Simulation and Characterization of UWB system coexistence with traditional communication Systems

Transcription

1 Simulation and Characterization of UWB system coexistence with traditional communication Systems Guided research by Oliver Wamanga International University Bremen Under suervision of Prof. Dr. Herald Haas Sring Semester 2004 Abstract This aer discusses roerties of Gaussian ulses and derivatives thereof used for UWB signaling. The Power Sectral Density of signals sent into the channel aear as discrete comonents resembling sikes with amlitudes that could adversely interfere with established communication systems. A mathematical model for the analysis of the PSD in the channel is introduced, a method to decrease the effect of the sikes is discussed and simulated in Matlab. It is established that the introduction of randomness into the transmitted signal has the effect of decreasing the amount of interference ower. Keywords: Ultra Wide Band, Sectral Shaing, Interference, Pulse Position Modulation.

2 Forward The radio frequency sectrum is a vast range of electromagnetic waves which travel at the same seed but vary in wavelength. We use the electromagnetic sectrum for a lot of everyday alications e.g. warming food in microwaves, taking X-rays, watching television, radar etc. The communications industry also has its stake in the electromagnetic sectrum felt by greatly advancing the various communication solutions available. The wavelength of a articular ortion of the radio frequency sectrum determines a lot of things and in communications, we are articularly interested in the distance the wave can travel while not getting overly attenuated by the medium and the amount of data the wave can carry in a fixed time interval. Figure 1 and Table 1 below give an overview of the diverse frequency sectrum, and some tyical alications of the said frequencies. Figure 1: The Radio Frequencies To achieve the requirements for a contemorary communications system, we realize that only a small slice of the available sectrum can satisfy our stringent needs. We thus have to find intelligent ways of squeezing all our communication systems into this limited resource, and ensuring that interference is avoided between systems.

3 Frequency Band Tyical Uses 10kHz to 30kHz Very Low Frequency (VLF) Power line carrier systems, low frequency electricity use e.g. Deutsche Bahn 30kHz to 300kHz Low Frequency (LF) Power line carrier systems, Radiolocation, Radio Beacons, Air traffic control, International Fixed Service, Intentional Radiators 1W max 300kHz to 3MHz Medium Frequency (MF) Power line carrier systems, Air traffic control, International calling, distress signaling when over water masses, Intentional radiators 100mW max, AM Radio, Amateur broadcast 3MHz to 30MHz High Frequency (HF) Radiolocation, Amateur broadcast, Flight Test Stations, Radio Astronomy, Intentional radiators 10,000 microvolts/meter at 30 meters max 30MHz to 329MHz Very High Frequency (VHF) Radio astronomy, Alarm systems, door oeners, remote switches, Baby monitors, Wildlife & ocean buoy tracking and telemetry, Cordless Telehones, Television channels, radio controlled aircraft, FM radio, Satellite communications, Military 329MHz to 2.9GHz Ultra High Frequency (UHF) Satellite communications and research, Global Positioning System (GPS), Student exerimental use, Airorts use, television stations, Biomedical telemetry devices, Cellular hones, Paging services, Point-to-Point Microwave, Military, Radio astronomy, Unlicensed sread sectrum transmitters, control of aircraft and missiles, 3rd generation mobiles, 2.9GHz to 30GHz 30GHz and above Suer High Frequency (SHF) Extremely High Frequency(EHF) Radar, Radiolocation, Vehicle identification systems, General Wireless communications Services, Television broadcasts, Military, Satellite communication, Intentional radiators, 250 millivolts/meter at 3 meters max, Local Multioint Distribution Service, Radiolocation, Sace research and communications, Radio astronomy, Amateur, Industrial Scientific and Medical use, Lots of roosed wireless emitters, Table 1: Frequency Sectrum *A detailed listing of frequency allocation is available at [9]

4 The maintenance of the very organized frequency sectrum shown and documented above is ossible because most of the transmission technologies make use of the modulation of a narrowband carrier that is sinusoidal in nature. We know that in the frequency domain, a deterministic sinusoidal tye signal has a very small sectral content which resembles a sike. Modulating this sinusoidal signal causes a small deviation from the mean of its sectral eak. If we can lace many of these sikes which all have a unique underlying sinusoidal carrier next to each other in the frequency domain without interfering with each other, we can have as many different communication systems as the number of sikes. The amount of ower used to transmit in a given band is not an issue as long as the frequency content of the band does not leak into other neighboring bands. However with the contemorary concerns about what radiation ower does to biological organisms, as well as the fact that esecially in mobile communications, minimal ower consumtion is of aramount imortance to rolong battery life, new communication methods must be ondered over. A novel aroach is to drastically reduce the ower used to transmit signals and let the frequency content of the transmitted signal leak into adjacent bands. Studies have been carried out in [1][3][6] which investigate among other things the effect of UWB signals on established communication systems, as well as the imact of these narrowband systems on bit error rates in UWB transmission. Their major findings are that the shae of the signaling ulse as well as the tye of modulation used have a large effect on the amount of interference caused. These investigations have assumed that the sent signal is random and modulated. In this study, attention is focused on worst case interference analysis and awareness is aroused to the unexected effects that aear during transmission using Gaussian ulses, which has imlications on the accuracy of bit error rate calculations on both the victim systems as well as UWB systems. The worst case analysis can be used to rovide uer bounds on results calculated using values derived from this and other studies. Figure 2: Frequency domain footrint of Various transmission systems.

5 Introduction to UWB A signal is defined to be Ultra Wide Band (UWB) if it occuies a bandwidth of 500 MHz or more, or has a fractional (-10dB) bandwidth of at least 25% of its center frequency. Above 2.5GHz, the former definition is the limiting factor, whilst below 2.5GHz, the 25% center frequency is the minimal requirement. Due to the inverse time frequency domain relationshi, this broad sectral footrint can only be caused by a signal in the time domain that is very narrow, in the order of fractions of a nano-second. The shorter the signals width, the greater its frequency domain footrint as demonstrated in Figure 3. which considers frequencies from zero u to the center frequency. As this signal leaks heavily into the other established communication systems sectrums, we have to ay secial attention to the amount of interference ower that the UWB signal causes at any given frequency to the other existing sectrums. Thus intensive scrutiny of the Power Sectral Density (PSD) of the UWB signals must be carried out in an attemt to ensure that its eak value(s) fall below a well defined limit defined by the Federal Communications Commission (in the US). All electronic devices suffer from noise interference which is rimarily caused by random motion of atoms at temeratures above 0 Kelvin. The PSD of this noise can be calculated, and if we can manage to lace the PSD of the UWB signal in that of the noise, the UWB signal would be unnoticeable to any system oerating in the given frequency range. Sectral shaing to conform with FCC limits as well as to ensure that the UWB signal looks noise-like must be carried out. Figure 3: Effect of ulse duration on frequency domain footrint

6 Different tyes of signal shaes can be used to generate the nanosecond ulse waveform. In this aer, the gaussian ulse shae and derivatives thereof are used for investigation of the roerties of UWB signals. Simulation Model The formula for the generic gaussian ulse is 1 wt () = e σ 2 t µ 0.5 σ where µ and σ are the mean and standard deviation resectively. Drawing this in Matlab for a ulse duration of 0.5 ns, we get a ulse resembling Figure 4. Figure 4. Gaussian Pulse Notable about the ideal ulse is its symmetry about its eak value. Due to the unique very short time nature of the ulses used, a large difference is observed between ulses generated and those in the channel after the transmission antenna. Antennas behave like low ass filters which differentiate whatever signals are sent through them, meaning the signal in the channel is the first derivative of the generated waveform. If a loo

7 antenna is used, the second derivative of the waveform results in the channel [1] This results in a signal which does not have any DC offset because all the derivatives of the Gaussian ulse integrate to zero over their ulse duration time. The receiving antenna has the same effect of differentiating the received waveform, thus the signal undergoes three transitions from transmitter to receiver. Figure 5 illustrates the different tyes of ulses used for signaling, as well as their derivative forms which aear in the channel after the transmitting antenna. Figure 5. The various ulses and the corresonding signal in the channel (in dotted lines). Clockwise from to, Gaussian Pulse, 2 nd derivative of ulse, Gaussian doublet ulse with searation time T w and 3 rd derivative of ulse

8 Investigation of the PSD of the signal in the channel must be carried out as this is where interference to is caused other systems. We are thus interested in the PSD of the signals in dotted lines of Figure 5. Intuitively, the maximum interference ower should be concentrated at the signals center frequency, which is calculated as shown in Table 2. Pulse Tye Center Frequency -10 db bandwidth Gaussian Pulse 1/T 2/T 2 nd derivative 1.73/T 2.1/T 3 rd derivative 2/T 2/T Gaussian doublet 1/T 2/T Table 2: Center frequencies and Bandwidths, where T is the ulse duration. [1] Taking the Fourier Transform of the ulses in figure 5 in Matlab, we get the following lot. Figure 6: Frequency content of 0.5ns ulses. Notable is that most frequency content is below 0 db The similarity between the enveloe sectral shae of the Gaussian ulse and the doublet is because they are formed from the same waveform. However, the doublet has eriodic dis in its sectrum. These dis give the doublet an advantage over the other waveforms resented here since if

9 ositioned strategically, the di could ensure minimal interference to a narrowband system. It must be noted that these dis are several MHz wide, which could easily accommodate the sectral footrint of some narrowband communication system. To be more recise, the sacing between adjacent dis is inversely roortional to the time T w between the lobes of the doublet ulse. For the results in Figure 5, T w was 1ns, resulting in the aroximately 1GHz searation of the eriodic dis. Transmission analysis When several ulses are transmitted over a channel, it is observed that the ower sectral density is not quite the retty icture as deicted in Figure 6. To investigate this in deth, an analysis of the underlying mathematical exression is needed. Assuming a constant train of ulses w t (t) consisting of a generic ulse shae we denote as w(t), we can exress the ulse train as a convolution of the waveform w(t) with delta ulses (delayed by a time T ) δ(t - nt ), where n is an integer. T can also be interreted as a time slot where a ulse is transmitted, analogous to TDMA signaling. w () t = w() t δ ( t nt ) dt t n= Taking the Fourier Transform of the above equation gives Wt ( f) = W( f) δ ( f n) T T n= To get the ower sectral density PSD, we square the above equation W t (f) Wt ( f ) = W ( f) δ ( f n) T n= T Somewhat analogous to [6], some imortant characteristics can be deduced from the above equation. 1. The PSD of the above waveform w t (t) is entirely deendent on the ulse shae w(t), and the transmit ower which is the ulse s amlitude. 2. The above PSD consists of comletely discrete lines in the frequency domain. 3. The sacing of the discrete lines is deendant uon the searation time T, more recisely they are searated by an intervals of 2 T Simulating such a ulse train in Matlab, we get a PSD resembling Figure 7. Clearly this PSD is not ideal for transmission as the sikes diminish its resemblance to a noisy signal and increases the resence of discrete as oosed to continuous comonents. In fact, it works comletely against what we have been trying to achieve in case one of the sikes which now have amlitudes above 0dB, fall straight onto a narrowband carrier system. π

10 The introduction of sikes into the sectrum as is the case for the ulse train concentrates frequencies in narrow bands, thus increasing the eak value(s) of the PSD and causing significant interference. This would make UWB an unaccetable signaling technology and methods must be found to decrease this interference by distributing the frequency comonents over a wide range, ideally as reresented in Figure 6. Figure 7: To, Gaussian ulse train, and below its Frequency sectrum. Introducing randomness With the same assumtions as in the examle above, if we now make a small change to the waveform by randomly tweaking the osition at which the signaling ulse is laced in its time slot T, we get the following new exression for our signaling wave function. w () t = w() t δ( t nt ξ) dt r n= where ξ is evenly distributed over [-T /2 to T /2 ]

11 Taking the Fourier Transform of the above equation gives Wr ( f) = W( f) δ ( f n ξ ) T T n= To get the ower sectral density PSD, we square the above equation W t (f) Wr ( f) = W( f) δ ( f n ξ ) T n= T We now notice that this PSD is in addition to the roerties mentioned above, also a function of the newly introduced distributed random variable ξ. Since this random variable is evenly distributed over [-T /2 to T /2 ], which is the sace between sikes, it has the effect of evenly sreading out the discrete sectral comonents over the interval between sikes. This consequently has the effect of reducing the eak values of the PSD, as can be seen in Figure 8, where the eak comonents are now back below 0dB. Figure 8: To, randomly laced Gaussian ulses, and below its Frequency sectrum.

12 From the Wiener-Khintchine theorem, we know that the integral over the PSD of the single ulse, the ulse train and the ulse train with random ositioning must be the same (since their autocorrelation functions are the same). This can be illustrated as follows; the autocorrelation function R(τ) of the single ulse w(t) is defined as R() τ = w() τ w( τ + t) dτ The autocorrelation function R ww (τ) of the ulse train w t (t) is defined as where T is the eriod of the ulse train T 2 R ( τ ) = w ( τ) w ( τ + t) dτ ww t t T 2 The autocorrelation function R rr (τ) of the ulse train with random ositioning ξ is defined as R ( τ ) = w ( τ) w ( τ + t) dτ rr r r T Here we observe that we are integrating strictly over one eriod of the signals. Since we are using the same generic ulse w(t) to form both w t (t) and w r (t), it follows that their autocorrelation function must be the same, i.e. R() τ = R () τ = R () τ ww The value of the autocorrelation function at τ=0 is equal to the integral over the PSD of the signal, which is referred to in more familiar terms as the total energy in the signal. Let us denote this energy with Ψ. The inference can be made that and Wt ( f) W( f) δ( f n ξ) T - n= T Ψ= = Wr ( f) W( f) δ( f n ξ) T n= T Ψ= = In Figure 7 where the PSD is concentrated in discrete frequencies searated by an interval 2 T π, it is observed that the eak value(s) rise above 0dB. This is because to satisfy the condition that the integral over its PSD must = Ψ, the amlitude of the sikes must increase. rr

13 In Figure 8,, the resence of the random factor ξ causes the sikes to be evenly distributed over the intervals, thus sreading the concentration of ower and the eak(s) are reduced back below the T 0dB oint. Notable is that the above signal w t (t) is not an information carrying signal, as it is eriodic and comletely deterministic. By tethering around with the osition of the ulses, we have not only smoothened its PSD, but we have also transformed it into an information conveying signal w r (t) as it is no longer deterministic. Summary UWB signals urosely leak their PSD into that of other existing systems. If the leaked energy is above a defined limit, the UWB signal will be causing an unaccetable amount of interference which will greatly degrade the other systems erformance. A very meticulous analysis of the PSD is thus in order to be able to vindicate the resence of UWB signals, esecially in frequencies where resent occuants have aid hefty sums to obtain licenses to oerate. In this analysis, a worst case scenario has been evaluated where a constant ulse train is sent over the channel. This is indeed a worst case analysis because if an information containing signal was used, a further random factor would be added to the model above, and this randomness has the general effect of sreading out the PSD of the transmitted signal even more then simulated above. Conclusion Signaling with Gaussian doublet ulses has the advantage that the eriodic nulls in its PSD can be strategically ositioned so as to offer a minimal amount of interference. Taking a look at the sacing of the discrete comonents in the PSD of the studied signals which is, we note that if we decrease the sacing between the ulses T we get fewer and fewer greatly T saced discrete comonents which must have bigger amlitudes in order to fulfill the Wiener- Khintchine theorem. Effort must be ut into trying to fill in this sace between discrete comonents, and this can be done by introducing randomness in the way ulses are sent. Other methods of introducing randomness are well known modulation schemes like On Off Keying (OOK) and Phase modulation. This study can be further enhanced by combining two modulation schemes in a worst case analysis to investigate the ossibility of further gain in terms of lower PSD.

14 REFERENCES [1] Jari H. Iinatti, Matti Latva-aho et al. On the UWB System Coexistence with GSM900, UMTS/WCDMA and GPS, [2] Forester, Green et al. Ultra-Wideband Technology for Short or Medium-Range Wireless Communications, [3] Hämäläinen, Iinatti et al, In-Band Interference of three Kind of UWB Signals in GPS L1 Band and GSM900 Band,. [4] John G. Proakis and Dimitris G. Manolakis, Introduction to Digital Signal Processing, 3 rd edition Pretence Hall, 2002 [5] Allan Oenheim and Alan Willsky Signals and Systems 2 nd edition., Pearson Education, 2002 [6] IEEE P Wireless Personal Area Networks [7] C. Müller, S. Zeisberg, H. Seidel and A. Finger Sreading Proerties of Time Hoing Codes in Ultra Wideband Systems [8] Leonard E. Miller Why UWB? A Review of Ultrawideband Technology Reort to NETEX Project Office, DARPA, 2003 [9] htt:// FIGURES Figure 1: The Radio Frequencies, Oliver Wamanga, 2004 Figure 2: Frequency domain footrint of Various transmission systems. Oliver Wamanga, 2004 Figure 3: Effect of ulse duration on frequency domain footrint, Oliver Wamanga, 2004 Figure 4: Gaussian Pulse, Oliver Wamanga, 2004 Figure 5: The various ulses and their corresonding signal in the channel Oliver Wamanga, 2004 Figure 6: Frequency content of 0.5ns ulses Oliver Wamanga, 2004 Figure 7: Gaussian ulse train and its frequency sectrum, Oliver Wamanga, 2004 Figure 8: Randomly laced Gaussian ulses and their frequency sectrum, Oliver Wamanga, 2004 TABLES Table 1: Frequency Sectrum, Oliver Wamanga, More detailed information available at <<htt:// >> Table 2: Center Frequencies and Bandwidths[1].