj transmitted during the k frame will contribute to yd,k (l ).j Thus, we can express yd,k (l ) asj yd,k (l ) Nt 1 L0 1 i 0l 0 α0ij (l) vk (l )xi0 (k ; t τ0 (l))dt. (6)The Rake receivers are followed by a Maximum Likelihood (ML)decoder where the decoding process is jointly performed acrossall Nr receive antennas, as shown in Fig. 1. In what follows,we analyze the receiver assuming different modulation and MAtechniques employed.A. TH-BPPMThe design of TH-BPPM receiver depends on the choice of themodulation delay, Td . In the followings, Td arg minTd γ(Td ),35270-7803-8794-5/04/ 20.00 2004 IEEE

as in [2]. The correlation waveform adopted at each Rake receiveris modelled as vk (t) w(t k Tf c0 (k )Tc ) w(t k Tf c0 (k )Tc Td ). After some manipulations, we obtain Nt 1E0 j yk (l ) [1 γ(Td )]di (k )α0ij (l ) njT,k (l ),Nt i 0 0which can be expressed in the matrix form as Yj [1 γ(Td )] E0 /Nt D0 Aj0 NjT ,(7)where D0 is the desired user’s transmitted ST symbol definedpreviously. Both matrices Yj and NjT are of size K L whose(k, l)th elements are ykj (l) and njT,k (l), respectively. An Nt Lmatrix Aj0 represents the multipath gain coefficient matrix inwhich (i, l )th element is α0ij (l ). Given the CSI on MIMOchannels, the decoder performs ML decoding by selecting acodeword D̂0 which minimizes the square Euclidean distancebetween the hypothesized and actual correlator output matrices.The decision rule can be stated as N r 1E0jD0 Aj0 2 ,(8)D̂0 arg min Y [1 γ(Td )]D0Ntj 0where X denotes the Frobenius norm of X [8].B. TH-BPSKThe reference waveform for TH-BPSK is vk (t) w(t j k Tf c0 (k )Tc ). From (2) and (6), we find that yd,k (l ) Nt 1 iij E0 i 0 d0 (k )α0 (l ). Using (5), and rewriting all L corNtrelator outputs of each receive antenna in the matrix form, weobtain Yj E0 /Nt D0 Aj0 NjT ,(9)in which Yj , Aj0 and NjT are in the same forms as the onesstated in (7). The decision rule can be written similar to (8) as N r 1E0jD0 Aj0 2 .(10)D̂0 arg min Y D0Ntj 0C. DS-BPSKThe DS-BPSKreceiver adopts the monocycle sequence N 11/Nc ncc 0 c0 (nc )w(t k Tf nc Tc ) as thevk (t) j reference waveform. Using (3) and (6), yd,k (l ) is given by L Nt 10 1E0 j di0 (k )α0ij (l)f (l, l ),(11)yd,k (l ) Nt i 0l 0 N 1 N 1where f (l, l ) Nc 1 ncc 0 c0 (nc ) ncc 0 c0 (nc )γ((nc nc )Tc (τ0 (l) τ0 (l ))). Combining (11) and (5), the correlatoroutput can be expressed in the matrix form as Yj E0 /Nt D0 Aj0 F NjT ,where F is an L0 L matrix whose (l, l )th element is f (l, l ),and Aj0 is of size Nt L0 in which (i, l)th component is α0ij (l).Subsequently, the decision rule can be stated as N r 1E0jD̂0 arg minD0 Aj0 F 2 . Y D0Ntj 0IEEE Communications SocietyGlobecom 2004IV. P ERFORMANCE A NALYSISFirst we can show that the noise sample njk (l ) isGaussiandistributed with zero mean and variance σn2 N0 2 v (l )dt. Define niu,k (l, l ) v (l )xiu (t 2 k kjj τu (l))dt. We express n (l ) (see (5)) as nM U,k (l ) Nu 1 Nt 1 L 1 ijM U,k i α(l)n(l,l).Usingthesameapuu,k u 1i 0l 0proach as in [7], one can show that niu,k (l, l ) is approximately Gaussian random variable with zero mean and variance2 (Eu /Nt )σa2 where σa2 T1f w(t s)v(t)dt ds. Assuming independent Nakagami-m fading coefficients, independent of the transmitted signals, and using central limit theorem,we can show that for sufficiently large L, Nt and Nu , njM U,m (k)is approximatelyGaussianrandom variable with zero mean and Nu 1 L 1variance σa2 u 1Eu l 0 Ωu (l). Hence, the MAI and noisenjtot,k (l ) is zero mean Gaussian random variable with variance Nu 1 L 1σn2 T σa2 u 1Eu l 0 Ωu (l) σn2 . Since the total noiseand interference can be approximated with Gaussian distribution,PEP can be evaluated in a similar fashion as in the conventionalnarrowband MIMO system. The value of σn2 , σa2 , and PEP dependon particular modulation and MA techniques, and will be givenin the following subsections.A. TH-BPPMBased on the reference signal in Section III-A, we can show2222that σn2 [1 γ(Td )] N0 , and σa 2(σ̄a σd ) where σ̄a 1122Tf γ (s)ds and σd Tf γ(s)γ(s Td )ds. Suppose thatD0 and D̂0 are two distinct transmitted ST codewords, followingsimilar calculation steps as in [6], the PEP conditioned on thechannel coefficient matrix {Aj0 } can be upper bounded by Nr 1 j 2 ρ j D0 D̂0 A0,P D0 D̂0 {A0 } exp4Nt j 0(12)2where ρ [1 γ(Td )] E0 /(2σn2 T ) which can be expressed as 1 N L 1u 12N0 /E0Eu σ̄a2 σd2Ωu (l) .ρ 42[1 γ(Td )][1 γ(Td )] u 1 E0l 0The upper bound of the PEP can be obtained by averaging (12)over all possible channel realizations. The resultant PEP can befound as [9]ρ m̃rNr LP D0 D̂0 G0 (m̃),(13)4Nt11 r 1 L 1Lrλ, m̃ where G0 (m̃) m̃ 1Ω(l)i0i 0l 0r 1Nt m(Nt m m 1) 1 , r is the rank and {λi }i 0representnonzero eigenvalues of matrix Z (D0 D̂0 )T (D0 D̂0 ). For asingle user system, since there is no effect of MAI, ρ reduces to[1 γ(Td )] E/2N0 . Thus, the PEP upper bound in (13) becomes m̃rNr L[1 γ(Td )] EP D0 D̂0 G0 (m̃).8Nt N0In this case, the exponent m̃rNr L determines the slope of theperformance curve plotted as a function of SNR, whereas theproduct G0 (m̃) displaces the curve. Hence, the minimum valuesof m̃rNr L and G0 (m̃) over all pairs of distinct codewords definethe diversity gain and the coding gain, respectively.35280-7803-8794-5/04/ 20.00 2004 IEEE

B. TH-BPSKSince the reference signal for TH-BPSK system is the shiftedmonocycle whose energy is unity, we can see that σn2 N0 /2and σa2 σ̄a2 . Following the same calculations as for BPPM, theupper bound of the PEP can be expressed similar to (13) withidentical G0 (m̃) and 1 1N L 1u 1E0Eu E02ρ 2σ̄aΩu (l) , (14)2σn2 totEN00u 1l 0which becomes E/N0 for the single user system.l 0C. DS-BPSKUsing similar calculation steps as above, we obtain σn2 N0 /2 and σa2 σ̄a2 . The upper bound of the PEP conditionedon the channel matrix is given by P D0 D̂0 {Aj0 } ρ Nr 1 jj (D0 D̂0 )Aj F 2 , andwhereββ exp 4N0j 0tρ E0 /(2σn2 tot ), which is in the same form as (14). Since Z isa real symmetric matrix, it can be decomposed into Z VΛVT ,where Λ is a diagonal matrix whose diagonal elements are theeigenvalue of Z. It follows that β j tr FT (Aj0 )T ZAj0 F tr (Bj0 )T Λ Bj0 , where tr(X) stands for the trace of X, andBj0 VT Aj0 F. Let Ix denote an x x identity matrix, represent the tensor product, and v(X) stack the column of Xin a column vector. Then, we haveN r 1j 0βj N r 1tr (Bj0 )T Λ Bj0 bT b,j 0Twhere INr L Λ, and b vT (B00 ) · · · vT (B0Nr 1 ) . Denote the correlation matrix of b by R E bbT . Since R isnonnegative definite, it has a symmetric square root U such thatR UT U [8]. Let q (UT ) 1 b̃. Since E qqT INt Nr L ,the components of q are uncorrelated. Now the conditioned PEPupper bound can be re-expressed as ρ TjTP D0 D̂0 {A0 } exp q U U q .4NtAssuming that R is full rank, U is also full rank [8]. Therefore,maximum diversity gain can be achieved by maximizing the rankof , which is equivalent to Nr L times the rank of Z. Hence,the rank criterion for DS-UWB ST system is identical to thatof TH-UWB ST system. In order to quantify the coding gain,it might be necessary to evaluate the statistics of q which isdifficult to obtain for Nakagami fading distribution. In SectionVI, we perform simulations to further investigate the performanceof DS-UWB ST system.V. UWB ST C ODES USING RODIn this section, we consider 2 transmit antenna system employing ROD ST coding scheme [5]. Generalization to UWB ST systems with higher number of transmit antennas is straightforward.The user subscript u is omitted for notation simplicity. Exploitingfull rate ROD code, the 2 2 matrix D is given by 0 dd1D . d1 d0IEEE Communications SocietyGlobecom 2004 1We can see that Z 4 i 0 δ di dˆi I2 . Define S [s1 s2 ],where s1 [1 1]T and s2 [1 1]T . For ROD ST code withrate 1/K where K is an even integer, the ST codeword is givenˆ 2 . Observe thatby D d(S T · · · S T )TK 2 , and Z 4Kδ(d d)Iboth full and reduced rate codes result in two equal eigenvaluesλ0 λ1 λ and the codeword matrix difference λI2 of full rank(r 2). Substituting the eigenvalues into (13), we obtain L 1 2m̃Nr Ω(l) ρλ P D D̂ .(15)m̃ 8With m̃, {Ω(l)}, L, and Nr being fixed, (15) depends only onthe value of ρλ. The higher the ρλ, the better the performance.Let us assume that the energy per bit Eb is fixed. For simplicity,we also assume that all users have equal transmitted energy perframe (E). Expressing E in term of Eb , we have E Eb forfull rate and E Eb /K for 1/K rate codes. It is obvious thatassuming one erroneous symbol, the eigenvalues for 1/K rateare K times larger than those for full rate code. We denote theeigenvalue of full rate code as λ̄.Consider the single user case. We observe that ρλ is equalto [1 γ(Td )] (Eb /2N0 )λ̄ for BPPM and (Eb /N0 )λ̄ for BPSK,regardless of the code rate. As a result, reducing the code rate doesnot improve the performance of single user systems. In addition, 1ρλ of TH/DS-BPSK systems are 2 [1 γ(Td )]times that ofTH-BPPM system. Since [1 γ(Td )] 2, TH/DS-BPSK tend tooutperform TH-BPPM system for every code rate. On the otherhand, we show in [9] that the multi-user system with reduced rateprovides higher value of ρλ, and hence likely to performs betterthan that with full rate.VI. S IMULATION R ESULTSWe performed simulations for UWB MA systems based onTH-BPPM, TH-BPSK and DS-BPSK schemes. We employ UWBsignals with Tf 100 ns and Tw of 0.8 ns. The receivedmonocycle is modelled as the second derivative of the Gaussianpulse [7]. The transmitted data takes value from { 1, 1} withequal probability. The modulation delay for BPPM signal isTd 0.22Tw . The hop interval is Tc Tw Td for THBPPM and Tc Tw for TH/DS-BPSK systems. We adopt discreteuniform random TH and spreading sequence so as to evaluate theperformances regardless of the choice of any particular code.We consider quasi-static frequency selective fading channels inwhich the delay profile is generated according to [10]. The channel envelopes are Nakagami-m distributed with 2 and the Lmu 1power of Lu paths being normalized such that l 0Ωu (l) 1.We assume that the power delay profiles of all users are similar.The thermal noise is real Gaussian random process with zeromean and variance N0 /2. The number of fingers for the Rakereceiver is chosen to be L 4.Figs. 2 and 3 show the BER performance of TH and DS UWBsystems in single-user and multi-user environments. We can seefrom both figures that MIMO systems outperform SISO systems,regardless of the modulation and MA techniques. Consider thesingle user case illustrated in Fig. 2. At any fixed SNR, theperformances of TH-BPSK and DS-BPSK systems are close toeach other, and both BPSK systems yield superior performancesto TH-BPPM. This observation is consistent with the theoretical35290-7803-8794-5/04/ 20.00 2004 IEEE

001010TH BPPM, N 1, N 1trTH BPPM, Nt 2, Nr 1TH BPPM, Nt 2, Nr 2TH BPSK, Nt 1, Nr 1TH BPSK, Nt 2, Nr 1TH BPSK, Nt 2, Nr 2DS BPSK, Nt 1, Nr 1DS BPSK, Nt 2, Nr 1DS BPSK, N 2, N 2 110t 2TH BPPM, Nr 1, R 1TH BPPM, Nr 1, R 1/2TH BPPM, Nr 2, R 1TH BPPM, Nr 2, R 1/2TH BPSK, N 1, R 1rTH BPSK, N 1, R 1/2rTH BPSK, Nr 2, R 1TH BPSK, Nr 2, R 1/2DS BPSK, Nr 1, R 1DS BPSK, Nr 1, R 1/2DS BPSK, Nr 2, R 1DS BPSK, N 2, R 1/2 110r 210BERBER1010 4 41010 5 510r 3 3100246810E /N (dB)b12141618102002864010E /N (dB)bFig. 2: TH and DS UWB single user systems.12141618200Fig. 4: UWB single user systems with ROD ST codes of different rates.010010TH BPPM, Nt 1, Nr 1TH BPPM, Nt 2, Nr 1TH BPPM, N 2, N 2trTH BPSK, Nt 1, Nr 1TH BPSK, Nt 2, Nr 1TH BPSK, Nt 2, Nr 2DS BPSK, Nt 1, Nr 1DS BPSK, Nt 2, Nr 1DS BPSK, Nt 2, Nr 2 110 2TH BPPM, Nr 1, R 1TH BPPM, N 1, R 1/2rTH BPPM, Nr 2, R 1TH BPPM, Nr 2, R 1/2TH BPSK, Nr 1, R 1TH BPSK, N 1, R 1/2rTH BPSK, N 2, R 1rTH BPSK, N 2, R 1/2rDS BPSK, Nr 1, R 1DS BPSK, N 1, R 1/2rDS BPSK, Nr 2, R 1DS BPSK, N 2, R 1/2 110 210BERBER10r 3 310 41010 410 510 5100246810Eb/N0 (dB)12141618200246810Eb/N0 (dB)1214161820Fig. 3: TH and DS UWB multi-user (Nu 5) systems.Fig. 5: UWB multi-user systems with ROD ST codes of different rates.results given in Section V. In Fig. 3, we show the systemperformances when 5 asynchronous users are active. In low SNRregime, TH/DS-BPSK outperform TH-BPPM scheme, and bothBPSK systems yield close performances. However, due to theMAI, the BER of TH multi-user systems slightly drop withincreasing Eb /N0 , and a high error floor can be noticed at highSNR. On the other hand, even in MA scenarios, we can still seeconsiderable improvement of DS-BPSK ST system.In Figs. 4 and 5, we show the performance of single andmultiple user systems employing ROD ST codes with full andhalf rates. Both figures illustrate that BPSK provides lower BERthan BPPM scheme, regardless of the code rate. From Fig. 4, wecan see that the performances of full and half rate ROD codesare close to each other for every modulation schemes. This isin agreement with the results in Section V, which say that forsingle user system, decreasing the rate of ROD ST code doesnot improve the performance. Unlike the single user case, theresults in Fig. 5 confirm our expectation that when the code rate islower, both TH-BPSK and TH-BPPM multi-user systems achievebetter performances, especially in high SNR regime. However,for DS-BPSK MA systems, the BER improvement obtained fromreducing the code rate is insignificant. This is because for Nu 5,the effect of MAI to DS system is considerably small, and RODST code provides close to maximum achievable performancewithout decreasing the code rate. Again, DS-BPSK ST systemoutperforms other modulation schemes.for two transmit antenna system. Both analytical and simulationresults show the performance improvement of the UWB MIMOsystems over the conventional SISO systems. For example, byemploying two transmit and one receive antennas for a system of5 users and Eb /N0 8 dB, the BER for TH-BPPM decreasesfrom 1.5 10 2 to 9.7 10 3 , for TH-BPSK from 10 2to 5.6 10 3 , and for DS-BPSK from 10 2 to 4.6 10 3 .We illustrate that in single user case, both DS-BPSK and THBPSK yields similar performance which is superior to TH-BPPMsystem, whereas in MA scenarios, DS-BPSK ST modulationoutperforms other considered schemes.VII. C ONCLUSIONSIn this paper, we investigate the UWB ST systems utilizingTH-BPPM, TH-BPSK, and DS-BPSK signals. The performancemetrics (diversity and coding gains) of UWB ST systems arequantified regardless of the particular coding scheme. We considered an example of UWB ST signals based on ROD ST codeIEEE Communications SocietyGlobecom 2004R EFERENCES[1] L. Yang and G. B. Giannakis, “Space-Time Coding for Impulse Radio”,IEEE Conf. on Ultra Wideband Systems and Tech., pp. 235-240, May 2002.[2] R. A. Scholtz “Multiple Access with Time-Hopping Impulse Modulation”,Proc. of MILCOM Conf., Boston, MA, USA, pp. 447 - 450, Oct. 1993.[3] M. L. Welborn, “System Considerations for Ultra-Wideband WirelessNetworks”, IEEE Radio and Wireless Conf., pp. 5-8, Aug. 2001.[4] J. R. Foerster, “The Performance of a Direct-Sequence Spread UltraWideband System in the Presence of Multipath, Narrowband Interference, andMultiuser Interference ”, IEEE Conf. on Ultra Wideband Systems and Tech.,pp. 87-91, May 2002.[5] V. Tarokh, H. Jafarkhani and A. R. Calderbank, “Space-Time Block Codesfrom Orthogonal Designs”, IEEE Trans. on Inform. Theory, vol. 45, no. 5,pp. 1456-1467, Jul. 1999.[6] J. G. Proakis, Digital Communications, McGraw-Hill, New York, 2001.[7] M. Z. Win and R. A. Scholtz, “Ultra-Wide Bandwidth Time-HoppingSpread-Spectrum Impulse Radio for Wireless Multiple-Access Communications”, IEEE Trans. on Commun., vol. 48, no. 4, pp. 679-691, Apr. 2000.[8] R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge Univ. Press,New York, 1985.[9] W. P. Siriwongpairat, M. Olfat, and K. J. R. Liu, “Performance Analysis andComparison of Time Hopping and Direct Sequence UWB-MIMO Systems”,EURASIP J. on Applied Signal Proc. Special Issue on ”UWB-State of theArt”, to appear.[10] S. S. Ghassemzadeh, L. J. Greenstein, T. Sveinsson, and V. Tarokh, “AMultipath Intensity Profile Model for Residential Environments”, IEEEWireless Commu. and Networking Conf., vol. 1, pp. 150 - 155, Mar. 2003.35300-7803-8794-5/04/ 20.00 2004 IEEE

the theoretical analysis. I. INTRODUCTION Ultra-WideBand (UWB) technology is defined as a transmis-sion scheme that occupies a bandwidth of more than 20% of its center frequency, or typically more than 500 MHz. The Multiple-Access (MA) capability of UWB system can be attained by incorporating the UWB signal with a pseudo-random Time

Related Documents:

Core Hopping 2.1 User Manual 1 Core Hopping User Manual Chapter 1: Introduction to Core Hopping Improving the activity of a lead compound is often done by varying the side chains that are attached to a core part of the compound. The object of this strategy is to find the optimal side chains.

has proposed using a spherical robot (SphereX) that achieves ballistic hopping mobility through the use of a miniaturized propulsion system and 3-axis reaction wheel system. In this paper, we present the design and control analysis of a mechanical hopping mechanism that can be used for SphereX. The mechanism is comprised of two mechanical .

7 City hopping: Munich - Berlin / Berlin - Prague - Vienna - Budapest 8 City hopping: Munich - Salzburg - Vienna - Budapest / Warsaw - Krakow 9 City hopping: Vienna - Salzburg - Munich - Berlin -Prague - Krakow 10 SCANDINAVIA Independent Tours: Copenhagen - Stockholm / Copenhagen - Oslo - Stockholm

guided laser was housed in an ILX Lightwave Model 4412 laser mount; the laser's case tem-perature and injection current were manipu-lated using a computer-interfaced ILX Light Motivation for concern about mode hopping Mode hopping in semiconductor lasers is undesirable in many applications since it intro-duces unwanted intensity noise. A prime

Asymptotic approach to the analysis of mode-hopping in semiconductor ring lasers S. Beri,1,2 L. Gelens,1 G. Van der Sande,1 and J. Danckaert1,2 1Department of Applied Physics and Photonics, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussel, Belgium 2Department of Physics, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussel, Belgium Received 22 May 2009; published 23 July 2009

towards classical time-frequency analysis techniques for the purpose of analyzing these low probability of intercept radar signals. This paper presents the novel approach of characterizing low probability of intercept frequency hopping radar signals through utilization and direct comparison of the Spectrogram versus the Scalogram.

- S. M. Girvin & K. Yang, Modern Condensed Matter Physics, Cambridge University Press (2019), Appendix J. bosons fermions for on-site energy hopping between sites i and j interaction between sites i and Single-particle basis Single-particle Hilbert space: Example: harmonic oscillator: Wavefunction: all values of Consider a single-particle .

343 BRIGANCE Readiness Activities Gross-Motor Skills Jumping and Hopping p hysical h ealth and d evelopment 6.4. Beans in the knees m aterials: One beanbag per child. group size: Individual, small group, or class. p rocedure: Have children try the following: Place a beanbag between their feet andof the rhyme, go around the circle and say each child’s name.