Justification of tactical and technical requirements for radio signal detection systems.

Kargashin Viktor Leonidovich
Candidate of Technical Sciences

Justification of tactical and technical requirements for radio signal detection systems

The stability over time of the established indicators of protection of the allocated premises requires continuous monitoring of the radio technical environment aimed at detecting sources of radio signals located in the protected premises. Such sources may be technical means of processing and accumulating information installed in the premises that have changed their parameters, or radio technical means that have been unauthorizedly brought into the premises. At present, radio signal monitoring and detection systems based on scanning radio receivers and providing monitoring of radio signals in several protected premises are proposed to solve such problems. The integral efficiency of such systems is determined not only by the technical parameters of the radio receivers, antennas, switches and other components of the systems, but also by the properties of the allocated premises and the radio technical environment in the region where the protected object is located. As a rule, the sensitivity of the radio receivers used is sufficient to detect radio signals of extremely low power (units of μW), and the main problem is the correct identification of the sought radio signals against the background of a large number of other radio signals (broadcasting, communications, industrial, special, etc.).

The most effective means of identifying sources of extraneous radio signals are systems that implement diversity reception methods, which allow for the automation of the process of signal detection and analysis and, if possible, minimal operator involvement in the operation of the system. Diversity reception methods allow for the implementation of a decision rule (criterion) for identifying radio signals based on the physical differences in the radiation of radio signal sources located in and outside the protected premises.

Criterion for identification of signals in diversity reception

In general, the problem of identifying radio signals from unknown radio sources (NIRS) is reduced to constructing a decision rule for detecting signals with a priori unknown parameters against the background of interference. Since most existing radio monitoring systems do not allow detecting radio signals operating under the guise of legal radio signals, we will conduct an analysis for the situation of NIRS operation in free frequency ranges. In such a situation, signals from NIRS and from outside sources operate in different frequency ranges (the problems of detecting ultra-wideband signals are considered in /1/and essentially do not differ in the identification algorithm from those under consideration).

The solution to the problem leads to an optimal radiometric receiver that analyzes the energy parameters of the signal, i.e. its power measured over a finite averaging time. A quasi-optimal solution allows us to use two receiving antennas located inside and outside the protected room. For large rooms (conference halls), it is possible to use 2-3 receiving antennas in the protected room. Diversity reception is based on the obvious physical fact of attenuation of the power of radio signals as they propagate in space from the source. Comparison of the signal powers in two antennas allows us to draw a conclusion with a certain probability about the spatial location of the signal source relative to the protected room.

The detection receiver has two antennas, one of which, No. 1, is located inside the protected room (internal), and the other, No. 2, is located outside the room (external). The control receiver is a radio receiving device that is capable of accidentally or deliberately receiving radio signals from the NIRS, thereby reducing the security of the premises.

We will write the signal in the first antenna as follows:

where — signal from NIRS, — signal from an external station, — number of extraneous stations.

Similarly, in the second antenna the signal is equal to:

where — signal from NIRS, — signal from an outside station.

Since the original signals from the NIRS and extraneous stations are identical for both antennas, the signals from them in the antennas are linear transformations of these original signals, taking into account the distances from the signal sources to the antennas, the presence of shielding obstacles, and the presence of interference phenomena. For a two-channel receiver, the decision rule is based on a comparison of some functionals from the signals received in both antennas. Statistical characteristics of signals for a finite observation time can be considered as such a functional. Since the sought and extraneous signals do not coincide in frequency range, the comparison of statistics must be carried out at each frequency of the monitored range. Let us have the same number of signal samples in each antenna:

.

A stable indicator of the difference in signals in antennas is their energy characteristic — power over a finite averaging time. Then the decision rule will have the following form:

Depending on the number of samples or averaging time, the power distribution (1) has a different form, which becomes Gaussian for infinite analysis time. Consequently, the distribution of the decisive statistics can be found from the distributions of the current power in two antennas. Moreover, since the phase characteristics are not taken into account when calculating the current power, the power value is determined only by the amplitude losses and the distances to the signal sources , where — function of changing signal power with distance, — integral coefficient of signal amplification or attenuation introduced by antenna and amplifying circuits, building structures.

In general, the value of the decisive statistics can be written as follows:

where: — the signal radiation power received for a process with zero mean value equal to its variance, — delay time for measuring the power of processes in different receiving channels, — time of measuring the current power of the process, — distance from the signal source to the corresponding antennas, — carrier frequency of the signal.

Since the current power is determined by expression (1), then even for independent Gaussian samples finding the distribution of the decision statistic (2) is a complex problem. For small values ​​of the power analysis time, the distribution of the value represents the distribution of the difference between two dependent — processes.

The solution is possible for the situation when the measurement time of the process exceeds its correlation time, when the normalization of the current power occurs. With a sufficiently long measurement time of the power of a random stationary process, its distribution becomes Gaussian with parameters /2/:

— average value ;

— variance , where — number of signal samples.

If the number of samples (signal analysis time) tends to infinity, then the process variance tends to 0, i.e. the power estimate represents its exact value and the comparison of signal powers can be carried out absolutely accurately.

From expression (2) it follows that in this case the distribution of the decision statistics will also be normal with the mean value equal to the difference of the mean values ​​of the processes, and the variance is equal to the sum of the variances of the processes. The parameters of the decision statistics for the signal and interference will be equal to:

where is a coefficient determined by the time of measurement of the current process power.

From the distribution of the decision rule, it is possible to determine the probabilities of false alarm and correct detection :

where — tabular integral of probability, — detection threshold.

For the radio monitoring complex, the probability of correct detection corresponds to the case of correct identification of the received radio signal as a signal from the NIRS, and the probability of a false alarm corresponds to the case when radio signal sources located outside the protected premises are identified as signals from the NIRS.

The detection threshold can be expressed in terms of the probability of a false alarm:

where — is the quantile of the probability integral function distribution.

Substituting (6) into the expression for the probability of correct detection, we can obtain its value in the following form:

where — signal-to-noise ratio by the radiation power of radio signal sources.

Let the spatial dependence of the signal and interference on the distance be determined by some power function, the same for distant and near sources, that is, , where is the exponent, which, according to experimental data, can take values ​​from 1.5 to 4. Let, as a first approximation, the magnitude of signal attenuation by shielding barriers be identical in both directions (for signals from the NIRS from antenna No. 1 to antenna No. 2, and for extraneous signals from antenna No. 2 to antenna No. 1) and be equal to .

By introducing normalization and the amount of attenuation by building structures, from expression (7) we obtain the final expression for the probability of correct detection of radio signals from the NIRS:

where — distances from the interference source to the first and second antennas, respectively, — distances from the signal source to the first and second antennas, respectively, where the first antenna is internal and the second is external, — signal-to-noise ratio at the input of the first antenna.

Let the amplitude unevenness of the paths by frequency be identical, which is true on average for practical systems and this indicator as an average value is specified in the technical requirements . In this case, the value is random and has an average value equal to 1. Then the probability of correct detection is written as follows:

It follows that the probability of correct detection is determined by three groups of parameters:

of the receiving complex – the detection threshold, set by the probability of a false alarm , the number of counts , unevenness of paths by frequency , conditions of antenna placement;

conditions of complex placement – ​​attenuation of building structures , distances from interference sources to complex antennas, interference source power;

NIRS – radiation power, distances from transmitter antenna to complex antennas.

When using the complex, the parameters of the detection threshold and the number of samples can be set independently of the conditions of the object's location, and their numerical values ​​are determined only by the a priori premise of the normality of the decision statistics. Let us consider the influence of the main groups of parameters on the detection efficiency (9).

Choosing the number of samples (radio signal analysis time)

To determine the requirements for the number of samples, let us consider a practically common case: there is no unevenness of the paths by frequency , the interference sources can be classified as «very distant», that is , at the receiver input the signal and interference powers are practically identical . Then:

Consider the requirements for the number of samples for two conditions:

— the NIRS antenna is located significantly closer to the internal antenna than to the external one;

— the NIRS antenna is located at approximately the same distance to the internal and external antennas.

In the first case, the probability of correct detection will be equal to:

In the second case:

If , that is, there is no shielding barrier, then expressions (11) and (12) become identical. From (11) and (12), we can determine the relationship between the number of samples and the parameters of the reception conditions:

for the case of and

for the case .

The figures show the dependences of the required number of samples to achieve a given value of the probability of correct detection on the magnitude of signal attenuation in building structures.

Case .

Case .

It is evident from the constructed graphs that the requirements for the number of samples (the time of signal and interference analysis at one step of radio receiver scanning) increase significantly if the predicted probability of correct signal detection increases, the probability of a false alarm decreases, and the absolute value of the signal attenuation between two antennas decreases. In general, this attenuation is the most powerful resource of the radio monitoring complex, since with a small value, the requirements for the analysis time become unrealizable and the solution to the problem is reduced to an unrealizable precision measurement of the powers of two random processes.

If then to distinguish signals by the decisive criterion, additional attenuation of building structures of at least 6 is requireddB, so that the number of readings at each step of the radio receiver scanning would be acceptable. If we assume that additional attenuation of building structures 4…6 dB exists, and the internal antenna is significantly separated from the external one, then we can limit the number of readings to 30…40.

The choice of analysis time can also be made from the limit values ​​of the probability of correct detection for a high-power signal . Then expression (9) for a small weakening value is reduced to the form:

The dependence of the maximum probability of correct detection is shown in the figure.

Thus, for reliable detection of a high-power signal, about 10 is required-ti signal counts, which corresponds to the practical normalization of the process of measuring the current power of a normal random process /2/.

Sequential analysis

Over several successive scan cycles of the radio receiver, the probability of correct signal detection can be increased even with a small probability of correct detection in one scan cycle.

Let us consider the possibility of increasing the probability of correct detection by multiple analysis in several successive receiver scanning cycles. It is known that for successive independent solutions the following expressions hold:

where is the number of receiver scanning cycles, is the probabilities of correct detection and false alarm per scanning cycle.

Since the condition is always satisfied, then . Thus, on the one hand, with an increase in the number of scanning cycles, the probability of correct detection increases, but on the other hand, the requirements for reducing the probability of false alarms also increase. For a limited detection time the benefits of multiple analysis may not be realized due to the need to increase the detection threshold proportionally to the number of scanning cycles.

Let's consider a typical practical case , , . Expression (11) takes the following form:

The number of samples can be expressed through the analysis time at each scanning step and the required frequency resolution — .

The receiver restructuring period can be defined as , where — scanning frequency range, — bandwidth of simultaneous analysis at each scanning step, — time of receiver readjustment for each new scanning step. Let us introduce the signal detection time as .

Substituting (16) into (15) and neglecting the tuning time (for a real receiver it is usually longer than the analysis time, but this does not determine the result of multiple analysis), we obtain:

From (17) it is clear that in the exponent increases the probability of correct detection, but decreases it in the expression in brackets. To analyze expression (17), we will take the following quantitative values: , , , , then

The figures show the dependence of the probability of correct signal detection on the number of scanning cycles and on the signal detection time for the selected parameters of the complex.

Thus, with an increase in the number of receiver scanning cycles with a limitation on the detection time, the probability of correct detection decreases compared to the analysis during one tuning cycle. That is, it is more advantageous to conduct a long analysis on one scanning cycle than to split this time into several periods (this only applies to continuous signals). If we limit the analysis time at each scanning step, then obviously with an increase in the number of scanning cycles, the probability of correct signal detection will increase.

Since the situation with the absence of a shielding barrier between the antennas is considered, the calculated detection time will be the maximum possible for the control complex with the created parameters. Let's take the number of readings equal to 80, and the probability of false alarm is 0.01, then expression (8) is reduced to the form:

где , .

Requirements for unevenness

amplitude characteristics of channels

Since the position of the signal and interference spectra in the frequency domain is unknown and can be arbitrary, the values ​​of the amplitude unevenness of the channels for the signal and interference can also be different. Usually, due to the remoteness of the second antenna, always and . Let's consider the case that is important for practice and , then from (19) we get:

Let the condition be satisfied, under which (20) takes the form:

From (21) we can determine the requirements for the degree of attenuation in various receiving channels. For a probability of correct detection of 0.9 we obtain:

.

Thus, for the situation under consideration, frequency unevenness is practically irrelevant, but the attenuation condition in the channels is quite strict. So, for the condition is equal to , that is, the signal attenuation in the second antenna should not differ from the signal attenuation in the first antenna by more than 0.7dB, which actually corresponds to the equalization of signal attenuation (amplification) by frequency in two receiving channels. The requirements for the amount of signal attenuation depend on the ratio of the probabilities of correct detection and false alarm: . If , then the requirement for signal attenuation in the channels will take the form , which, given the a priori unknown value of the shielding, leads to the need to equalize the gain (attenuation) in the receiving channels regardless of the distances between the receiving antennas.

Since the frequency range of the signal and interference is unknown, this automatically leads to the need to comply with the condition . Then expression (19) will take the following form:

The influence of the amount of signal attenuation between antennas

To assess the influence of the attenuation coefficient between the antennas, we will consider several conditions regarding the distances from the antennas to the source.

Let there be a distant interference source and a nearby signal source . In this case, taking into account the condition expression (22) will be written as follows:

The figures show the dependence of the change in the probability of correct detection on the magnitude of signal attenuation between the antennas.

The dependence of the probability of correct detection on the value of has a very sharply decreasing character with a decrease in the value of signal attenuation — the limits of the probability decrease from 1 to 0 are 0.4…2dB. Reliable detection of an extremely low-power signal is possible with an attenuation value of at least 3 dB. This attenuation value is usually realized in practical situations for reinforced concrete and brick buildings.

If the requirements for the false alarm probability value are increased, the required attenuation value increases significantly. The figures show the dependences of the correct detection probability on the signal attenuation value between the antennas for the maximum false alarm probability equal to 0.

From the graphs shown in the figure, it follows that detection of small signals is impossible without false alarms. At the same time, detection of signals whose power exceeds the interference power by 1…2 dB is possible already with a signal attenuation value between the antennas of about 6 dB.

Assuming that , expression (23) is reduced to the form:

From (24) it follows that there is such a value , at which the expression for the argument is always negative, that is, the probability of detection is more than 0.5 depending on the signal-to-noise ratio. Such a limiting value of attenuation is equal to 0.632, that is, minus 2 dB.

Degree of isolation between channels

Let the complex be multi-antenna, i.e. in addition to one external one it also includes internal antennas, then due to parasitic re-radiation of the signal from channel to channel the decision rule will change its value. The signal in an arbitrary internal antenna (located in its protected room) can be written as follows:

where — the signal power in the internal volume, received approximately equal in all antennas without taking into account the influence of distances, — the reradiation coefficient from channel to channel, — the reradiation coefficient from the internal antenna to the external one.

The signal in the external antenna will be equal to:

Taking into account (25) and (26), the decision rule for the signal from the NIRS, provided that the re-radiation coefficients for different antennas are equal, will be determined by the expression:

Similarly, you can obtain an expression for the decision rule for interference :

From (27) and (28) it is evident that depending on the number of channels and the magnitude of signal attenuation, the value of the decision statistics may increase or decrease. Without considering the influence of the re-radiation coefficient on the final parameter of the probability of correct detection, we will conduct a qualitative assessment of the requirements for the value of antenna decoupling.

If we do not take into account the distribution of the average power of the processes, then (27) and (28) describe the ideal case of decision making, when the probability of a false alarm is equal to 0, and of correct detection is 1, if the threshold is equal to 0. The figure shows a diagram for the decision statistics, provided that all re-radiation coefficients are much less than 1.

With a zero detection threshold and no fluctuations in the measured power, the decisive statistics for the signal are always positive and negative for the interference. The degree of resolution of the signal and interference can be characterized by their relative spacing:

After all transformations, expression (29) is reduced to the form:

If the parasitic interference between the internal channels and the external channel is identical to the internal , then expression (30) is simplified and is independent of the number of channels . That is, the error in calculating the decisive statistics is equal to the value of the parasitic re-radiation coefficient from channel to channel. If we take 1% as the permissible error, then it is sufficient to have a parasitic coupling value of no more than 20 dB. Taking into account the influence of fluctuations in the average power of the measured processes, the real requirement for the re-radiation coefficient can be about 30 dB.

Distances from the NIRS to the receiving antennas

To assess the influence of the distances between the antennas on the probability of correct detection, we will consider the case with the signal attenuation value between the internal and external antennas of 6 dB and the signal-to-noise ratio equal to 1. Then expression (22) will take the following form:

Let's consider the most typical case of a remote interference source — , then the probability of correct detection will be equal to:

Provided expression (32) is 1, that is, the complex allows for reliable detection of signals.

The figures show the dependences of the probability of correct detection on the ratio of the distances and the signal decay rate index .

Thus, with uncertainty in the law of signal change with distance, one should focus on the maximum ratio of distances no more than 1.5, which, together with the attenuation of the signal between the antennas, will allow reliable identification of signals. Therefore, it is necessary to ensure that the ratio of the distances between the NIRS antenna and the receiving antennas is approximately 1. Substituting this value into expression (31), we obtain the dependence of the probability of correct detection on the ratios of distances for interference in the following form:

The figure shows the dependences of the probability of correct detection on the ratio of distances to the antennas of a distant source.

To obtain reliable solutions for signal identification, the degree of remoteness of the interference source must be significant. Since the law of signal change with distance is unknown, then, focusing on the maximum coefficient equal to 4, the ratio of distances from the antenna of the distant source to the receiving antennas (internal and external) must be no less than 0.8. This is always feasible for really distant broadcasting stations, for which the distances to both antennas are comparable. For a conditionally distant source (a cell phone, a car communication station, etc.), the occurrence of such a situation is quite real, for example, a car with a signal source near a building, and an external antenna is located on the roof of the building. Then the ratio of distances can be less than 0.5, which excludes guaranteed signal identification by the decision rule. For such situations, it is necessary to use several internal antennas installed in rooms adjacent to the protected one. Then the identity of signals in several adjacent antennas may be a sign of an external source. In addition, for such cases, additional identification methods should be used — signal statistics, time and duration of operation, listening to the modulation signal.

All of the specified criteria and indicators are fully implemented in the radio monitoring complex «Kvadrat», which is not only supplied to consumers, but also calibrated and installed in accordance with the conclusions obtained in this article. The complex allows for optimal detection and identification of radio signals from sources located in protected rooms in the frequency range from 30 to 2600 MHz with the possibility of expanding the frequency range to 7800 MHz with a bandwidth of 10 MHz for simultaneous analysis. The user interface is designed for automatic operation of the complex with the ability for the operator to set the initial tactical parameters for signal identification.