Ultra Wide Band Signal Simulations Using FDTD Method Kazimierz Kai Siwiak Time Domain Corporation Tadeusz M. Babij Florida International University 27-28 September 2001 The Boston Marriott Hotel Newton, Massachusetts 1
Introduction 4 UWB signals generally more complex than sinusoids [1, 2] 4 Sinusoids remains sinusoidal throughout link 4 UWB waveforms and spectra change from transmitter, to radiation, to the receiver 4 FDTD method used to study waveforms across link 4 Compared with measurements 4 Receiver efficiency predicted 4 UWB Wireless link characterized 2
UWB Wireless Link Waveform pulses s t (t) sent at rate R pulses per second P t H y (t) s(t) s c (t) E b /N 0 out SNR out FDTD s t (t) n f Filter h(t) Transmitter E b /N 0 in Integrate Template p(t) P t = transmitter power n f = receiver noise factor H y (t) = copolarized transverse magnetic field s t (t), s(t) = transmitter and received voltage waveforms p(t) = template waveform h(t) = receiver filter impulse response Data RX analysis 3
FDTD Simulations 4Radiation between UWB dipole pair [3] simulated [4] with Finite Difference Time Domain (FDTD) method [5] Transmitting dipole Receiving dipole 4
Waveform A : Stimulus and Response Calculated: Measured: A(t) 1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1 0 0.35 0.7 1.05 1.4 time 1.75 2.1 2.45 2.8 3.15 3.5 TX s(t) 0.03 0.025 0.02 0.015 0.01 0.005 0 0.005 0.01 0.015 0.020 0.35 0.7 1.05 1.4 1.75 2.1 2.45 2.8 3.15 3.5 time RX 5
XFDTD Simulations of UWB Waveforms and their Spectra A at TX antenna: H-field: RX antenna load: In time: db 0 In frequency: db 0 db 0-25 -25-25 -50-50 -50-75 -75-75 -100 0 2 4 6 8 10 12 14 Frequency(GHz) -100 0 2 4 6 8 10 12 14 Frequency(GHz) -100 0 2 4 6 8 10 12 14 Frequency(GHz) 6
Waveform B : Stimulus and Response Calculated: Measured: B(t) 0.32 0.28 0.24 0.20 0.16 0.12 0.08 0.04 0 TX 0 0.35 0.7 1.05 1.4 1.75 2.1 2.45 2.8 3.15 3.5 time s(t) 0.015 0.012 0.009 0.006 0.003 0 0.003 0.006 0.009 0.012 0.015 0 0.35 0.7 1.05 1.4 1.75 2.1 2.45 2.8 3.15 3.5 time RX 7
Transmitted Power Spectral Density 4 Sine wave equivalent power density at distance d is P DENSITY,CW = P t G t ( f c )/(4πd 2 ) 4 Power spectral density is P D ( f ) = F {H y (t)} 2 η 0 4 Which integrates to P DENSITY and includes transmit antenna gain G t ( f ) 8
Receive Antenna Aperture 4 Received co-polarized signal is: P RX = ı F {H y (t)} 2 η 0 A e (f ) df 4 And F {H y (t)} 2 η 0 = P D ( f ) power spectral density of H y (t) integrates to P DENSITY ; η 0 = µ 0 c = 376.73 ohms 4 Aperture factor for a unity gain antenna is: A e (f ) = (c/f ) 2 /4π 9
UWB Propagation 4UWB transmissions analyzed, for convenience, by free space propagation at a center frequency f c 4Propagation assumed to be sine wave equivalent at the center frequency 4For a given EIRP=P t G t, the CW or sinewave equivalent is: P RX, CW = P DENSITY,CW A e (f c ) 10
The Sine Wave Equivalent Propagation 4 Actual received signal relative to the sinewave equivalent signal is A F = η 0 ı F {H y (t)} 2 A e (f ) df A e (f c ) P t G t ( f c )/(4πd 2 ) 4 Value of A F is waveform dependent, but generally close to 1; hence sine wave equivalent propagation usually justified 11
Example: Gaussian Derivative H-Field 4If: magnetic field at distance d in time domain can be represented by H y (t) = t 2 1 τ 2 exp 4Then: magnetic field at distance d in frequency domain is H y ( f ) = (f τ) 2 exp 1 2 1 2 t 2 τ 2 τ 3 (2π f τ)2 τ 8 3 4 π 6 π 9 4 12
Example: A F for Gaussian Derivative H-field 10-80 Signal level, ma/m 5 0-10 -15-20 -200-100 0 100 200 Time, picoseconds Signal level, db ma/m -100-120 -140-160 0 2 4 6 8 10 Frequency, GHz A F = η 0 ı F {H y (t)} 2 A e (f ) df A e (f c ) P t G t ( f c )/(4πd 2 ) = 1.15 13
14 UWB Path Link 4 Receive antenna gain is constant over bandwidth of pulse 4 Path attenuation between unity gain antennas: P L 20 log c A = F L d d w d > w Φ 4πdf c 4 A F = antenna sine-wave equivalent aperture factor 4 L w = in-building attenuation, db/m 4 d w = distance to first wall ( ) ( d w )
Bit Energy to Noise Density 4At receiver antenna load: [independent of wave shape!] 4At correlator output: Ratio E b = N 0 E b N 0 c:out in = s( t) 2 dt ı N 0 n f s(t)h(t-t) dt ıı N 0 n f ı p(t) dt 2 p(t)h(t-t) dt ı 2 dt 4 Efficiency: 4Optimum for: e c = (E b /N 0 ) c:out / (E b /N 0 ) in p(τ)h(t-τ) dτ = Cs(t) ı 15
Signal A and Pulse Template 4Red: Signal at correlator input: s c (t) 4Blue: Optimum width template: p(t) 1 0.5 0 0.5 p(t) s(t) -1 0 0.5 1 1.5 2 2.5 t f c Rectangular pulse is optimally centered at signal amplitude peak, [better templates possible] 16
Sampler Cell Efficiency A Waveform 4Efficiency e c vs. template width tf c with rectangular template pulse p(t) 0.6 0.5 Efficiency: -2.8 db 0.4 e c 0.3 0.2 0.1 0 0 1 2 3 4 t f c 17
Signal B and Pulse Template 4Red: Signal at correlator input: s c (t) 4Blue: Optimum width template: p(t) 1 0.5 0 0.5 s(t) p(t) Template pulse is optimally centered at signal amplitude peak 1 0 0.5 1 1.5 2 2.5 3 3.5 4 t f c 18
Sampler Cell Efficiency B Waveform 4Efficiency e c vs. template width tf c with rectangular template pulse p(t) 0.4 Efficiency: -4.5 db 0.3 e c 0.2 0.1 0 0 0.5 1 1.5 2 2.5 3 3.5 4 t f c 19
Signal Waveform B and 4Red: Signal Bipolar Sampler غ øß exp - t - t 0 Ł s ( t) = sin 2 p f c ( t - t 0 ) 4Blue: Optimum width bipolar template p f c Q R ł F ( t) 1 0.5 p 1 (t) 0 Efficiency: -1.6 db 0.5 s(t) 1 0 0.5 1 1.5 2 2.5 3 3.5 4 t f c 20
Receiver System SNR 4Received power [6] is: P RX = P EIRP (A f c/4πdf c ) 2 10 -L w(d-d w )Φ(d >d w ) 4Input signal to noise at impulse rate R: SNR in = (E b /N 0 ) in R/B RF = P RX / n f ktb RF 4Receiver implementation losses: L sys = -10 log(e c /n f ) 21
Receiver System SNR 4Integrating I impulses per bit a R bps: R I = B data 4System signal to noise at output: SNR out = (E b /N 0 ) out R/B data = (e c /n f )P RX /ktb data 4Finally, processing gain is: PG = SNR out / SNR in = e c B RF / B data 22
Receiver Sensitivity 4Receiver sensitivity S is: S = 10log(kTB)+SNR+NF+ e c 4Assuming a needed SNR=7 db, noise figure NF=3 db and loss e c = 2 db S = -104 dbm/mhz 4System gain is S db/mw EIRP 23
Summary 4 Impulse transmissions studied using FDTD method 4 Link performance impacted by UWB wave forms 4 UWB Receiver performance characterized 4 Watch future IEEE VTS News for: UWB Radio: an Emerging PAN and Positioning Technology 24
References 1. K. Siwiak, Ultra-Wide Band Radio: Introducing a New Technology, Invited Plenary Paper, Conference Proceedings of the IEEE VTC- 2001, Rhodes, Greece, May 6-9, May 2001. 2. Robert A. Scholtz, Moe Z. Win, Impulse Radio, Invited Paper, IEEE PIMRC'97, 1997, pp. 245-267. 3. Hans Gregory Schantz, Larry Fullerton, The Diamond Dipole: A Gaussian Impulse Antenna, IEEE APS Conf., Boston MA., July 2001. 4. Zhong Yang, Finite Difference Time Domain Analysis of Antennas Used in Personal Communications, Florida International University, M.S.E.E. Thesis Defense, 22 June 2001. 5. K. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics, CRC Press Inc., 1993. 6. K. Siwiak, A. Petroff, A Path Link Model for UWB Pulse Transmissions, Conference Proceedings of the IEEE VTC-2001, Rhodes, Greece, May 6-9, May 2001. 25
Kai Siwiak, Vice President Strategic Development kai.siwiak@timedomain.com +1(954)-755-6828 +1(256)-990-9062 Time Domain Corporation 7057 Old Madison Pike Huntsville, AL 35806 Tadeusz M. Babij, Professor Department of Electrical and Computer Engineering babij@eng.fiu.edu +1(305)-348-2683 Florida International University University Park Campus, Miami, Florida 33199 26