Complex radio frequency (RF) communications with virtual pulses

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Computers and Electrical Engineering 34 (2008) 423–437 www.elsevier.com/locate/compeleceng

Complex radio frequency (RF) communications with virtual pulses Joshua Y. Maina a,*, Marlin H. Mickle a, Michael R. Lovell b, Laura A. Schaefer b a

Department of Electrical and Computer Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania, USA b Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania, USA Received 31 May 2005; accepted 18 September 2007 Available online 26 December 2007

Abstract A novel complex pulse forming technique has been developed using ultra wideband (UWB) frequency concepts where multiple carriers are modulated by the pulse width of the primary signal source. Specialized modulation of the pulse train provides an effective communication medium with inherent advantages of an UWB system. The multiple frequency nature of the non-traditional ‘‘pulse” formation provides a means of implementing UWB without the necessity of complex pulse formation of the classical UWB. The particular example of the research implemented in this paper allows explicit user choice of the specific UWB frequencies, e.g., ISM frequencies, to avoid current restrictions of the Federal Communications Commission (FCC). The reported method also contains an implicit property to support secure information transmission to receivers at known distances. The objective of this technique is an easy to form communication pulse having UWB low energy advantages along with the freedom of implementation without license requirements from regulating authorities, while adhering to the set limits of intentional radiators. The method chosen in this case was based on having the sum of energies from multiple frequencies remain within the restricted radiation limits at the correlated receiver. Included in the implementation technique is the inclusion of the signal fading effect as part of the modulation technique. The relevance of this pulse forming technique is in the simplicity of spreading the transmitted power among multiple frequencies without the issue of decay factor in the current methods. The result presented gives two sets of relative amplitudes of the transmitted frequencies identifying the transmitted character, e.g., 0 or 1. A form of amplitude encryption, due to the RF signal fading effect was also presented as advantage in the technique. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Complex pulse; UWB; ISM frequencies; Modulation; Fading; Cumulative

1. Introduction Ultra wide band (UWB) technology has received a great deal of attention from almost all wireless communications organizations and the FCC. UWB classically comprises of an extremely short-pulse width while *

Corresponding author. E-mail address: [email protected] (J.Y. Maina).

0045-7906/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compeleceng.2007.09.005

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taking advantage of an ultra wide bandwidth. The attractive characteristics of UWB technology include immunity to jamming, coexistence with licensed channels, and multiple access characteristics. Because UWB signals have high bandwidths and frequency diversity, they are particularly well suited for high-speed data communication in environments, such as indoors, where multi-path fading is much likely. The radio spectrum is considered to be fully utilized and, in fact, in short supply. By their nature, UWB signals utilize spectrum already designated for other use and regulated by the Federal Communications Commission (FCC). Emerging short-range radio applications, however, have recently encouraged the development of low-power emission systems and the low-power density of these signals allows them to overlay present usage without harmful interference [1]. The original concept of ultra wide band (UWB) developed by Time Domain, Inc., involves the formation and transmission of a complex pulse comprising a series of frequencies, fundamental and harmonics, all of which were correlated in time thus making them relatively easy to detect by a receiver designed for the known methodology at very poor signal to noise ratios including signals below the noise level. The organization of this paper proceeds with some Related work in the following section, which highlights some UWB pulse forming techniques. Followed by brief explanation of the Reported work, where the concept of ultra wide ISM (UWISM) is introduced along with the purpose of the technique being presented. This section also states the chosen method of implementation. Section 2 is the Theoretical bases, where Fundamental frequency and Harmonics were explained as they relate to the formation of Virtual pulse. This section also elaborates on the formation of Virtual pulse which is a key component in the formation of the UWISM. The Virtual pulse leading to Radio frequency (RF) pulse with an example at the end of the section. Section 3 explains the calculations of the coefficients as functions of magnitudes of the individual frequencies being transmitted. The coefficients in this section were used to generate pulses of different amplitudes and widths depending on the determined coefficients. Sections 3.2 and 3.3 deal with the idea of having the transmitted frequencies arriving at the receiving end at such magnitude that creates the correct pulse shape, width, and amplitude. This is important in the detection process. Section 3 ends with some examples of received pulses as a result of all the transmitted frequencies arriving at the predetermined distance. Section 4 elaborates on the advantages of spreading the energy content of the signal among multiple frequencies to avoid interference during communications. This section also stresses the long term impact in the aspect of frequency and channel reuse, because of the low energy level. The Paper ends in Section 5, where the results and claims of the work were summarized. 1.1. Related work Unlike continuous wave (CW) technology where sine wave is used to relay information, ultra wide band (UWB) technology employs transmission of very short impulses of radio energy. Because UWB has very low energy levels, lower than noise level and wide frequency spectrum, it is possible to utilize existing channels without causing any interference. Ultra wide band radio is some times referred to as baseband, impulse or free radio. Although UWB is not a new concept only recently has it been possible to efficiently generate and control UWB signals and apply modulation techniques, coding techniques, multiple access techniques in UWB technology. There are numerous techniques used in the generation of UWB pulses, and a number of research efforts have been carried out for the purpose of realizing this promising technology. Considered, as the most basic element of UWB radio technology is the practical implementation of a Gaussian monocycle. The monocycle could be realized both in the frequency and time domains. The monocycle is a wide bandwidth signal, with the center frequency and the bandwidth completely dependent on the monocycle’s width. In the time domain, the Gaussian monocycle is mathematically similar to the first derivative of the Gaussian function [6]. It has the form t 2 t V ðtÞ ¼ eðsÞ s

ð1Þ

where s is a time delay constant that determines the monocycle’s duration and t is time. In the frequency domain, a Gaussian monocycle’s spectrum is of the form

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V ðF Þ ¼ jF s2 eF

2 s2

425

ð2Þ

The center frequency is then proportional to the inverse of the pulse duration, i.e. 1 ð3Þ s The center frequency of a monocycle is the reciprocal of the monocycle’s duration and the bandwidth is 116% of the monocycle’s center frequency. Thus, for the 0.5 ns monocycle, the center frequency is 2 GHz and the half power bandwidth is approximately 2 GHz. The earliest techniques for the generation of short-pulse RF waveforms utilized the rapid rise and fall times of a baseband pulse to impulse or shock excite a wide band antenna. The antenna, in turn, generated its characteristic impulse response which, for a wideband structure, typically consisted of an electromagnetic burst containing only a few RF cycles of energy. By varying the physical dimensions of the antenna, the frequency and bandwidth characteristic of the resulting UWB pulse could be adjusted. From the research work carried out by Robert Scholtz, impulse radio was described as a baseband pulse of very short-duration spreading the energy of the radio signal from near direct current to a few gigahertz. The pulse propagates with distortion when applied to a properly designed antenna. Spread spectrum techniques are employed to solve the problem of interference to or by the UWB signal. The simple technique suggested [8] was time hopping with data modulation accomplished by additional pulse position modulation at the rate of many pulse per data symbol. A great advantage of the use of the impulse radio to tackle the problem of coexistence with other radio systems is the multi-path resolution, which is down to a nanosecond in differential path delay leads to a significant multi-path fading. Due to it’s significant bandwidth, an impulse radio based multiple access system may accommodate many users, even in multi-path environment. Impulse radio can be manufactured inexpensively because it is baseband. One of the earliest baseband sources [9] used a Max generator a fast rise-time, high-voltage step, which, would, in turn be applied to a step recovery diode (SRD) positioned at the aperture or feed point of the antenna. Invented by Max in 1924, the Max generator is a cleaver way of generating high-voltage short-duration waveforms by charging a number of capacitors in parallel, then quickly discharging them in series. While originally based upon the use of air-dielectric spark gaps to provide the switching mechanism, solidstate variants utilizing avalanche diodes or other solid-state switching devices have been used to generate nanosecond duration pulses having amplitudes exceeding several thousand volts of dc [10]. The SRD further sharpens the rise-time of the Max generator output to approximate a true baseband impulse excitation [11]. Since SRDs are generally limited to breakdown voltages of less than 100 V or so, multiple SRDs were often connected in series across the antenna aperture to permit the development of very large voltage pulse or baseband excitation. The resultant baseband pulse p(t) typically consisted of a relatively fast subnanosecond rise time followed by a slower multiple nanosecond decay. However, there were several problems with this approach. Firstly, the energy in the baseband excitation pulse drops logarithmically with frequency, which is a natural consequence of the doubly exponential time domain behavior. For example, a simplistic mathematical model for the baseband excitation pulse is given by the relationship t pðtÞ ¼ t exp ð4Þ u1 ðtÞ a Fc /

where a is the effective rise-time (for a positive-going pulse) and u1 is the unit step function. The magnitude squared of the Fourier transform of p(t), i.e. the signal energy density, has an asymptotic behavior given by 2

jP ðF Þj ¼

a4 16p4 F 4

ð5Þ

which exhibits a 12 dB per octave decay with frequency, as a result the amount of energy available at microwave frequencies is significantly lower than full bandwidth baseband power. The FCC has only recently licensed this concept. There is some concern that the signal strength in the frequency bands carrying the actual information will be a source of future interference with the licensed bands as well as interference among multiple users of this technology.

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1.2. Reported work The research reported in this paper is based on an UWB concept involving Industrial, Scientific, and Medical (ISM) frequency bands. Thus the term ultra wide ISM (UWISM) is used for the particular concept being reported. The ISM bands are available for experimentation and some communication, e.g., IEEE 802.11 and Bluetooth, but these bands do not form a simple harmonic set for implementing the original UWB concept of Time Domain, Inc. The purpose UWISM is to foster a method of generating UWB pulses for implementation particularly in specialized applications without the normal bottlenecks of licensing. Security issue was also taking into consideration by the fading effect of signals propagating a distance from the transmitter. In this technique the signal is received by a correlated receiver at a predetermined distance as the correct signal while being undetected by an uncorrelated receiver because of the faded signal level. Because the receiver is expecting signals at very low energy levels, concept of channel reuse becomes one of the advantages of this method of pulse generation. The problem of energy dropping logarithmically with frequency due to exponential time domain characteristics is not an issue with the presented technique, because there is total liberty in choosing the transmitted frequency and incorporation of the fading effect in the modulation. Consider the set of ISM frequency bands making up the UWISM bands without any loss of generality. Approximate center frequencies are used as the identifiers for the individual frequency bands. Thus, there is a set of bands (frequencies) F = {F1, F2, . . . , Fn} which bear no particular harmonic relationship. The ISM bands are used without any loss of generality because this technique applies to any set of bands. However all of the demonstrations have been on the basis of the ISM bands. Consider two frequencies, Fi,Fj, 2 F where the difference of any [Fi  Fj] is a minimum. With this difference as a basis, further subdivide the difference such that there is some [Fi  Fj]/m, where there exists a set of integers {ai} such that for all Fi,2F there exists a number ai * [Fi  Fj]/m that equals the frequency Fi. In the technique under discussion, the [Fi  Fj]/m value becomes the fundamental frequency of a virtual pulse string to be demonstrated that can be pulse width modulated such that the coefficients making up a Fourier series type representation of the pulse train at two different pulse widths will represent either a one ‘‘1” or a zero ‘‘0”. Thus, in concept, the virtual pulse is an abstract concept that can be repeated to communicate data while varying the width of the abstract virtual pulse. In essence, the square wave or pulse train is a carrier with the carrier being modulated by the width of the pulse or alternatively the duty cycle. In practice, there is no need to actually construct the pulse, thus overcoming one of the fundamental problems of the original UWB communication. Instead, a series of frequencies can be transmitted with the proper amplitude and possibly phase relationships. Although the modulation was indicated to be 0/1, it is possible by considering additional virtual pulse widths to communicate a larger set of characters. The UWISM is thus a set of sinusoidal carrier frequencies that can be amplitude modulated, phase modulated or a combination of both. In the strictest sense, the set of relative amplitudes of the transmitted frequencies identify the transmitted character, e.g., 0 or 1. Thus, at the point of transmission, it would seem that the relevant amplitudes (a set defining a 0 or a 1) would be transmitted in the proper ratio. However, the strength of the signals will not remain constant as they to the receiver. It is well known from the radar equation  travel from   the transmitter k 2 of the Friis equation P R ¼ P T 4pD GT GR that the attenuation of the frequencies increases as the distance increases according to the wavelength (frequency) of the transmitted signal. It is important to note that this distinction is a function of relative magnitudes not the absolute magnitudes. Thus, the relative amplitudes within the set representing the transmitted character appear to be distorted or lost as the distance between the transmitter and the receiver change. However, this apparent difficulty is actually a means of securing the transmission without additional encryption. The encryption is automatically provided by the physics of the situation in terms of the attenuation of the signal. Consider the situation of transmitting to a receiver at a known distance, say m miles. Knowing this distance allows the transmitter to calculate the attenuation for each frequency within the 0 or 1 set for that particular distance. This attenuation is then compensated for at the transmitter so that the proper signal strength ratio is only obtained at the desired distance. For an omni directional antenna, this would be a circle of radius m miles. However, a directional antenna can be used to more precisely focus the transmitted energy to the

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desired receiver. It is also possible to provide a more precise area for secure reception with power addition at the receiver with multiple transmitters. This UWISM method of communications is obviously not intended for general coverage radio communication. However, it is significant for specialized secure transmission applications where the signals can have a relatively poor signal to noise ratio. In addition, the UWISM does not need special licensing by the FCC when the ISM frequency is used. However, with the appropriate electronics, non-ISM frequencies can be used for the pulse formation using the same technique. Because the technique proposed here utilizes the fading effect of RF signal, it becomes appropriate for clandestine operations. 2. Theoretical basis 2.1. Fundamental frequency In this research, an innovative method of creating a radio frequency pulse using multiple frequencies has been developed. The ISM frequencies have been specifically used in this research for the purposes of example. When the Fourier transform is applied on N samples, it is assumed that the signal is periodic over N samples. Therefore, the fundamental frequency of the signal is equal to the inverse of the time T of the N samples. The fundamental frequency is expressed as [5,2,7] F 0 ¼ 1=T

ð6Þ

T can be written as a function of sample time, s, and total number of samples chosen N, to alternately express the fundamental frequency in terms of the sampling frequency Fs and N. F 0 ¼ 1=sN ¼ 1=ðs=sampleÞ  Total no: of samples F 0 ¼ F s =N

ð7Þ

This frequency, referred to as the fundamental frequency of the signal, is a type of resolution frequency, meaning the target signal components are resolved into multiples of this resolution frequency. For example, sampling the signal at a sample interval of 1/900 * 106 s and observing 1800 * 106 samples, then the fundamental frequency is F 0 ¼ F s =N ¼ 900  106 =1800  106 ¼ 0:5 Hz The Fourier transform is computed by simply multiplying the fundamental frequency by integers to obtain multiples with appropriate magnitudes. For example, with F0 = 15 MHz, the next harmonic would be F1 = 30 MHz and so on. An alternate way to view these harmonics of the fundamental frequency is as bins, which collect energy. In the discrete Fourier transform (DFT) they are called cells. Now the nth harmonic can be expressed as n multiplied by F0 F n ¼ nF 0 This is equal to F n ¼ n=sN ¼ nF s =N

ð8Þ

The harmonics of the transform are multiplied by the fundamental frequency to produce individual frequencies of the transform. The coefficients correspond to magnitudes of the signals at their respective frequencies. These coefficients are very important in the modulation technique currently under discussion. 2.2. Virtual pulse construction There is a mechanism by which a virtual repeating square wave can be transmitted when one considers the DFT. If all frequencies of the DFT of a square wave are transmitted with the corresponding DFT coefficients while accounting for fading, the square wave can be reconstructed at the receiver from the sum of received frequencies. The analysis and understanding of the square wave formation and reconstruction unveil numerous avenues for investigations and applications. This section of the paper provides an example [5].

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If the frequencies derived from the DFT of a rectangular pulse train are to be transmitted as individual RF continuous waves (CW) with the proper phase relationships, the specific frequencies derived from the DFT might not be available for use in transmission simply because of FCC regulations. In addition, it is not clear what the FCC will do in the future about multiple frequencies below the noise threshold. For new and innovative research purposes, ISM frequencies have been used to demonstrate the technique of ultra wideband multiple frequency communication as related to the research reported in this paper. In addition, although ISM frequencies are available for experimentation, the spacing between the frequency bands, whose union makes up the ISM spectrum, might not be consistent in integer ratios compared to a nominal harmonic series. For the virtual pulse set of frequencies, a common denominator is the virtual fundamental frequency of the chosen ISM frequencies. In order for this to be feasible, due to the non-integer nature and necessary precision, floating point numbers must be used to determine the multiples of the fundamental frequency for each of the chosen ISM frequencies. These frequencies are not harmonically related in the traditional sense, but the sum of these frequencies does represent some signal, which has the desired corresponding spectral content and which can be conceptually modulated. This signal with the desired spectral content is termed the virtual pulse or virtual pulse train.

2.3. An example situation Consider a virtual pulse train having a fixed period Tv and variable pulse duration sv as shown in Fig. 1. Therefore, because the period is fixed, the fundamental frequency of the DFT is given by Taking the DFT of this virtual pulse train provides an ensemble of frequencies that are hypothetically harmonically related. The spectrum of these frequencies constitutes the chosen ISM frequencies along with potentially many other frequencies. The remainder of the frequencies, which are non-ISM, may fall within the spectrum already allocated by the FCC and as such are assumed as not being available for general RF communications. This problem is resolved by forcing any non-ISM frequency coefficients to be zero. The set of Industrial, Scientific, and Medical (ISM) frequencies has been determined to be an appropriate candidate for this research because these frequencies are available for use within certain tolerances and restricted power levels. As indicated previously, the set of ISM frequencies is not harmonically related in the RF spectrum. Therefore, what is termed the virtual pulse concept will be used to find a common denominator that can be considered the virtual fundamental frequency among the chosen ISM frequencies. For the purpose of this example, consider the following five ISM frequencies, 315 MHz, 418 MHz, 433 MHz, 915 MHz, and 2450 MHz. A common denominator can be found among these numbers that will provide the means for deriving the fundamental frequency (which may not be unique) to relate the chosen frequencies and facilitate modulation by varying the pulse width. One simple technique is to look at the differences among subsequent frequencies moving from the lowest to the highest. The smallest difference between any two frequencies happens to be between 418 MHz and 433 MHz, which is exactly 15 MHz. The fundamental frequency for the purpose of this example from the DFT of the virtual pulse train has a period Tv at 0.06 ls and is given by F v0 ¼ 1=T v ¼ 1=0:06  106 ¼ 15 MHz Fv0 = 1/Tv τ A

T 0

Tv

2Tv

Fig. 1. Picture of a virtual pulse train.

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Because the fundamental frequency is known, the multiple for each of the five example ISM frequencies can be found using the relationship N F ISM  F v0 ¼ F ISM

ð9Þ

where FISM is the ISM frequency and N F ISM is the harmonic number of the ISM frequency. Hence, for each of the five frequencies the following numbers are the multipliers of the fundamental frequency [5]: 315 ¼ 21 15 418 N 418 ¼ ¼ 27:867 15 433 ¼ 28:867 N 433 ¼ 15 915 N 915 ¼ ¼ 61 15 2450 ¼ 163:333 N 2450 ¼ 15 N 315 ¼

The expressions can now be written as N 315  f0 ¼ 21  15 ¼ 315 N 418  f0 ¼ 27:867  15 ¼ 418 N 433  f0 ¼ 28:867  15 ¼ 433 N 915  f0 ¼ 61  15 ¼ 915 N 2450  f0 ¼ 163:333  15 ¼ 2450 When the DFT of the virtual pulse is obtained, the frequencies spread from the DC component to frequencies beyond 2450 MHz. However, for this application, only these dominant five frequencies are utilized, and the remaining frequencies within this spectrum are kept at a zero level (switched off). Thus, it is the cumulative energy of these frequencies that represents the information being transmitted. 2.4. Radio frequency (RF) pulses One of the essential elements of this research is the investigation of the possible implementation of the technique of RF pulse formation for the purpose of communication. As mentioned previously, when the components of a Fourier transform are known for a particular pulse train, the Fourier series of the components can be used to reconstruct the pulse train. Fig. 2 shows the reconstructed rectangular pulse from a series having a fundamental frequency of 15 MHz and a period of 0.06 ls. Because of the presence of a number of high frequency components, it can be observed that the Gibbs effect [4] is almost eliminated in the reconstructed rectangular pulses. In this example, the specific interest is in amplitude modulating multiple ISM frequencies (315 MHz, 418 MHz, 433 MHz, 915 MHz, and 2450 MHz) according to the discrete Fourier transform. These five frequencies are then combined to form an RF pulse sufficiently distinct to be detected by a phase correlated receiver. It can be seen here that the modulation technique is two-fold. Amplitude modulating the individual ISM frequencies forms a five frequency spreading of the bit energy in the form of a digital code. For example in this case, we are transmitting F315, F418, F433, F915, and F2450 to represent the code 10011 which can be interpreted as a ‘0’ or ‘1’ depending on the Hamming distance [4] (number of bit positions where each received code differs) chosen for the reception. When these five frequencies are combined, an RF pulse is formed whose width can be varied by applying different sets of coefficients to the individual frequencies, respectively.

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Fig. 2. Fourier series reconstruction of a rectangular pulse using frequencies from the fundamental to the 165 Harmonics.

3. Design considerations 3.1. Choice of coefficients The choice of the respective coefficients for the individual ISM frequencies was carried out with the goal of creating distinct pulses to represent a ‘‘0” and a ‘‘1”, respectively. The choice of the frequencies and the coefficients is not unique. The distinction in this instance is the ‘‘width” of the pulse in order to perform a pulse width modulation. For the purpose of having a clear distinction between the two different pulses, a minimum ratio of 1:2 for bits ‘‘1” and ‘‘0” was chosen for this example. The first pulse is the wider pulse. Therefore because the coefficients are responsible for the pulse shape and width, the manipulation of the magnitudes of these coefficients facilitates the formation of the ratio of the two pulse widths representing ‘‘1” and ‘‘0”. Thus as one method, some or all of the coefficients used in generating the pulse could be divided into halves to produce the set of coefficients for the second pulse in order to establish the suggested ratio of 1:2. Most of the effort involved in choosing the coefficients happened during the creation of the wider pulse (first pulse), and the following steps were taken:  To avoid having an infinite range of alternatives, a range of 0.01–10.0 was set for the choosing of the coefficients  Because the effect of some of the frequencies tends to be higher than the others, the frequencies with greater influence on the pulse shape can have coefficients maintained as integer numbers while the frequencies with lesser influence on the pulse shape are maintained as floating point numbers [5]. For the shorter pulse (second pulse) the coefficients of the pulse with greater influence on the pulse shape are reduced to a value as close to one half as possible. This will reduce the width of the pulse to at least half. The pulse in these cases is the envelope of the function jsin xm tj * sin xct where xm is a modulation frequency and xc is essentially a set of carrier frequencies. The carrier frequencies are implemented within the ISM bands, and the non-integer frequency is readily available. The method of generating these carrier frequencies relies on a conceptual analogy with a Fourier analysis with floating point coefficients for the ‘‘Harmonics” to generate the set of carrier frequencies.

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The choice of coefficients is essentially a trial and error process other than possibly the initial choice of the smallest differential between the set of available frequencies. However, in the described embodiment, these are assumed to be ISM frequencies with no loss to generality. Obviously, the combination of frequencies is given by n X ai sin xi t F 0;1 ¼ i¼1

where F0,1 represents the two sets of coefficients for the multiple frequencies for characters 0 or 1, respectively. The search process is similar to a combinatorial problem in chemistry. The combinatorial selection in general will be governed by the fading problem at the higher end of the spectrum. The chosen coefficients are to be based on the distance to the receiver with the transmitter coefficient strengths accounting for the fading of the frequencies. The introduction of fading gives rise to the fixed distance concept also presented later in this paper. Fig. 3 shows the result of combining the five ISM frequencies within the coefficients: a315 ¼ 0:10;

a418 ¼ 0:10;

a433 ¼ 0:05;

a915 ¼ 5:00;

a2450 ¼ 0:3

These RF pulses transmit a bit ‘1’ communicated to the receiver. Fig. 4 shows a different set of RF pulses constructed by changing the sets of coefficients to a315 ¼ 0:10;

a418 ¼ 0:15;

a433 ¼ 0:2;

a915 ¼ 3:00;

a2450 ¼ 0:3

These RF pulses transmit a bit ‘0’. Through this technique, pulse width modulation is implemented by way of manipulating the coefficients of the individual frequencies whose combination forms the pulses. As depicted by Fig. 3 and figure for the pulse widths are 0.01 to 0.01 and 0.005 to 0.005, respectively, showing the width of the later to half the width of the former. 3.2. Transmitted power consideration From the transmitter side, the energy levels of each modulated channel (ISM frequency) are set with respect to the presumed propagation distance and fading effect such that the correct energy range for the respective information is received at the destination. Fig. 5 is an illustration of the basis of determining energy levels at the transmitter. A similar technique is used at the receiver end to collect the cumulative energy received [5].

Fig. 3. Construction of pulses using the 21st, 27.867th, 28.867th, 61st, and 163.333rd harmonics only with one set of coefficients.

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Fig. 4. Changing the RF pulse width by applying a different set of coefficients.

PT1 PT PT2 PT3 PT4 h1

h2

h3

h4

PT5 h5 h6

Fig. 5. Relative energy levels of transmitted frequencies.

Fig. 5 illustrates the relative energy levels of multiple frequencies individually transmitted by separate transmitters that may be correlated. The power levels of all the transmitters are set such that the relative powers PT1, PT2, PT3, PT4, and PT5, of the respective channels are calculated for the transmitter. The power levels are established bearing in mind the attenuation of the signal before reaching the receiver as it propagates. The expected cumulative power at each of the multiple frequencies is received only when the receiver is at the proper distance. The expressions for the relative power levels are as follows:   h1 h2 h3 h4 h5 P T1 ¼ ; P T2 ¼ ; P T3 ¼ ; P T4 ¼ ; P T5 ¼ ð10Þ h2 h3 h4 h5 h6 where h1, h2, h3, h4, and h5 are the power levels of f315, f418, f433, f915, and f2450 respectively. It is assumed that the energy ratios of the multiple frequencies vary according to a constant ratio because of the fixed value of Lambda for each frequency. 3.3. Received power considerations The inverse square law [3] can be used to illustrate the relative power levels at the receiver. Although in practice, the steady fading of PT might not be realistic because signals having different frequencies fade at different rates due to the difference in wavelengths. A more appropriate relation for the received power in a multiple frequency situation is the radar equation, expressed as

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 PR ¼ PT

2 k GT GR 4pD

433

ð11Þ

PT is the transmit power, GT and GR are transmitter and receiver gains respectively, D is the distance traveled by the signal, and k is the wavelength of the signal given by k ¼ c=F

ð12Þ

where c is the speed of light in a vacuum (3 * 108), and F is the frequency of the signal. From Eq. (12), it can be seen that k is a function of the frequency under consideration. When it comes to multi-frequency situation, the expressions below give the relative power levels PR1, PR2, PR3, PR4, and PR5 at the receiver after PT1, PT2, PT3, PT4, and PT5 have traveled the distance D from the transmitters 8 2 2 9 2 2 > = < P R1 ¼ F ðP T1 ; DÞaP T1 k315 =½4pD ; P R2 ¼ F ðP T2 ; DÞaP T2 k418 =½4pD ; > 2 2 ð13Þ P R3 ¼ F ðP T3 ; DÞaP T3 k2433 =½4pD ; P R4 ¼ F ðP T4 ; DÞaP T4 k2915 =½4pD ; > > ; : 2 2 P R5 ¼ F ðP T5 ; DÞaP T5 k2450 =½4pD : Alternatively power at the receiver can be represented as follows: 8 9 2 2 2 2 < P R1 ¼ h1 k315 =½4pD2 ; P R2 ¼ h2 k418 =½4pD2 ; P R3 ¼ h3 k433 =½4pD2 ; P R4 ¼ h4 k915 =½4pD 2 ; = h k =½4pD h k =½4pD h k =½4pD h k =½4pD 2 418

:P

3 433

R5

4 915

5 2450

;

2

=½4pD ¼ hh5 kk2450=½4pD 2 :

ð14Þ

6 418

The values of PT1, PT2, PT3, PT4, and PT5 represent the bit ‘‘0” or ‘‘1”, and the combination of any three of five bits gives the value, for example 10011. Here, the 1s represent the frequencies that are switched ‘‘ON” (1st, 4th, and 5th frequencies in this example) and the 0s represent the frequencies that are switched ‘‘OFF” (2nd and 3rd frequencies in this example). Due to the difference in fading of the multiple frequencies, the valid power levels of the individual frequencies will be set at different magnitudes. This means the lower value frequencies will be expected to arrive at a higher relative magnitude than the higher value frequencies. Ranges of the received signals can be categorized as lower boundaries and higher boundaries for the purpose of correct interpretation of the received signal. In the inequality expression below, 1LR1 and 1UR1 represent the lower and upper boundaries of received power level which stands for a bit ‘‘1” for the first frequency, while 0LR1 and 0UR1 represent the lower and the upper boundaries of the received energy level which stands for a bit ‘‘0” for the first frequency. Similarly, the rest of the frequencies have their boundaries based on the anticipated fading. 1LR1 6 P R1 6 1U R1

0LR1 6 P R1 6 0U R1

1LR2 6 P R2 6 1U R2

0LR2 6 P R2 6 0U R2

1LR3 6 P R3 6 1U R3 ) 0LR3 6 P R3 6 0U R3 1LR1 6 P R4 6 1U R4 0LR1 6 P R4 6 0U R4 1LR5 6 P R5 6 1U R5

0LR5 6 P R5 6 0U R5

Using the radar equation the lower and upper boundaries can be set as follows: LRi ¼ RRi  ðP Ri  0:1Þ U Ri ¼ RRi þ ðP Ri  0:1Þ where the subscript i is an integer number from 1 to n with n being the maximum number of frequencies. In this case, it ranges from 1 to 5. These boundaries establish the range for the valid power for the individual multiple frequencies. 3.4. Examples of received pulses For the five ISM frequencies chosen as an example in this paper, the received power is expected to differ after traveling the same distance assuming the transmitters’ powers are all set at the same level. Knowing

434

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Fig. 6. Received pulse at a distance of 20 m – representing a bit ‘‘1”.

Fig. 7. Received pulse at a distance of 20 meters – representing a bit ‘‘0”.

the rate of attenuation for the individual frequencies enables us to set the power for each frequency such that the combined frequencies at the receiver give an expected virtual pulse. For the pulse in Fig. 3 representing a ‘‘1”, the pulse in Fig. 6 is received at a distance of 20 m from the transmitter. A similar result was obtained for the pulse in Fig. 4 representing a ‘‘0”, Fig. 7 illustrates the received pulse at a distance of 20 meters from the transmitter. Without encryption, the transmitted signal security can be added by deliberately setting the individual frequencies such that from the transmitter side it appears distorted but at the received end the received pulse appears distinct enough due the fading effect. An example is shown in Fig. 8 for the intentionally distorted transmitted pulse and in Fig. 9 for the correctly received pulse after fading within the predetermined distance. Using this method, only a receiver at the correct distance is able to receive the correct pulse shape for the intended information.

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Fig. 8. Distorted transmitted pulse representing a ‘‘1” or a ‘‘0”.

Fig. 9. Corrected received pulse after fading effect, representing a ‘‘1” or a ‘‘0”.

4. Scientific relevance and long term impact The field of communications is one of the advanced and thriving areas in the sciences, in particular the wireless RF segment. The wireless communication sector is implemented only by abiding to strict rules as earlier stated in this paper. Part of the reasoning for the rules is to reduce interference to the bearable minimum. Because the RF spectrum is approaching saturation, it is becoming increasingly difficult to facilitate non-interference among adjacent channels. The radio frequency (RF) communications using a virtual pulse presents a technique of spreading the transmitted information among multiple frequencies with a possibility of maintaining the energy of the individual frequencies at levels that become relatively insignificant with respect to their individual adjacent spectrum band. The multiple frequency concept in this paper makes interference highly unlikely and this can be interpreted as a security phenomena. In addition, the fading effect of RF signals as a function of distance traveled has typically been classed as one of the drawbacks in wireless communications; whereas in this paper we have presented the fading effect as an added security for a transmitter and receiver whose proximity influences the received pulse shape and amplitude.

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One of the long term impacts of this technology is the possibility of implementing this technique to nonISM frequencies. As the demand for application specific RF systems grows the need for cost effective jam proof architecture enlarges also. A consideration for a system on a chip using this technique will be worthy of implementation in the future. 5. Concluding remarks This research has developed a conceptual complex pulse formation using multiple ISM frequencies from a concept derived from ultra wideband radio pulse using pulse width modulation. The developed technique helps resolve the licensing problem and the interference with respect to existing allocated bandwidths. NonISM frequencies can possibly be utilized in the pulse formation provided certain sophistications are incorporated to overcome the problem of interference. The modulation implemented in this research has also added to the importance of this technique in that the fading effect of the individual multiple frequencies becomes part of the modulation process. The chance of detection by an uncorrelated receiver at a random distance becomes extremely difficult. References [1] Roberto Aiello G, Ho Minnie, Lovette Jim. An emerging technology for wireless communications. Paco Alto, USA: Fantasma Networks, Inc; 2000. [2] Glisson TH. Introduction to system analysis. New York: McGraw-Hill; 1985. [3] HyperPhysics, General inverse square law, . [4] Lafrance P. Fundamental concepts in communication. Prentice-Hall, Inc.; 1990. [5] Maina JY. Dissertation. Complex pulse forming technique using AM detector type circuitry and the application of CDMA to RFID for the simultaneous reading of multiple tags. University of Pittsburgh, Pittsburgh, Pennsylvania, 2004. [6] PulsON Technology. Time modulated ultra-wideband for wireless applications. Time Domain Corporation; 2000. [7] Senturia SD, Wedlock BD. Electronic circuits and applications. New York: John Wiley & Sons, Inc.; 1975. [8] Win Meo Z, Scholtz Robert A. Impulse radio: how it works. IEEE Commun Lett 1998;2(1). [9] Bennett CL, Ross GF. Time-domain electromagnetics and its applications. Proc IEEE 1978;66:299–318. [10] Baker RJ, Johnson BP. Applying the max bank circuit configuration to power MOSFETs. Electron Lett 1993;29(1):56–7. [11] Lesha MJ, Paoloni FJ. Generation of balanced subnanosecond pulses using step-recovery diodes. Electron Lett 1995;31(7):510–1.

Joshua Y. Maina received his PhD degree from the University of Pittsburgh in 2004. He is currently researching Complex RF Matrix Systems focusing on Multiple Inputs, Multiple Outputs. Other interests are in wireless and RF communications and signal management, RFID technology and automatic data capture, multiple access techniques, and parallel computations.

Marlin H. Mickle is currently the Nickolas A. DeCecco Professor and Executive Director, RFID Center of Excellence. He is active in the areas of energy harvesting and high technology applications, a Life Fellow of the IEEE. He received the Carnegie Science Center 2005 Award for Excellence in Corporate Innovation. Michael Rhodes Lovell received his PhD degree from the University of Pittsburgh in 1994. Currently he is the Associate Dean for Research, School of Engineering University of Pittsburgh. Professor Lovell’s research is currently geared toward further improving manufacturing processes for electronic components, developing methods streamlining processes using virtual and physical simulation techniques.

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Laura A. Schaefer is an Associate Professor in the Mechanical Engineering and Materials Science Department and Deputy Director of the Mascaro Sustainability Initiative at the University of Pittsburgh. She conducts energy systems research in areas such as microchannel flow, fuel cells, heat transfer in 3-D circuits, and thermoacoustics.