UPTEC F 18064
Examensarbete 30 hp December 2018
The Impact of Antennas on Radiolink Performance in Frequency Hopping Scenarios
Sofia Bergström
Teknisk- naturvetenskaplig fakultet UTH-enheten
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Abstract
The Impact of Antennas on Radiolink Performance in Frequency Hopping Scenarios
Sofia Bergström
This paper investigates how the communication performance of frequency hopping systems are affected by the antenna parameters. The data are generated from Antenna Toolbox in Matlab for the case of two dipole antennas is free space.
Non-orthogonal and orthogonal frequency hopping are used and the statistical impact from the antenna on the SINR is investigated. The results can be used to see the wave propagation margin and also see the effects of out-of-bands emissions in frequency hopping systems.
The numerical generated model is compared to two isotropic antenna models and it shows that the isotropic models are relatively good despite its simplicity in this case.
It does however not capture the spread caused by the directivity. Another model is created which mimic the numerical generated statistical distribution. This model uses the theoretical probability of a collision for both orthogonal and non-orthogonal frequency hopping. The model also uses mean values of directivity, s-parameters and the spread of the gain to calculate a statistical antenna model. This model is better than the isotropic for the tested cases and shows that it is possible to generate a statistical model.
Examinator: Tomas Nyberg Ämnesgranskare: Mikael Sternad Handledare: Tore Lindgren
Popul¨ arvetenskaplig sammanfattning
Inom detta examensarbete har antennens egenskaper och dess inverkan p˚a kommunikationssyste- met unders¨oks for frekvenshoppande system som en del av KORINT-projektet p˚a Totalf¨orsvarets forskningsinstitut, FOI. En antennmodell som tar h¨ansyn till antennf¨orst¨arkning, impedans- matchning och kopplingen mellan antenner ¨ar implementerad i Matlab. V¨arden p˚a isolation, intern reflektion och direktivitet ¨ar generade med Antenna Toolbox i Matlab f¨or ett fall d¨ar tv˚a dipolantenner ¨ar placerade i fri rymd. Olika scenarios relaterade till frekvenshop ¨ar testade och den statistiska f¨ordelningen av SINR ¨ar unders¨okt.
Modellen ¨ar j¨amf¨ord med tv˚a vanligt f¨orekommande isotropa modeller och det visade sig att b˚ada isotropa modellerna ¨ar relativt bra trots grova f¨orenklingar. Vad modellerna inte g¨or ¨ar att f˚anga spridningen orsakat av antennf¨orst¨arkningen eller f¨or¨andringen d˚a avst˚andet mellan antennerna ¨andras vilket kan resultera i felber¨aknad ¨overf¨oringsf¨orm˚aga. En ytterligare modell har skapas med m˚al att imitera den Matlabgenererade modellen vilket den lyckas g¨ora bara f¨or medelv¨ardet p˚a s-parametrar, direktivitet och f¨or spridningen p˚a antennf¨orst¨arkningen. Model- len visar att det inte kr¨avs mycket information f¨or att skapa en godtycklig modell. Modellen har ocks˚a f¨ordelen att den inte beh¨over anv¨anda Antennpaketet fr˚an Matlab eller n˚agra upprepade Monte Carlo loopar. Modellen anv¨ander teoretiskt ber¨aknande sannolikheter f¨or kollisionsrisken med sidband och det visar sig vara relativt bra p˚a att prediktera sannolikhetsf¨ordelningen. Alla modeller i denna rapport ¨ar grovt f¨orenklade men kan ¨and˚a anv¨andas f¨or att ge en f¨orsta inblick i hur antennen p˚averkar ett frekvenshoppande kommunikationssystem.
Contents
1 Introduction 1
1.1 Background . . . 1
1.2 Thesis objective . . . 1
1.3 Scenarios . . . 2
1.3.1 Delimitations . . . 2
1.4 Related work . . . 2
1.5 Outline of the thesis . . . 3
2 Theory 4 2.1 The communication system . . . 4
2.2 Antennas . . . 5
2.2.1 Directivity and gain . . . 5
2.2.2 The antenna as an electrical component . . . 5
2.2.3 Impedance matching . . . 7
2.3 Signal, noise and interference . . . 9
2.4 Frequency hopping system . . . 10
3 Antenna setup 11 3.1 Preprocessing . . . 11
3.1.1 Generate data . . . 11
3.1.2 Impedance matching . . . 12
3.2 Dependence of distance . . . 12
3.2.1 s-parameters . . . 13
3.2.2 Directivity . . . 13
3.2.3 Data for statistic model . . . 14
4 The model 17 4.1 Simulation setup . . . 17
4.2 Antenna models . . . 18
4.2.1 Matlab model . . . 18
4.2.2 Previously used models - isotropic . . . 18
4.2.3 Statistic model . . . 18
5 Comparison of models 19 5.1 Overview . . . 19
5.2 Probability comparisons . . . 20
5.3 Dependence of distance . . . 22
6 Discussion 24
6.1 Discussion of models . . . 24
6.1.1 Matlab model . . . 24
6.1.2 Isotropic model . . . 25
6.1.3 Statistical model . . . 25
6.2 Discussion of method . . . 26
6.3 Future work . . . 26
7 Conclusion 27 A Motivation of collision probabilities 29 A.1 Probability for direct hit . . . 29
A.2 Probability for collision with a sideband in non-orthogonal frequency hopping systems . . . 29 A.3 Probability for collision with a sideband in orthogonal frequency hopping systems 30
Chapter 1
Introduction
1.1 Background
Wireless communication has since the first radio transmission in 1895 increased to a technique which the modern society relies on. A reliable radio communication is important in many situations and especially in military systems where the requirements often are higher also in terms of robustness and security. Knowing the properties of the communication system is important to use the right techniques such as coding and transmitting power, to be able to transmit the message with sufficient means.
Many used simulation models does not take the antenna properties into account with risk of wrongly estimated throughput as results. On military platforms, several different radio systems are integrated on the same limited area. These antennas interfere with each other but also with the platforms itself and surrounding environment as a part of a complex system. Measurements of the radiation pattern of antennas integrated on platforms are expensive and have a high level of uncertainty. A computer model is cheaper but to obtain a model for the whole platform is a time-consuming process which also may omit important information or change rapidly for changes on the platform or in the surrounding. What is relatively simple to measure are the internal electrical properties of the antennas such as reflection coefficient and the isolation between antennas in the same system, later in this report called s-parameters, because these can be obtain by measuring a ratio of voltages.
In this report the theoretical values of those s-parameters and the radiation pattern are investigated in Matlab for a specific scenario. In the scenario, two dipole antennas interact in different frequency hopping systems. In military systems it is common to have one liaison unit who communicate with the platforms but also simultaneously communicate up in the hierarchy.
Normally it uses frequency hopping to increase the robustness to both unintentional disturbances as well as intentional disturbances from an enemy. This realistic but very simplified scenario is used in the report.
1.2 Thesis objective
This degree project aims to explore the concept of antennas in telecommunication. The antenna is an essential part of communication system and has been well investigated as a component. It isn’t however as well explored when interacting with other techniques as a whole. The project is carried out at FOI, Swedish Defence Research Agency and investigates how the communication performance of frequency hopping systems are affected by the antenna parameters. In particular the antenna gain, impedance matching and the mutual coupling of antennas are inserted in an
existing software framework to evaluate its impact.
The questions that will be answered within this master thesis are,
• How the radiolink performance is affected by the antenna in frequency hopping systems.
• How good the frequently used isotopic antenna model is.
• If it is possible to create a simple model to mimic the statistical performance of the antenna.
1.3 Scenarios
Antennas are integrated in an existing framework for evaluating communication performance in Matlab. The previous model uses Communications Toolbox to create an AWGN channel and uses a BPSK modulator-demodulator to calculate the bit error probability, BEP, for different values of SNR. The new model updates the SNR and SINR values for different scenarios which can be used to analyse the SINR directly or to be sent into the BEP-model.
In this report two dipoles of length λ/2 are placed in free space at various distances, simulat- ing two antennas on the same platform. Another antenna further away is trying to communicate with the platform but the channel is disturbed in various ways according to scenario. For each simulation, different directions for both platforms are chosen randomly. Same goes for the two frequencies used in the frequency hopping scenarios. The scenarios are,
• No collisions The second antenna is switched off or using a distant frequency.
• Frequency hopping The two antennas are using frequency hopping within the same frequency range.
• Orthogonal frequency hopping Same as above but orthogonal frequency hopping are used ie not allowing both systems to simultaneously use the same frequency.
1.3.1 Delimitations
The unreal case with two dipoles in free space are by purpose kept simple as every additional feature is making the model less general. This report does not include wave propagation issues nor the electromagnetic behaviour of the setup. The first because it is not possible to control with platform design and that this model later will be evaluated in a software called detvag90, where the wave propagation is calculated. The second because it soon can lead to complex time consuming calculations. Other important parts of the communication system as coding and modulations is not included as the main part is to investigate the impact from the antenna and with said parts included, the antenna characteristic may be hidden or mitigated.
1.4 Related work
In military applications the robustness of a communications is of great importance. The project RICOM (Robust Integration of Wireless Telecommunication Systems) [1] as well as its ongoing successor KORINT are major projects within the area. Both projects approach interference problems both at a single platform and multiple colocated ditto. Another report from FOI is [2] where interference in colocated frequency hopping systems are evaluated. Said report does not take the properties of the antenna into account. On the other hand [3] evaluates the effect of antenna integration from an electrical point of view but it does not include the impact to the communication system.
1.5 Outline of the thesis
In Chapter 2 the theoretical background is given including antenna characteristics, an introduc- tion to disturbance in form of noise and interference and also properties of frequency hopping systems. The antenna setup is described in Chapter 3 and illustrates how the antenna data is generated in Matlab and how the properties of directivity, gain and s-parameters vary with distance. Chapter 4 is describing the actual model and Chapter 5 shows the result in terms of comparisons of models. A discussion follows in Chapter 6.
Chapter 2
Theory
2.1 The communication system
Information can be transmitted with several techniques but the main chain is the same. The analogue message is first formatted into a digital bitstream. The bitstream is encoded, modu- lated and send over a channel to a receiver where the analogue signal is demodulated, decoded and formatted back to the original analogue message, see Figure 2.1. A source encoder can use data compression to lower the redundancy and a channel encoder use coding to increase the reliability. Most channels are so called waveform channels and cannot send a sequence of binary number without first converting it, with a modulator, to a form compatible to the channel [4].
No real channel is ideal and the simplest method to simulate it is to use an additive white Gaussian noise, or AWGN, channel, motivated by the central limit theorem. It just adds normal distributed noise with a constant power spectral density to the signal. This model is simple and widely used in telecommunication since it is easy to combine as the output still is AWGN.
Another noise model is called Middleton’s Class A interference model. It is more relevant as it can include the non-Gaussian behaviour of impulse noise. For example, other electronic devices and engines on the same platform may cause impulsive noise. One such noise source is often not a problem statistically but with multiple sources the combined noise can be intractable [1].
Formating Encoding Modulation
Analogue message signal
Transmitter
Formating Decoding Demodulation
Receiver Analogue
message signal
Channel
Figure 2.1: The digital communication chain.
2.2 Antennas
An antenna is an interface for transition between a guided and a free-space wave [5]. It is a device for both transmitting and receiving of electromagnetic waves and the same model can often be used for both cases since the device is reciprocal under most conditions, it is just a matter of convenience [6]. Although antenna comes in a wide variety they all operate according to the same rules of electromagnetics. Electromagnetic waves are oscillations of electric and magnetic fields that transmits power at the speed of light and persist in absence of its source [7].
The simplest case of a transmitting antenna is a rod in which an alternating current is fed. As for a receiving antenna the incoming electromagnetic field pushes the electrons in the rod back and forth and the created oscillating current is measured by the receiver. The said antenna can be found in the large class of dipole antennas. A dipole antenna has two conductors arranged symmetrically around a feeder, who typically is a quarter wavelength long. The dipole can be connected to form larger structures such as Yagi-Uda which is a common antenna for terrestrial television receiving [8]. Another similar antenna type is monopole antenna in which one conductor is omitted and replaced by a groundplane [7].
2.2.1 Directivity and gain
A hypothetical antenna that radiates equal power in all direction is called an isotropic antenna, and is often used as a reference when comparing antennas [6]. If a λ/2 dipole antenna is placed in free space the radiation pattern is rotationally symmetric in the perpendicular plane, with a gain of 2.15 dB compared to the isotropic case [5]. The total power emitted is the same but it is distributed differently and for a dipole there is no power radiated in the extension of the dipole axis. In reality there is always some structure in the surrounding, anthropogenic or natural, that changes the pattern. Also worth mentioning is that antennas often are constructed to radiate in one particular direction, by using reflectors or several cooperating antennas. The strongest direction is often refered to as main lobe unlike side lobes and back lobe [7].
The directivity gain is one of the most important parameters of antennas and describes how the power density is distributed in spherical coordinates. Usually it is plotted in form of a radiation pattern in the azimuth angle as seen in Figure 2.2. The unit of directivity is usual dBi, where i stands for isotropic as it measure the value relative to an isotropic antenna [9].
The gain of an antenna is the actual increase or decrease of signal power density in a particular direction. Losses can occur when the power heats up the structure instead of radiate or when there is a mismatch in the antenna connections, see Section Impedance matching.
These losses are included in the dimensionless efficiency factor, 0 ≤ e ≤ 1, so the relation of the directivity, D, and the gain, G, can be written as Equation (2.1) [5].
G = e · D (2.1)
2.2.2 The antenna as an electrical component
An antenna is a complex structure consisting of a large number of components. To simplify the analysis an equivalent circuit model can be used [8]. Two port-theory is a tool to represent circuits as a black box with, as the name reveals, two ports. Each port has a voltage and a current associated as shown in Figure 2.3a. The voltage and current can be represented by linear combinations of the other voltages and currents assuming all components in the 2-port are linear, time invariant and causal. The most convenient scheme in RF are the scattering-parameters or
Figure 2.2: The directivity pattern from a λ/2-dipole at 300 MHz disturbed by an identical dipole at a distance of 2λ to the right. Generated by Antenna Toolbox in Matlab.
simply called s-parameters. The derivation is more convoluted than for other transfer matrices but the s-parameters are easier to measure, because they are ratios of voltages. Another benefit is the physical interpretation [7]. It relates the outgoing waves, bi, to the incoming waves, ai [10] where s11 can be interpreted as voltage reflection coefficient for waves arriving at port 1 while s21 as the voltage transfer coefficient from port 1 to port 2 [7]. See Equation (2.2) and Figure 2.3b.
b1 b2
=s11 s12
s21 s22
a1 a2
. (2.2)
The parameter s11 (and s22) are also known as the reflection coefficient, Γ or return loss but in this report s11is used. Ideally an antenna should have high efficiency, radiate a majority of the power delivered, and eliminate reflections to be stable. s12 (and s21) should also be low since low coupling is often desirable. The isolation and the efficiency, e, can be calculated from the complex s-parameters using Equation (2.3) and (2.4). The values of sij are dependent on antenna arrangement, frequency and the characteristic impedance, Z0, but they can also be tuned with so called impedance matching.
isolation = |s12|2 (2.3)
e = 1 − |s11|2 (2.4)
V1
I1 I2
+
V2 +
Text
(a)
Z0 Z0
a1 b1
a2 b2
(b)
Figure 2.3: (a) A two-port with voltages and currents. (b) Incoming, ai, and outgoing waves, bi, of the two-port where Z0 is characteristic impedance of the transmission line.
2.2.3 Impedance matching
Impedance matching is an important part of the design process of antennas and other electronic devises. Impedance is measured in ohm, Ω, and has a real part and a complex part which is formed by a resistance respective and a reactance component. For DC transmission the complex part is negligible but not for high frequencies as in a transmission line. When tuned incorrectly radio frequencies, RF, may be reflected in joints as the medium has different properties. A solution is to use impedance matching to minimize the reflection or to maximize the power transfer.
Voltage Standing Wave Ratio or VSWR is a way to measure how well matched an antenna and a transmission line are and it is a function of the return loss, or s11-parameter, see Equation (2.5). Usually the VSWR should be lower than three which correspond to a |s11|2-value of -6 dB, or an efficency of more than about 75 % [7].
VSWR = 1 + |s11|
1 − |s11| (2.5)
In impedance matching a matching network is placed between the transmission line and the port of the antenna. The transmission line is usually said to have a characteristic impedance, or Z0, of 50 Ω and the corresponding value of a λ/2-dipole antenna is 73 Ω. For example does a value of 50 + 0j Ω mean that the magnitude of the forward voltage wave at a certain cross section is 50 times higher than the current ditto. The phase shift, how much the current lags the voltage, is given by the the angle in the complex plane, which in this case is zero.
The voltage reflection coefficient of a junction is given by s11 = ab2
1|a2=0 = VV1oi 1
where V1i and V1o is forward and backward traveling voltage from port 1 seen in Figure 2.3. This ratio of voltages equals to ZZL−Z0
L+Z0 and from this one can see that the line is matched if Z0 = ZL, since the reflection is zero [7].
L-section impedance matching
One of the simplest method to achieve matching, if just a narrow bandwidth is required, is to use filters, for example the L-match circuit. It uses one inductor and one capacitor connecting the source and the load as seen in Figure 2.4, where the complex load and generator impedances are ZL= RL+ jXLand ZG= RG+ jXG. The figure shows both normal and reversed L-section, to be used under different conditions. A guideline is to use the normal for RG> RL and opposite
ZG jX2
ZL jX1
Zin
(a)
ZG jX2
ZL jX1
Zin
Text
(b)
Figure 2.4: (a) Normal and (b) reverse L-section matching networks.
for the reverse. The derivation below is for the normal case but the reversed result can be reached by exchanging ZL and ZG in Equation (2.7) [10].
The goal of the matching network in either form is to maximize the transferred power ie transform the load impedance into the complex conjugate of the generator impedance, see Equation (2.6), where Zin is the input impedance looking into the L-circuit and Z1 = jX1 and Z2 = jX2. The solution is shown in Equation (2.7).
(Zin= ZG∗ Zin= ZZ1(Z2+ZL)
1+Z2+ZL
(2.6)
X1= XGRG±RGQ
RL−1
X2= −(XL± RLQ) Q =
qRG
RL − 1 + RXG2
GRL
(2.7)
From X1,2the values of the capacitor and the inductor be calculated from Z1,2 = jX1,2 = jωC1 and Z1,2 = jX1,2 = jωL where ω = 2πf . The solution is shown in Equation (2.8)-(2.9). The values of X1 and X2 has different signs representing the two types of components. The negative one is used for the capacitor due to the negative phase shift, similarly the inductor’s sign is positive.
C = 1
−ωX1,2 (2.8)
L = X1,2
ω (2.9)
Cascaded two-port
Several two-port can be cascaded, for example the input matching circuit, the antenna itself and the output matching circuit. The following is a derivation for two cascaded two-ports but it can easily be expanded.
Equation (2.2) who related the input waves to the output can be rewritten as transmission parameters illustrating how one side of the circuit affecting the other, Equation (2.10). How to convert s-parameters into t-parameters are shown in [7], chapter 8.6.
b1 a1
=t11 t12 t21 t22
a2 b2
. (2.10)
If connecting two two-port after each other, the output port of the first equals the input port of the second, ie a(1)2 = b(2)1 and b(1)2 = a(2)1 , so the system can be rewritten as a sum of transmission matrices, as in Equation (2.11). The cascaded s-parameters are then obtained by re-converting the new t-matrix using [7].
"
b(1)1 a(1)1
#
=
"
t(1)11 t(1)12 t(1)21 t(1)22
# "
t(2)11 t(2)12 t(2)21 t(2)22
# "
a(2)2 b(2)2
#
. (2.11)
2.3 Signal, noise and interference
Signals measured at a receiver are often weak due to attenuation but since the receiver usually has a high amplification it is not a particular problem. What causes more problem is noise, interference and other disturbances [8]. In wireless communication SNR is an important param- eter. SNR stands for signal-to-noise ratio and is the power of the signal compared to the power of the noise. Similar quantities are SIR, signal-to-interference ratio and signal-to-interference- plus-noise ratio, SINR.
The received power is a function of the transmitted power, Pt, as well as the gain of transmit and receive antenna, Gt and Gr. The loss the signal suffers on its way is called the elementary path loss, Lb[8]. The noise power is often calculated as thermal noise, dependent on Boltzmann’s constant, k and the absolute temperature of the component, T . The total noise is measured over the bandwidth, B, and also includes F , which is locally generated noise and the noise factor of the receiver. The total SNR is therefore shown in Equation (2.12) [2].
SNR = Psignal
Pnoise = PtGtGr
LbkT0F B (2.12)
An ideal transmitter is just broadcasting in the intended frequency range but in reality the power is also leaking to the adjacent frequencies. The term sideband is used to describe how many channel to each side of the center frequency that are affected over a considerable level.
The level and spread of the disturbance is effected by modulation method, filtering and phase noise among others. This power can be measured in relation to the main frequency, commonly in dB and there are standards specifying requirements for different applications [2].
The SIR calculation is using the same function for signal power as SNR. The interfered power is also using the same form, as the interference is received power but from an unwanted source. The elementary path loss is however replaced with the isolation and the noise power is attenuated if the disturbing source is sending on a sideband. This can be simplified, see Equation (2.13), where Pd is the power of the transmitter which is disturbing.
SIR = Psignal Pinterference
=
PtGtGr
Lb
Pd·attenuation isolation
(2.13)
The SINR, Equation (2.14), gives the theoretical upper bound of the channel capacity since it captures both interference and noise. If no interference, the equation equals the SNR and the other way around. The lowest value of SNR or SIR is the one affecting the most.
SINR = Psignal
Pnoise+ Pinterference
= 1
1
SN R +SIR1 (2.14)
2.4 Frequency hopping system
A frequency hopping system uses techniques from both time and frequency multiplexing. The available bandwidth is divided into narrower channels and the time is divided into slots. For every time slot the transmitter changes frequency according to a predefined hop sequence also known by the receiver. Several transmitters can be active in the same frequency range and if the hopping sequences are chosen so the slots does not overlap, the system is orthogonal [8].
There are two main drawbacks of frequency hopping systems; the need for accurate time synchronisation and frequency selectivity. However the technique are resistant to disturbances.
In a Rayleigh fading environment where deeps nulls can occur locally at a single frequency, frequency hopping in combination with coding can decrease the errors as a missing part of a codeword are able to recover. In military communication systems the ability to withstand interference are of great importance both by intentional disturbance from an enemy or by unintentional interference from neighbouring platforms [8].
The probability of using the same frequency as another transmitter is a function of the number of frequencies available, nf, see Equation (2.15). The probability of using a frequency which are affected by the other transmitters sidebands is given in Equation (2.16) where s is the number of sidebands on one side of the center frequency of the interfering transmitter. The same probability but for orthogonal frequency hopping is given in Equation (2.17). All equations are for two transmitters and are motivated in Appendix A.
pcollision(nf) = 1
nf (2.15)
psideband,FH(nf, s) = (nf − 2s)2s + 2 ·P2s−1 i=s i
n2f (2.16)
psideband,O-FH(nf, s) = (nf − 2s)2s + 2 ·P2s−1 i=s i
(nf− 1)nf (2.17)
Chapter 3
Antenna setup
This chapter describes how the antenna data is generated in Matlab and how the properties of directivity, gain and s-parameters varies with distance. Some characteristic properties of the said antenna parameters are stored to be used in later models.
3.1 Preprocessing
3.1.1 Generate data
The Antenna Toolbox in Matlab is used to generate directivity and s-parameters. The toolbox uses the Method of moments to numerically calculate the antenna properties. Method of mo- ments was first introduced in antenna calculation by Harrington [11] and is nowadays a common method for antenna design [12]. It is a three-part method which first mesh the metal surface into rectangles, then create basis functions to calculate surface currents. The last step is to fill an interaction matrix by solving the integral equation obtained from Green’s function [13].
Two dipoles in free space are evaluated at various distances from each other, and for various frequencies. The settings are shown in Table 3.1.
Table 3.1: Parameter values used to create two dipoles.
Dipole length l = 0.5 m
Dipole width w = 0.01 m
Dipole distance 0.9 ≥ d ≥ 4 m Frequency range 240 ≥ f ≥ 350 MHz Characteristic impedance 50 Ω
Second dipole turned off
The second dipole is turned off when the directivity pattern and the s-parameters are gen- erated for all scenarios, even the ones where both antennas are assumed to transmit at the same time. The reason is that the setup in Matlab states that both antennas transmit the same signal, which is not what is wanted here. In such case, the lobes can be design with so called beamforming. In the used scenarios however is the directivity pattern shaped by the second dipole but just as a passive metal rod as its not transmitting the same signal.
3.1.2 Impedance matching
To perform impedance matching with L-circuit, a voltage divider with an inductor and a ca- pacitor is created with RF Toolbox according to Figure 2.4. The values of the components are obtained to match the dipole’s impedance at 300 MHz to a cable with characteristic impedance of 50 Ω. For that the reverse version of Equation (2.7) is used with ZL= 90.3498 + j43.6140 Ω and ZG = 50 Ω where the value of ZLis calculated with Matlab command impedance from An- tenna Toolbox. The solution are either X1 = 178.1149 and X2 = −55.4091 or X1 = −70.0251 and X2 = 55.4091 from Equation (2.7), but in this case the goal is to minimize the maximum s11-value for the whole frequency range not just the main frequency.
The combination of capacitance and inductance for which the maximum s11-value of the cascaded system are the lowest, still around the above calculated value, are for 658 pF and 4.84 µH. For said values the s11 is always lower than -6 dB as can be seen in Figure 3.1 where the s-parameters before and after matching are shown.
Figure 3.1: The s-parameters before and after matching.
3.2 Dependence of distance
The directivity pattern and the s-parameters are a result of the interference between the anten- nas which in turn is caused by the relative distance between the antennas and the wavelength.
In the following figures the dependence of distance is showed for the two dipole antennas from Table 3.1. Two cases are tested, one with a fix frequency of 300 MHz and one simulating a frequency hopping system with 23 frequencies uniformly distributed between 240 MHz and 350 MHz. The system with the fix frequency at 300 MHz illustrate the dependence of wavelength since the wavelength at that frequency is close to 1 m.
3.2.1 s-parameters
The variation of s-parameters for 300 MHz is shown in Figure 3.2. The s12-parameter, or the isolation, has the form of a damped sine wave with the period of λ/2. The s11-parameter, the internal reflection, has a linear decay in log-log scale.
For the frequency hopping case the oscillations in s11 are not as clear. The different fre- quencies has different wavelength and in extension different distances. The mean are hence smeared as seen in Figure 3.4. The standard deviation and the range are also shown in the figure, which shows a variation of more than 2 dB, which is huge compared to the oscillations for the single frequency case shown in Figure 3.2. For the s12-parameters the variations are more predictable. A higher frequency shifts the curve up, a direct result of the larger number of wavelength between the antennas.
Figure 3.2: s11 and s12 as a function of distance measured in wavelengths, for 300 MHz.
3.2.2 Directivity
The directivity pattern is generated before the impedance matching is inserted which means that there is a difference between the generated pattern where the dipoles are assumed to be in free space and the scenarios where the dipoles are connected to the impedance matching circuit and other cabling in free space. There is a limitation in Matlab behind this simplification. It may be a visible difference in the directivity pattern but the results is broadly the same. The difference lies probably in the extreme values of the pattern which cause a bigger spread in the statistical distribution.
The directivity for a single frequency is shown in Figure 3.3. The pattern is illustrated by the mean value, the standard deviation and the range in which the directivity varies. It can be seen that the mean values goes towards 2.15 dBi for larger distances which is the theoretic
value for a dipole in free space. The variations also disappear slowly for larger distances as the theoretic isolated dipole has an isotropic radiation pattern.
For the frequency hopping case the directivity pattern is shown in Figure 3.6. No major differences can be seen compared to the single frequency figure; the directivity pattern may vary a lot in terms of number of lobes and its directions but as a whole, its properties does not vary.
Figure 3.3: Directivity, D, as a function of distance for 300 MHz.
3.2.3 Data for statistic model
The curves in Figure 3.4-3.7 are used to estimate functions later used in the statistic model.
For directivity, s11 and s12 the mean values are used to create functions seen as a blue dotted line in the figures. From the gain, the difference between the 10 and 90 percentile are used to estimate the spread used in the statistic model. In Figure 3.7 the percentiles are shown as dotted black lines while the generated model is seen as a blue dotted line using the right hand side y axis. The functions are generated by the Matlab function fit and the estimated functions of all four estimated lines are shown in Equations (3.1)-(3.4). The equations are generated for 0.9 ≤ d ≤ 4 m and are hence valid for that range.
s11(d) = −25.58 · e0.05638·d+ 16.76 · e−0.8443·d (3.1)
s12= −7.0481 (3.2)
D(d) = 2.087 · e0.004709·d− 0.7521 · e−1.738·d (3.3) spread(d) = 21.78 · e−2.025·d+ 5.746 · e−0.2376·d (3.4)
Figure 3.4: s11 as a function of distance for a frequency hopping system.
Figure 3.5: s12 as a function of distance for a frequency hopping system.
Figure 3.6: Directivity, D, as a function of distance for a frequency hopping system.
Figure 3.7: Gain, G, as a function of distance for a frequency hopping system on the left side axis and estimated spread, the difference between the 10 and 90 percentiles used in the statistic model, on the right axis.
Chapter 4
The model
4.1 Simulation setup
The scenario described in Section 1.3 is implemented with values from Table 3.1 and 4.1. It is calculating SNR from Equation (2.12) based on conditions such as transmitted power, ele- mentary path loss and bandwidth. If needed, SIR and SINR is also calculated from Equation (2.13) and (2.14). SINR is now an antenna dependent parameter since it includes directivity, efficiency and isolation.
The model is based on a Monte Carlo method which means it uses stochastic numbers multiple times to get a statistical idea of the behaviour. First, one direction out of 360 is randomized then two random frequencies are obtained. The frequencies can be fixed at 300 MHz or be random either in discrete or continues step within the range 240 MHz to 350 MHz.
Two types of frequency hopping systems are inserted, orthogonal or non-orthogonal with the simple difference that orthogonal does not allow the two antennas to use the same frequency which eliminate direct hits.
The model can handle cases when there is no collision which means the other antenna on the same platform is not broadcasting or is on a well separated frequency. In that case SIR is not included, ie is infinite. In case of collisions there are different types; collision with a sideband or a direct hit. The sidebands has an attenuation of 80 dB and a direct hit has 0 dB which are inserted in Equation (2.13) to calculate SIR. The spectrum model with attenuation of 80 dB is used and motivated in [2]. The region for which a sideband collision occurs is set to 25 MHz on both sides of the main frequency, which is just a hypothetical value who can be changed.
Table 4.1: Parameter values used in the model.
Transmitting power Pt= 50 W
Transmitting power of disturbance source Pd= 50 W
Bandwidth B = 1 MHz
Noise spectral density kT0 = −204 dBW/Hz
Noise factor F = 17 dB
Elementary path loss Lb = 0 dB
Sideband range, one side fs= 25 MHz
4.2 Antenna models
Three different antenna models are implemented, all using its own values for directivity and s-parameters. One using data generated by Matlab, one using an isotropic model, and one model tries to mimic the behaviour of the system, and still be simple. All models except the latter uses Monte Carlo simulations.
4.2.1 Matlab model
This model is using data generated from the Antenna Toolbox for the settings in Table 3.1.This model is assumed to be correct, but as simplified as its input data. To obtain frequencies in between the generated frequencies with spacing 5 MHz, interpolation is used.
4.2.2 Previously used models - isotropic
The simplest possible model is to set the gains, Gtand Grin Equation (2.12) to 0 dB. A slightly more advanced model is to assume efficiency of one and an isotope radiation pattern which for a dipole has a directivity of 2.15 dBi. Both is used here together with a constant isolation of -25 dB. The former is used for comparison as it symbols the system where the antenna is completely removed.
4.2.3 Statistic model
This model is using the adapted functions for directivity, s11, s12and spread of the distribution from Equation (3.1)-(3.4). Each parameter is a constant for each distance between the antennas.
These parameters are used together with the elementary path loss and the SNR to calculate the decrease in SINR for the different scenarios. It calculates the theoretical probabilities of collisions from Equation (2.15)-(2.17) and uses the spread to mimic the randomness in the antenna and the platform. The random values of gain are assumed to be uniformly distributed within the range, in other words, the slope of a cumulated distribution function is here constant.
Some example of analytical collision probability for a direct hit and for collisions with sidebands for both orthogonal and non-orthogonal frequency hopping are show in Table 4.2. All values are for a bandwidth of 1 MHz within the range of 110 MHz and for 25 MHz sidebands.
The difference is the separation of channels, either 1, 5 or 10 MHz. For example allows a separation of 5 MHz a total of 22 different bands within the range, where 5 channels on each side are regarded as sidebands. The separation of channels used in the report are 5 MHz.
Table 4.2: Analytical collision probabilities for different separation of frequency bands within the 110 MHz range. The bandwidth is 1 MHz and the sideband reach 25 MHz from the main frequency.
Channel separation 1 MHz 5 MHz 10 MHz
Direct hit 0.90 % 4.35 % 8.33 %
Sideband collision, orthogonal frequency hopping 40.13 % 39.53 % 31.82 % Sideband collision, frequency hopping 39.77 % 37.81 % 29.17 %
Chapter 5
Comparison of models
5.1 Overview
Three different scenarios are tested: orthogonal and non-orthogonal frequency hopping as well as a case without collisions. All three can be seen in Figure 5.1 where the Matlab generated data are compared. The figure shows the probability of different SINR-values. For example is the probability of having a SINR higher than 120 dB around 60 % and 58 % for the frequency hopping scenarios but as much as 100 % without collisions. The reason for the high SINR-values on the x-axis are that the elementary path loss, Lb, is omitted from the calculations. The SNR value without antenna and interference is 144.0 dB.
Figure 5.1: Matlab generated data for the three cases.
5.2 Probability comparisons
These three scenarios can in turn also be seen in Figure 5.2-5.4 where the Matlab model is compared to the isotropic and statistic models when the distance between the dipoles are 2 m.
Figure 5.2: Comparison of the different models for a scenario without collisions.
Figure 5.3: Comparison of the different models for a scenario with orthogonal frequency hopping.
Figure 5.4: Comparison of the different models for a scenario with frequency hopping.
5.3 Dependence of distance
The Figures 5.5-5.7 illustrate how the 99, 95 and 50 percentiles from Section 5.2 are moving as the distance between the dipoles are changed. The solid lines symbols the 50 percentile while the dashed and dashed-dotted lines illustrate the 95 and 99 percentile respectively.
Figure 5.5: How the 50 (solid line), 95 (dashed) and 99 percentile (dash-dotted) changes for different distances between the dipoles for the case without collisions.
Figure 5.6: How the 50 (solid line), 95 (dashed) and 99 percentile (dash-dotted) changes for different distances between the dipole for the case with an orthogonal frequency hopping system.
Figure 5.7: How the 50 (solid line), 95 (dashed) and 99 percentile (dash-dotted) changes for different distances between the dipole for the case with a frequency hopping system.
Chapter 6
Discussion
The impact of the antenna, seen as a system component integrated on a platform for frequency hopping radio links is something which is not well investigated. It is however of great interest as the antenna is an important part and can affect the throughput significantly if poorly integrated on the platform. The model used in this report is very simplified but can still give an insight of its behaviour, even though its values and figures should not be used as truth, just guidelines, for future projects.
The questions that will be discussed below are,
• How the radiolink performance is affected by the antenna in frequency hopping systems.
• How good the frequently used isotopic antenna model is.
• If it is possible to create a simple model to mimic the statistical performance of the antenna.
as well as the models reliability and when and how it can be used. The delimitations taken into account when creating the model is discussed and ideas for future extensions are given.
6.1 Discussion of models
6.1.1 Matlab model
• How the radiolink performance is affected by the antenna in frequency hopping systems.
Both the internal reflection, the isolation and the directivity is affecting the SINR-value in this model. This simplified case has just two dipole antennas in free space but the values are affected by the number of wavelength between the antennas and, for the directivity, also by the direction. For a frequency hopping system, this leads to a complex model in which the frequency and hence also the number of wavelengths between the antennas, changes constantly.
Impedance matching is used in this report to lower the highest s11 parameter to a value below -6 dB, to be more realistic but it is also a factor affecting the performance. The report has showed that s11, s12 and directivity are all important in determining the SINR. Another type of impedance matching may lower s11and s12with several dB which of course will have a impact on the end results.
Another important aspect of the model is the impact of several frequency hopping systems on the same platform. The probability that two systems simultaneously uses the same frequency is a function of the available hopping frequencies and the SINR decreases significantly for frequency
collisions. Even collision with a sideband affect the SINR. In this cases the sidebands are modelled with a simple model where all sideband has a attenuation of -80 dB. This is also an unrealistic simplification but it shows the general trend.
The parameters which affects the antenna are internal reflection, isolation and directivity pattern. Both the internal reflection and the directivity affect the antenna gain which causes a spread of SINR of around 4 dB in this case. To know about this spread may be important as the worst percentiles is relevant when calculating which throughput that can be guaranteed.
Every decibel of isolations increase the SINR by one decibel for the collisions and is hence also relevant.
The choice of orthogonal and non-orthogonal frequency hopping and how many hopping frequencies are parameters which affect the throughput even more according to this simplified model. Important is the spectrum and how the attenuation of neighbouring frequencies increase.
This model is realistic for the scenarios described as Matlab uses Method of Moments which in general gives accurate results. What is not realistic are the simplifications such antenna setup, spectrum model or parameter values and the model is not better than its settings. The antenna calculation complexity increase however for additional features as antennas and groundplane and it may lead to timeconsuming calculations. Generally it can be assumed that more complex input data causes a larger spread.
6.1.2 Isotropic model
• How good the frequently used isotopic antenna model is.
The two isotropic antenna models, the with gain of one and with gain of 2.15 dBi, are enclosing the Matlab generated gain distribution as seen in Figure 5.2 where the former model has a SNR of 144.0 dB and the latter 148.3 dB. Not regarding the antenna at all produce an average SNR of around 2 dB lower than the Matlab generated and the optimistic model with gain of 2.15 dBi produces in turn a higher SNR. Both models are wrong in aspect of distribution and mean value compared to the Matlab model. The variation of around 4 dB is not included and even if the mean value are correct, the true model can result in lower throughput than predicted due to the spread. The isotropic model does not either take into account that the distance between the dipole can change. From Figures 5.5-5.7 it can be seen that the difference between the Matlab model and the isotropic model varies with distance.
Disregarding the lack of spread, both isotropic models are relatively good, at least when compared to its complexity. It can be used to see effect from frequency hopping and visualise how actions affect the system.
6.1.3 Statistical model
• If it is possible to create a simple model to mimic the statistical performance of the antenna.
A very simple model was created from the mean value of directivity, s11, s12 and from the spread of the gain. This model show promising results as it mimics the spread of the antenna is a way the isotropic model can not. It is also able to capture the behaviour as the distance between the antennas are changed in a way the isotropic models is not. Another benefit of the model is that it can be used to predict the impact from the antenna in the scenarios without having to do any time consuming Monte Carlo loops of calculations. It is promising that just four estimated constants can be used to calculate the behaviour of the antenna in the tried scenarios, and even mimic the distance dependent relationship. What should be remembered
is that the Matlab data was used to obtain the constants so the conformity cannot be fairly analysed.
Useful in this model is also the theoretical probability of collision with sideband for frequency hopping systems. Previously used models, for example in [2], was using a simplified model who did not regard probability of hitting a sideband of an edge frequency. The model in this report is theoretically correct for this simplified model, and it can with minor work be used in future reports.
6.2 Discussion of method
The antenna setup in this model with two identical dipole antennas in free space, is an unreal case. Also the spectrum model, the values of the antenna parameters which is assumptions and the Monte Carlo model where the platforms are changing direction randomly for every frequency hop. Neither of this is very realistic but it is a first step to create a model which can be expanded.
It is also a way to identify the most important antenna properties for radio communication.
The same applies for coding, electromagnetical properties, fading or non-Gaussian noise, which is not discussed.
6.3 Future work
In this thesis project the most simple model is used as proof of concept. No actual values are used as antenna size, shape, setup nor as frequency range, spectrum model or other parameters.
The values are realistic but are assumptions or simplifications. The next step would be to use realistic values. It would be interesting to see the agreement between measurements of directivity and the Matlab model as the measurement are difficult of obtain, but relatively simple to calculate in Matlab. The s-parameters are easier to measure and maybe the measured values can be used in later models together with an assumed spread to increase the conformity.
Chapter 7
Conclusion
In this degree project some antenna parameters are inserted into a Matlab model to evaluate the impact of the antenna in a frequency hopping system. The model is simple but still shows that it is possible to create a model from Antenna Toolbox data. It also shows general trends such as how the directivity and s-parameters affect the system.
The two isotropic models often used are simple but has a quite good conformity. A created statistical model shows that only a few properties is needed to mimic the statistical behaviour of the antenna to a certain degree. This comparison is done relative to the Matlab data, which was used to create the model, so the model should be used with care but the created model is likely better than the isotropic models as it includes the statistic spread and also follows the dipole distance dependence. This model can be used as a first model to test other design parameters.
The next step would be to adapt for real scenarios with for example other spectrum models, real s-parameters or actual system parameters. A comparison with real measurement is also desired. If the Matlab model can be expanded so that the conformity with real measurement is good, the simulation can be used instead which saves resources.
Bibliography
[1] S. ¨O. Tengstrand, P. Eliardsson, E. Axell, B. Johansson, K. Wiklundh, Methods for Valuation of Measures that Increase Robustness of Wireless Communication Systems. Technical Report FOI-R–4302–SE, FOI, 2016.
[2] K. Fors and S. Linder, Konsekvenser av interferensmilj¨on vid samgruppering av frekven- shoppande radiosystem, FOI-R–4318–SE, FOI, 2016.
[3] T. Lindgren, Simulation of the performance of communication antenna systems integrated on platforms. Technical Report FOI-R–4221–SE, FOI, 2016.
[4] J. G. Proakis, Digital Communication, McGraw-Hill Book Company, USA, 1989.
[5] J. D. Kraus, R. J. Marhefka, Antennas For All Applications, McGraw-Hill Higher Education, 2002.
[6] S. R. Saunders, Antennas and Propagation for Wireless Communication Systems, Wiley, Chinchester, 1999.
[7] S. W. Ellington, Radio Systems Engineering, Cambridge University Press, 2016.
[8] L. Ahlin, J. Zander, Principles of Wireless Communications, Studentlitteratur AB, Lund, Sweden, 1998.
[9] D. M. Pozar, Microwave Engineering, Wiley, 2011.
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[11] R. F. Harringhton, Field Computation by Moment Methods, New York: Macmillan, 1968.
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[13] Matlab documentation, Method of Moments Solver for Metal Structures https://se.mathworks.com/help/antenna/ug/method-of-moments.html, October 2018.
Appendix A
Motivation of collision probabilities
A.1 Probability for direct hit
The probability of a direct hit is a function of the number of frequencies, nf. The terms in the sum of Equation (A.1) are the probability of transmitter A respective B choosing frequency fi, ie a collision happen. A collision can occur at all available frequencies hence the sum.
pcollision(nf) =
nf
X
i=1
p(fi,A) · p(fi,B) =
nf
X
i=1
1 nf · 1
nf = nf · 1 nf · 1
nf = 1
nf (A.1)
A.2 Probability for collision with a sideband in non-orthogonal frequency hopping systems
The risk of colliding with a sideband is different for different frequencies. For the first and last frequency in the range, f1 and fnf, the number of sidebands, ns, are s while for the central frequencies, s + 1 ≤ i ≤ nf − s, the number is 2s. The other frequencies are stepped between the extrema as seen in Equation (A.2).
ns(fi) =
i + s − 1, 1 ≤ i ≤ s
2s, s + 1 ≤ i ≤ nf − s nf − i + s, nf − s + 1 ≤ i ≤ nf
(A.2)
The probability of colliding with a sideband in a frequency hopping system is hence shown in Equation (A.3) where p(fi,A) is the probability of transmitter A choosing frequency fi.
psideband,FH(nf, s) =
nf
X
i=1
p(fi,A) ·ns(fi) nf
= 1 n2f
nf
X
i=1
ns(fi)
= 1 n2f
s
X
i=1
i + s − 1 +
nf−s
X
i=s+1
2s +
nf
X
i=nf−s+1
nf − i + s
= (nf− 2s) · 2s + 2 ·P2s−1 i=s i
n2f (A.3)
A.3 Probability for collision with a sideband in orthogonal fre- quency hopping systems
The argument is the same for an orthogonal frequency hopping system as for the non-orthogonal system in section A.2 with the difference that the available frequencies for transmitter B now are n − 1, see Equation (A.4).
psideband,O-FH(nf, s) =
nf
X
i=1
p(fi,A) · ns(fi) nf − 1
= (nf − 2s)2s + 2 ·P2s−1 i=s i
(nf− 1)nf (A.4)
