Performance of UWB-Impulse Radio Receiver Based on Matched Filter Implementation with Imperfect Channel Estimation

Transcription

1 Perormance o UWB-Impulse Radio Receiver Based on Matched Filter Implementation with Imperect Channel Estimation Giorgos Tatsis a, Constantinos Votis a, Vasilis Raptis a, Vasilis Christoilakis a,b, Spyridon K. Chronopoulos a, Panos Kostarakis a a Physics Department, University o Ioannina, Panepistimioupolis, Ioannina, 45, Greece b Siemens Enterprise Communications, Enterprise Products Development, Athens, 4564, Greece s: gtatsis@grads.uoi.gr, kvotis@grads.uoi.gr, vraptis@grads.uoi.gr, basilios.christoilakis@siemens-enterprise.com, schrono@cc.uoi.gr, kostarakis@uoi.gr Abstract. UWB communications have attracted considerable interest, targeting applications in high-speed data transer wireless communication systems. This paper studies the eects o matched ilter receiver in the perormance o such a system. Such eects are evaluated in terms o the Bit Error Rate (BER) or a Binary Pulse Position Modulation (BPPM) scheme, considering multipath propagation channel and the presence o noise. The case o imperect channel estimation is taken into account. Dependence o BER on parameters such as signal to noise ratio, number o estimation pulses and correletor taps is also presented. Keywords: UWB, Impulse Radio, Sotware Radio, Matched Filter, Channel Estimation. PACS: 84.4.Ua INTRODUCTION Ultra-wideband (UWB) transmission has recently received great attention in both academia and industry or applications in wireless communications. A UWB system is deined as any radio system that has a -db bandwidth larger than % o its center requency, or has a -db bandwidth equal to or larger than 5 MHz. It is expected that many conventional principles and approaches used or shortrange wireless communications will be reevaluated and a new industrial sector in short-range wireless communications with high data rate will be ormed [, ]. Essentially, UWB communications come in one o two types, single-band and multiband. Impulse radio, is a single-band UWB system. In impulse radio, the signal that represents a symbol consists o serial pulses with a very low duty cycle. The pulse width is very narrow, typically in nanoseconds. This small pulse width gives rise to a large bandwidth and a better resolution o multipath in UWB channels. The purpose o this paper is to study the impact o imperect channel estimation on the perormance o an UWB receiver with Impulse Radio technics. The system consists o an impulse generator as transmitter and a receiver using a matched ilter or signal detection. Assuming no intererences and perect synchronization we derive results o error probability as unction o noise, estimation procedure and ilter taps. CP3, 7 th International Conerence o the Balkan Physical Union, edited by A. Angelopoulos and T. Fildisis 9 American Institute o Physics /9/$5. 573

2 THEORETICAL ANALYSIS The modulation that is selected or the system is Binary Pulse Position Modulation (BPPM). The transmitted pulses have the orm o a Gauss monocycle, i.e. the irst derivative o a standard Gauss pulse. The bit period, which in case o BPPM is the same as the rame period, is T and the time oset Δ represents the modulation index. A logic transmits a pulse at a multiplicate o T, while sending a is delayed in time by Δ. The modulated pulses waveorm st () is expressed by Eq. () below, N s() t = Ebw( t jt bjδ) () j= where, wt () is the pulse shape normalized to have unity energy, Eb is the energy per bit, T is the bj is the j-th bit, Δ is the BPPM modulation index, N is the total number o transmitted pulse period, pulses. For the analysis, we consider the transmit and receive system model shown in Fig.. The transmitted signal, st (), described above, propagates through a multipath channel with impulse response ht () The signal at the receiver is rt () = xt () + nt () = st () ht () + nt () () where () denotes convolution and nt () denotes AWGN. The noise has a mean value o zero and a N N double side power spectral density, i.e. nt () N(, σn), σ n =. FIGURE. System transmission-reception model The channel impulse response is given by the IEEE 8.5.3a model [3], and it is expressed as ollows, X i k,, l k hi()= t α δ(t T τ ) l l k l (3) where, k, l denotes the rays and clusters respectively, α kl, are the multipath gain coeicients, T l is the delay o the l-th cluster, τ kl, is the delay o the k-th component relative to the l-th cluster, X i represents the lognormal ading with i denoting the i-th channel realization. A more compact orm or the channel is given in equation below, L ht ()= α δ(t τ ) (4) l l= l where, L is the number o resolvable paths, α l and τ l the amplitude and delay o the l th path and δ( t ) the Dirac delta unction. 574

3 The matched ilter at the receiver has an impulse response gt () as shown in Fig. and it is matched to the dierence o the received waveorm o the pulses ( () x t ) and it is given in the Eq. 6 below. gt () = x ( T t) x ( T t) (5) where, () denotes estimated signal. The output o the matched ilter is sampled every T seconds and the output is compared with zero. I the value is greater than zero the bit is, otherwise it is. We assume perect time synchronization or reception and that there is no intererence between sequential bits. From this point, and without loss o generality, we continue the analysis or the reception o the irst bit ( < t < T ). The input signal in the matched ilter is expressed as ollows, L rt () = xt () + nt () = st () ht () + nt () = αlst ( τ l) + nt () (6) l= This type o receiver requires a good knowledge o the channel. To estimate the received waveorm we send a number o pilot pulses. I we transmit K pilot pulses, one every T seconds, then the estimated waveorm is obtained by averaging the received pulses. The template waveorms are respectively given as, K K j j j x() t = r () t = ( x() t + n ()) t K j= K j= (7) x () t = x ( t Δ ) (8) Assuming that the multipath channel is static over the estimation process and perect time synchronization, Eq. 7., becomes, K j x() t = x() t + n () t = x() t + n() t (9) K j= The second term o this equation n () t is noise, normally distributed, with zero mean and variance σn N σ = =. K K Similarly the estimated waveorm or is, x ( t) = x ( t Δ ) + n ( t Δ ) = x ( t) + n ( t) () The decision metric, D as shown in Fig., at the sample time, can be expressed as ollows, 575

4 + D= y( T ) = { r() t g() t } = r() g( t ) d t= T τ τ τ = + = r( τ) ( x( T t+τ) x( T t+τ) ) dτ = T T = r( ) x ( ) () x( ) τ τ τ dτ= x() t + n() t ( x() t x() t ) dt = T ( () ())( () () () ()) ( xt () nt ())( x() () + ()) t= T t= T = xt + nt x t x t + n t n t dt= T = + t x t n t dt m We merge the two terms () n () t into nm () t with total variance σ n N σ m =σ +σ = =, and using vector representation we obtain, K K ( ) ( ) T T T T D = x x -x + x n + n x -x + n n () m m where () T denotes transpose. All vectors have length L, which is the number o the strongest channel paths. The received signal x, can be either x or x. I we transmit a, Eq.. becomes, ( ) ( ) T T T T D = x x -x + x n + n x -x + n n () m m And or a the decision metric is expressed by, ( ) ( ) D = x x -x + x n + n x -x + n n (3) T T T T m m 576

5 NUMERICAL RESULTS Ater the above analysis we proceed to the calculation o the bit error rate (BER). The simulation process, actually produces a large number (~ 5 ) o decision metrics, rom Eq. and 3 and we calculate the error probability by counting the total amount o error bits. I one sends a, error detection will cause the decision metric D to be negative. On the other hand i we send a an error occurs when D >. Because the two outputs has the same values but opposite, we continue the calculations only or zeros and i we assume that ones and zeros are sent with equal probabilities then the error probability o zeros is the BER. Table. includes the parameters used in the simulation program. TABLE (). Simulation parameters. Description Frame period ( T ) Modulation index ( Δ ) Gauss pulse width Channel model Sampling requency Values nsec nsec 3psec CM GHz Fig. shows the error probability or dierent number o pilot pulses ( K ) with 4 (let) and (right) ilter taps, as a unction o the SNR. We can observe that as the number o pilot pulses increases the BER decreases. That improvement occurs or all SNR values. In the same graph there is the case with perect channel estimation (denoted with PE). Fig 3. shows the error probability or dierent number o matched ilter taps ( L ) with (let) and 6 (right) pilot pulses. A decrease o BER as the number o taps increases is expected and it is shown that the improvement occurs mostly at the area with larger SNR. FIGURE. BER vs SNR, or dierent number o pilot pulses 577

6 FIGURE 3. BER vs SNR, or dierent number o ilter taps CONCLUSION In this paper a study o the perormance o an UWB-Impulse Radio was investigated. A simple model o transmit-receive system was analyzed. Assuming perect timing synchronization, results o the bit error probability are given. The most critical parameters o the perormance are the signal to noise ratio, the number o matched ilter taps and the number o pilot pulses or channel estimation. Results show that a ew tens o pilot pulses are critical to reduce errors. The number o taps is also signiicant and it is not necessary to exceed a hundred, because the improvement is negligible. REFERENCES. X. Shen, M. Guizani, R.C. Qiu, T. Le-Ngoc, Ultra-wideband wireless communication and networks, Wiley 6.. Kazimierz Siwiak and Debra McKeown, Ultra-Wideband Radio Technology, Wiley Jerey R. Foerster, Marcus Pendergrass and Andreas F. Molisch, A Channel Model or Ultrawideband Indoor Communication. Mitsubishi Eletric Research Laboratory, Inc., TR-3-73, November