Signals Of Opportunity System With Two Receivers Computer Science Essay

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Signals of Opportunity are highly efficient and effective alternative for the Global Positioning System (GPS). The SOP system helps navigation by precisely measuring the time difference between the signals arriving at two points, namely base station and mobile unit. The principal difficulty involved in establishing the SOP is the time and cost required for setting up the base stations. The paper proposes a novel approach for the SOP system, which equips the mobile unit with two receivers and eliminating the base station. The Novel SOP approach is shown to be more efficient than the conventional method.

The Global Positioning System (GPS) is a widely used navigation system that provides accurate positioning with a high degree of reliability [1]. The GPS system, equipped with 24-32 satellites in the higher earth orbits positions at least three to four satellites monitor any location on the earth at any instant of time. The GPS module being compact and highly efficient has found market share in both the Military and Civilian domains. The primary Military application of the GPS is to help the soldiers identify their location in unknown territories. Other applications include Target tracking, Missile and Projectile Guidance, Search and Rescue, Reconnaissance and Map Creation. The Military investment on the GPS program is enormous. The U.S Department of Defense (DoD) estimated that so far $8 billion have been spent in the GPS program and the investment in this program may rise to $ 22 billion by the year 2016 [2]. Though the GPS was initially designed for Military use, it has found many applications in the civilian domain. The civilian applications include vehicle routing and navigation providing service as a surveying tool. It is estimated that the complete market value of the GPS by the year 2013 will be $ 75 billion. However, the GPS system is facing some threats. Advances in missile technology have enabled them to destroy long range targets. Thus GPS system has become vulnerable to such attacks. Under such an attack scenario, the entire investment on the GPS program will go waste. GPS being a very complex system, the time required to set up a new system to replace the existing one will be prohibitive and very expensive and its replacement cost will exceed the total investment which has already been made in the system. Thus the destruction of GPS system can play havoc for the civilian and military applications, installations and equipment. Therefore, it is very pertinent for national security and civilian communication to have an alternative to GPS system. Many researchers actively contributed to this area to find an alternative to the GPS system. One of the highly effective techniques found is that the normal radio waves used for TV, cellular or any other kind of applications can also be used for navigation. Signals of Opportunity use such signals, which use Time Difference Of Arrival (TDOA) to provide navigation.

Time Difference Of Arrival Systems

The TDOA system, as the name suggests uses the difference of the signals in time at two locations, one: whose position is known and the other: unknown, to find the location of the unknown point. The basic principle involved is that when the difference of arrival of the same signal at two locations is known, then the position of one of the location can be found, if the position of the other location and the position of the source are known. There are two possible ways of achieving such a system.

When two transmitters, whose locations are known, transmit the same signal at the same time, then based on the TDOA of these two signals at the unknown point, its position can be determined.

A single transmitter transmitting the signal, received by two receivers, one in known location and other in unknown position.

The former method is difficult to implement as the two transmitters have to be synchronized in time. The receivers can be more easily synchronized and hence most of the TDOA systems including SOP system use the second approach.

Signals of Opportunity

A Signal of Opportunity (SOP) system has the following advantages making it potentially more powerful:

Availability: SOP signals can be anything right from AM signal to a Digital TV signal. So there is no lack of availability of signal resources for an SOP system [3].

Flexibility of Choice: In general any populated area has a spectrum of signals ranging from simple telecast signals to highly encrypted data signals. The reason that SOP can operate on any signal gives the system a choice to select any of these signals for navigation and this choice gives flexibility and scope for improvement [4].

Tolerable to timing errors: In a GPS system, the distance between the GPS satellite and the Receiver (RX) is so large that even a time synchronization error of a micro second may lead to a positional error of hundreds of meters. In SOP system, the transmitter and receiver are not separated by more than a few kilometers; therefore, small timing errors do not affect the performance of the system to a great extent [5].

Cost effective: The SOP system uses existing signal infrastructure in an area and thus minimizes the cost.

Performance: It has performance comparable to GPS based Navigation Systems.


Transmitter: Multiple Transmitters are required for proper functioning of the system. The SOP transmitter can be any existing signal source in an area, provided that the receivers are capable of processing the signal properties like frequency, modulation and power.

For a simple SOP system, the transmitter is expected to avoid considerable deviation in frequency of the carriers. If the deviations are considerable in comparison to the intended carrier frequency, difficulties arise for the receiver to lock on to the signal. For using such signals for the purpose of navigation requires redundant signal processing equipment centered at different frequencies. Frequency Modulated waves (FM) cannot be considered as such signals as the deviation of the FM waves are kept low as compared to the signal carrier frequency to minimize the bandwidth required for the signal. The signals generated using the spread spectrum techniques can be classified into this category as the carrier frequency is switched rapidly within a given bandwidth.

The height of the transmitter is a crucial factor in urban areas. The height of the transmitter ensures that the signals have a direct line of sight with the receivers ensuring minimum signal to noise ratio (SNR) by aiding the signals in clearing the human made structures. The transmitter with poor height forces the SOP receiver to switch to other sources, even though the transmitter possesses good navigational properties. The height of the transmitter also provides additional gain to the signals increasing the geographical range within which the signals can be used for navigation.

Base/ Reference receiver: The base or reference receiver is used for providing a reference signal for time difference of arrival calculation at the mobile receiver.

The base receiver is positioned in such a way to avoid all the human structure interferences and minimize any kind of atmospheric turbulences. The base receiver's important attributes are antenna specifications, transmission bandwidth and power source. The antenna used is generally Omni-directional since it incorporates new transmission towers that can be set up in the near future. The antenna is preferred to have high sensitivity as it allows margin for additional noise effects. The transmission link which is used for communication with the mobile receiver, during the set up must be given a bandwidth that is not interfering with any of the transmitting sources in the vicinity. However, installation of new transmission sources with overlapping bandwidth in the future can cause problems to the transmission link. To avoid such issues, the data being transmitted must be encoded so that the mobile receiver can extract the data signal from other interfering signals. In Military applications, the transmission link in enemy territories is preferred to have overlapping bandwidth with a high power transmission source, as the presence of base receiver will be unnoticed. The power source is very critical component for the base receiver as the signal processing equipment and the transmission is entirely dependent on it. For commercial applications, low maintenance power sources like solar power sources are highly beneficial as they are highly scalable to meet the increasing power requirements.

Mobile Receiver: This block constitute the User whose position is to be determined. The Mobile unit can be either equipped with an Omni directional antenna or a set of directional antennas, with higher sensitivities. The locations of the SOP Transmitters and the Base Receiver are determined by surveying and constitute the apriori knowledge which is stored in the memory of the system. The SOP system calculates the relative position of the User or Mobile Receiver with respect to the SOP Transmitters and the Base Receiver and then integrates them with the stored data to know the actual position of the mobile receiver.

The hardware required for the mobile receiver system and the base receiver system is sophisticated. The receiver system should have a highly sensitive Omni-directional antenna that could receive weakest signals. The antenna system for the mobile system has to be more sensitive than the antenna of the base station. The locations of the all the transmitters with respect to the base station are known and hence a proper antenna system for the base station can be installed. The antenna system and the receiver systems have to be equipped with the ability to process a wide range of frequencies. This requires large number of processing elements for various spectrums, increasing the complexity of the hardware. The alternate cost effective is to use a computer simulator, that generates the received signals in simulations and all the processing is done. The GNU radio is one such example of the simulator.


A simple SOP system has two transmitters and a stationary base receiver to locate the position of the mobile receiver (assuming its altitude is zero). Fig. 1 shows the general Mobile network model.

The location of the Transmitters 1 and 2 and the position of the base receiver is known (and is stored in the mobile unit), using which the mobile unit has to figure out its location.

Fig 1: Mobile Network Model

Assume that the Mobile unit is closer to the transmitter 1 than the base receiver. When the transmitter starts to transmit the signals, because of the closer vicinity, the Mobile Unit receives the signals first when compared to the base receiver [5, 6]. Let the delay of the signal taken to reach the base receiver, when compared to the mobile unit be δ. Fig. 2 shows the Range of the Base station and Mobile Unit from the transmitter. Let r1 and r2 be the radius associated with the base receiver and Mobile Unit with Transmitter 1 as the center.

Thus, radial difference between base receiver and Mobile Unit with Transmitter 1 as the center= r2-r1 = δ*c

c=velocity of light.

Thus, As the radius r2 (distance between Transmitter 1 and Base Receiver is Known), the distance between Transmitter 1 and Mobile Unit is r1=r2- δ*c.

Using r1, we can plot the range hyperboles which indicate the points where the Mobile Unit can be present with respect to Transmitter 1. Fig. 3 shows the Range hyperboles of the Transmitter 1 to the Mobile Unit

Fig 2: Mobile Unit Network: Range of the Base station and Mobile Unit

Using the Same Concept, we plot range hyperboles of the Mobile Unit w.r.t the Transmitter 2. The point where both the range hyperboles intersect is the location of the Mobile Unit. Fig. 4 shows the intersection of range hyperboles to locate the Mobile Unit.

Fig 3: Mobile Unit Network: Range hyperboles of the Transmitter 1

Therefore, δ can be estimated as


t1=clock time of the Mobile Unit

t2=clock time of the Base Receiver.

Fig 4: Mobile Unit Network: Location of Mobile unit

If δ>0, then the Mobile Unit received the signals later than the base receiver

If δ<0, the Mobile Unit received signals earlier than the base receiver.

However, synchronizing the Mobile Unit Clock and the base receiver clock is extremely critical. Even though, the clocks are synchronized to perfection, this approach has another principal disadvantage. In this approach, we assumed that the transmitter started its transmission, once the Mobile Unit is in its Vicinity. In real scenario, the transmitter would have been transmitting the signals which are all received by the base receiver, even before the Mobile Unit is in its vicinity. Since the base receiver is receiving signals at all clock times, how can the Mobile Unit identify what is the base receiver's clock time with which it has to compare its own clock time.

To avoid such confusion, there is an alternate approach: convolution of signals [7]. Convolution of two signals here is used to compare the similarities of the two received signals.

The conventional SOP system has the following limitations:

The base Receiver has to be a fixed station. So, one can only use this navigational technique when a base station is installed in an area making the system expensive.

Different signals have different navigational properties. For instance, Digital Television signals have been delivering high accuracy for the Indoor Positioning, while AM signals are highly effective in open areas or rural areas. So the SOP system has to screen all the available signals present in the area to narrow down on the signal with the highest navigational potential. This is computationally very expensive and time consuming.

The signal path from the transmitter to the base receiver is different from the signal path from the same transmitter to the mobile receiver. These two paths may pass through different environmental conditions and thus experience different noise distortions (the noise spectral densities of the two paths are not the same). The SOP system has to properly accommodate for these noise effects in both these paths for accurate results.

In the Military scenario, there is a lot of importance for navigation when the army is in the enemy territory. It is very difficult to collect any information regarding the transmitter stations in that enemy zone. However, even if the information is attained, it is highly impossible to install large number of base stations in the enemy land and also if installed, it is highly impossible to maintain the base stations.

Improved Signals of Opportunity Systems

The stationary base receiver is eliminated and a second receiver is embedded in the mobile unit. This approach does not compromise on the performance and elimination of the base receiver makes the system portable [6].

This approach has the following characteristics:

1. Since the rover has both the receivers, the noise spectral densities of the received signals are same. Therefore, even when the Signal to Noise Ratio (SNR) is less, the correlation of the two received signals can be used to extract the time delay with minimum error.

The noise spectral densities are used to estimate the amount of noise in a given environment or in a given signal path. Since both the receivers experience similar environment, the noise spectral densities affecting both the received signals are similar and hence, the correlation has minimum error due to noise.

2. The complexity to implement the proposed architecture in hardware will be extremely complex as the hardware will be required to detect timing resolutions of the order of nano seconds. Therefore, the use of software radio to simulate the proposed SOP signals will be very efficient.

Mathematical Validity of the Proposed Approach:

Fig. 5: Proposed Architecture of SOP with Two Mobile Receivers

Fig. 6: 2D Geometrical Representation of Proposed SOP Architecture with Two Mobile Receivers

In this section we illustrate the feasibility of the proposed approach mathematically. Fig. 5 shows the architecture of the proposed SOP system with two mobile receivers. The fixed receiver has been replaced with the mobile receiver. Thus there are two mobile receivers in the mobile unit.

Fig. 6 represents the geometrical representation of the proposed SOP architecture illustrating the distances between transmitter and receiver and the angle of arrival. A represents the transmitter and C and D are the two mobile receivers. AE is the height of the transmitter. ED is the distance between transmitter and mobile receiver. CD is the distance between the two receivers. X is the additional distance travelled by the delayed signal, θ is the angle of arrival.

AE = h = Height of the transmitter

θ = Angle of arrival.

ED = d = Distance between the transmitter and the mobile receiver

CD = x = Distance between the two mobile receivers

X = additional distance travelled by the delayed signal.

Y = signal path from the transmitter to the receiver C.

AD = t = signal path from the transmitter to the receiver D.

AD = y = signal path from the transmitter to the receiver C.

Initially, when the transmitter transmits the signal, it is received at different instances of time by the two mobile receivers. Since, the location of both the receivers is unknown, a direct application of TDOA does not provide a solution. Therefore, the Angle of Arrival (AOA) of the transmitted signal is calculated. Using the angle of arrival, the three dimensional SOP structure is transformed into a two dimensional model to reduce the computational complexity. Then by, mathematical analysis, the distance between the transmitter and mobile unit d is calculated.

Angle of Arrival calculation based on triangulation and correlation of received signals. The advantage with this approach is that the synchronization between the receiver clocks is not necessary, which reduces the complexity of the hardware circuitry and saves a great deal of computation time. When the signal from the given transmitter is received by both the receivers in the mobile unit, the time delay between the two received signals is calculated by using the correlation function [7]. The correlation of the two signals reveals the phase difference between them. Using this phase delay, the angle of arrival of the signal is calculated. By using this time delay, the additional distance travelled by the delayed signal is calculated, which is assumed as the distance between the two receivers. This additional distance travelled by the delayed signal is assumed to be the distance between the two mobile receivers. The reason for this is that, if this assumption is not made, the geometry of the transmitter and the two mobile receivers will become a three dimensional in structure which becomes too complex to solve. This assumption converts the three dimensional geometry to a two dimensional one simplifying the problem.

As shown in Fig. 6, Height h of the transmitter can be expresssed by equation 1.

h=(d+x) cotθ ………… …………(1)

Squaring equation 1 on both the sides,

h2=(d+x)2cot2 θ ………………….(2)

From triangle AEC,


Substituting the above equation h in equation 2 ,

y2-(d+x)2=(d+x)2cot2 θ ……….....(3)

Thus the distance from the transmitter to the mobile receiver C is given by equation 4.

y2=(d+x)2(1+cot2 θ)……………….(4)

In Fig. 6, AD (represented as t) and AC (represented as y) are the respective paths of the signals transmitted from the transmitter to the mobile receivers. BD is the perpendicular drawn from D (one of the mobile receiver) to AC.

y=y1+xsin θ

y= (d2+h2-x2cos2θ) 1/2+xsin θ …………………………..… .(5)

y2= ((d2+h2-x2cos2 θ) 1/2+xsin θ)2 …………………….. (6)

(d+x) 2(1+cot2 θ) = d2+h2-x2cos2 θ + x2sin2 θ +2xsin θ (d2+h2-x2cos2 θ) 1/2……………………………………………………. (7)

substituting (2) in (7)

d2+ d2 cot2 θ+ x2+ x2 cot2 θ+2dx+2dx cot2 θ= d2+(d+x)2cot2 θ+ x2sin2 θ +2xsin θ (d2+ (d+x)2cot2 θ - x2cos2 θ) 1/2 …… (8)

x2(1- sin2 θ )+ 2dx(1+cot2 θ)= 2xsin θ (d2+ (d+x)2cot2 θ - x2cos2 θ) 1/2

x2(cos2 θ )+ 2dx(1+cot2 θ)= 2xsin θ (d2+ (d+x)2cot2 θ - x2cos2 θ) 1/2

The quadratic equation is solved to obtain the distance d of the mobile unit from the transmitter.

Mobile Environment

The Langley Rice propagation model is used as a propagation model in the simulations as it is specifically intended for the frequency range of 20 MHz to 40 GHz. Alternatively known as ITU Irregular Terrain Model (ITU-ITR), it estimates the median signal loss of a radio wave in a radio environment. The model is tested for a signal range of 2000 Km and for antenna heights between 0.5 m to 3000 m. The two variations of the Langley Rice model include the area predictions and point to point predictions [8].

The Langley rice model does not implicitly specify the transmitter and receiver; it describes the signal relationship between two terminals, either terminal capable of being designated as a transmitter or a receiver. The model considers factors like effective earth radius, conductivity of the surface , the effective antenna heights and the interdecile range define the irregularities of the terrain. The interdecile range compensates the effective height of the particular area based on its nature. The incorporation of this factor allows for the area to be viewed as a plain smooth surface. The model also accommodates diffraction losses.


The entire geographical area is assumed to be in a x-y coordinate axes. The distance of one unit in the xy axes corresponds to 0.1 km in the real world. The base transmitter is assumed to be at the origin (0, 0). The Mobile Unit is assumed at the coordinates (4, 4). For, the conventional SOP system, the base receiver is stationed at the coordinated (10, 10). For the Improvised SOP system, the second receiver (which is also present in the Mobile unit) is positioned at coordinates (4.004, 4.004). The simulation produces two signals in each model, one signal at each receiver. These two signals are correlated to estimate the distance of the Mobile Unit from the transmitter.

Fig 7: Correlation in noiseless environment

The Mobile Unit is assumed to be travelling at a speed of 40 km/h in the direction of the transmitter. Fig. 7 shows the correlation in noiseless environment. In a noiseless environment, the correlation maximum occurs at shift of 3001 instances and it accounts to the distance 0.5659 km.

Fig 8: Correlation in noisy environment for conventional SOP system

In the conventional SOP system, the signal received at the base receiver is transmitted again to the Mobile unit in the noisy environment; hence the correlation between the two signals will be distorted. Fig. 8 shows the correlation in noisy environment for conventional SOP system. The correlation maximum is achieved at shift of 3241 samples, and the Mobile unit is indicated to be at a distance of 0.54685 km.

In the improved SOP system, the Mobile Unit has the both the receivers and hence the signal environment is approximately the same for both the signals and hence the correlation is smoother than the conventional SOP system. Fig 10 shows the correlation in noisy environment for improved SOP system.

The correlation peak is attained at 2959 samples, which translates to a distance of 0.57762 km.

Fig 9: Correlation in noisy environment for improved SOP system.

Table 1. Comparison of conventional and Improved SOP systems


Distance of the Mobile Unit (Km

Error in positioning (km)

Conventional SOP system



Improved SOP system



Table 1 shows the comparison of both the techniques. The conventional SOP system has an error of 18 meters with respect to the actual Mobile Unit positioning, while the improved SOP system has a position error of 11 meters and is thus 38.88 % more efficient than the conventional SOP system.