Topicality of the subject
Modern wireless systems is characterized by a final transfer of radio signals to using the program of restructuring the operating frequency (frequency hopping), and communication in the network access time [28]. In today's networks particular attention is paid to improving radio protection from organized jamming, stealth transfer of any types of information and its secrecy, adaptive access subscribers different priorities to the necessary and available only to users of this category of data, increasing the number of communication channels, providing EMC with all other existing and developed RES. Application of the new signals will certainly lead to the expansion of directions of its use [26].
An example of such a system could be radio communication system described in [30].
The structure of signal detection is given packet with duration 
, consisting of a periodic sequence of radio pulses with duration information 
and repetition period
. Connection of each subscriber is carried out within the prescribed him a standard time period (STP) with duration
T.
The unique character of radio communication systems, their opportunities are determined by the structure of the signal and non-traditional methods of sharing information [28].
Purpose of work - study of the detection receiver based on the j-correlation signal processing. The main task of the receiver is the effective detection of PSK signals with frequency hopping. To achieve this task should be to:
Research methods. In conducting research using methods of statistical radio engineering, the theory of correlation analysis, the theory of signals and processes in electronics, methods of optimum detection and the method of analysis models using a virtual software environment LabVIEW.
A brief review of widely known methods of detection
Typically, the signal operating at the receiver input s(t), is characterized by numerous parameters that change randomly, such as amplitude, initial phase, the law frequency hopping, the duration of the signal at the receiver input and more. The more unknown parameters, the more difficult to create a receiver detection.
An analysis of detection methods known in the literature always begins with an analysis of the theory of optimum detection. Although this method is rarely used in practice, its settings are limiting and permit an assessment of the capabilities of other methods [8].
The correlation receiver is completely known signal
Let the receiver input signal s(t) and additive Gaussian white noise n(t) are valid. Resulting in a total
 |
(1.1.) |
The quality of the receiver detection is estimated the minimum signal to noise ratio at the input, at a given signal-to-noise ratio at the output. The level of noise voltage at the receiver output noise is determined by the properties of a linear path.
The mathematical expectation of the signal at the receiver output when no signal at the input equal to the mean value of white noise
 |
(1.2.) |
The mathematical expectation of the presence of an input signal is determined
 |
(1.3.)[3] |
Hence the parameter detection receiver, which defines the signal to noise ratio
 |
(1.4.) |
The expected signal s(t) - PSK signal with frequency hopping.
The main step in the processing of the fluctuations is to compute the integral
 |
(1.5.) |
To get the integral z requires a priori information about the signal s(t) to create an identical copy of it on the receiving end.
The scheme which computes the integral (1.5) is shown in Figure 1 [4]. As shown in [3] provides the maximum signal to noise ratio (1.4) on the output of the receiver, so this device is called an optimal receiver. It consists of the correlator, integrator, which computing z, and a threshold device (ПУ), in which the output value of the integrator z is compared with a threshold z0.
Figure 1. Block diagram of correlation receiver.
The correlation receiver has several advantages compared with other receivers detection, which allows to get the best value of SNR. From the marked and the results of data analysis [1, 3, 4, 5, 8, 11] is directed that the receiver requires a priori information about the received signal.
This deficiency removes this receiver role of the idealized model of the receiver detection in the theory of optimal signal processing. As noted by [8], the results should be regarded as a theoretical upper limit for the performance of detection.
Correlation receiver for detecting signals with unknown initial phase
Analysis of optimum detector is carried out by the condition known in advance of the initial phase, ie, the known time of arrival of the signal at the receiver input detection. However, in the real situation signal arrival time is usually not known, and can not be known for numbers of objective reasons.
So in the case of a moving target phase signal is variable. If changing of the phase is denoted by
D(t), in case of use as a receiver detection the optimum detector reference signal s(t) must specify all possible initial phases and only one of them will give the maximum correlation processing in the output signal level, ie will be optimal. Such a multiple procedure for establishing of the initial phases of the reference signal to substantially complicate the detection receiver [2].
However, this is possible to do without it - if to use the orthogonal components of the reference signal, presenting them as
 |
(2.1) |
|
where |
(2.2) |
For the orthogonal components of s1(t) and s2(t) and the received signal х(t) calculated the correlation integrals
 |
(2.3) |
Cross-correlation function of the received signal х(t) and the expected signal s(t), is
 |
(2.4) |
where 0 - the initial phase of the reference signal.
Since we are talking about the orthogonal components, then y1 and y2 are the projection of the signal at the coordinate axes, then
 |
(2.5) |
Then the quantities y1/Y and y2/Y do not exceed in absolute value unit and the sum of their squares is unity, then one of them is taken as the sine, the other - for the cosine of an angle , where
 |
(2.6)[2] |
Thus, the optimum detector for signals with unknown initial phase is directly involved in operations on the input signal x(t), given by (2.1) and (2.3), and consists of two parallel-connected correlator output signals are combined in quadrature (Fig. 2) [1] .
Figure 2. Block diagram of the optimum correlation receiver with unknown initial phase.
In the correlators are calculated y1 and y2 values, and after their mergered - the envelope Y. For the optimum receiver for signals with unknown phase requires a somewhat larger threshold signal to noise ratio for comparison with the correlation receiver for a signal with completely known parameters [4].
In view of the fact that the initial phase of the received signal, not a single parameter, a priori knowledge of which are absent - this receiver should also be considered as an idealized model.
Along with the correlation receiver is used filtering receivers that are optimal for the received signals.
Matched filter
It is known that the response of a linear filter on the input action x(t) described by the integral Duhamel
 |
(3.1.) |
where 
- the impulse response
Comparison of the Duhamel integral (3.1) with the correlation integral (1.5) indicates their similarity.
The integral (3.1) performs the function of cross correlation, impulse response within a constant factor k0 is the mirror image of the expected signal. This filter is called matched. Block diagram of the receiver matched filters (MF) is shown in Figure 3 [2]
Figure 3. Block diagram of the optimum receiver with MF (СФ - MF, ПУ - threshold device).
According to the theory of matched filtering the frequency response of the filter is the complex conjugate function of the input signal within a constant factor [3]. Phase-frequency response of the filter MF provides the maximum peak value of the accumulation signal. A distinctive feature of MF compared with the correlation receiver is invariant with respect to signal delay. The literature also notes its consistency for signals with unknown amplitude. SNR at the output of MF depends only on the energy signal and noise spectral density. No other filter than the matched filter, can not give more signal to noise ratio [2].
In the known literature is marked not the usefulness of MF for complex signals. PSK signals with frequency hopping signals is a complex of high secrecy. As a consequence, the practical application of MF in the receiver detection is not possible [30].
Quasi-optimal filter with recirculator
Application of the theory of matched filtering in practice is much more complicated for complication of type signal, so use the filters, which are agreed on certain parameters. Such filters are referred to as quasi-optimal.
The recirculation circuit (Fig. 4) as indicated [1,3,8] allows us to effectively accumulate repetitive pulses of signals.
Figure. 4 Block diagram of recirculator (ЛЗ - delay line).
Despite the fact that the PSK signal is transmitted with frequency hopping as a pulse packet to detect a signal at a radio frequency is not possible. As shown in [2] is associated with a phase mismatch of the input pulse packet with a recirculating cycle of accumulation.
To be able to separate the signal without the consent of the phase selection signal is carried out at video frequency. At the output of a linear path is put amplitude detector, which selects the envelope and ensuring its persistence within a period of high frequency [4]. The scheme of quasi-optimal receiver detection recirculator is shown in Figure 5.
Figure 5. Block diagram of quasi-optimal receiver with recirculator (линейный тракт - лінійний тракт, амплитудный детектор - amplitude detector, рециркулятор - recicrculator, пороговое устройство - threshold device).
Quasi-optimal receiver detection with recirculator can detect PSK signal with frequency hopping only on the video frequency. The disadvantages of the considered receiver detection should also include increased requirements for energy performance signal, which reduces the probability of correct detection signal at a given level of false alarms [4].
Figure 6 show a generalized scheme of the analysis of known detection methods.
Figure 6. A generalized scheme of the analysis of known detection methods. (помехи - interference, корреляционный приёмник - correlation receiver, корреляционный приёмник обнаружения для сигнала с неизвестной начальной фазой - correlation receiver for detecting signals with unknown initial phase, согласованный фильтр - matched filter, квазиоптимальный фильтр с рециркулятором - Quasi-optimal filter with recirculator).
(This figure is animated. File size: 53 Kb; size: 497 × 307 px; number of frames: 5; number of cycles of repetition: infinitely).
Conclusions
The analysis of existing detection methods showed that the only method with using quasi-optimal receiver with recirculator capable of providing signal detection with a frequency hopping. At the same time this receiver has some limitations in the use of detection signals from the frequency hopping. New methods of detection may give impetus to the development of this area. That alternative approach is necessary when considering the J-correlation receiver detection.
List of references
Note. Now graduation work is in progress, so the material described in this abstract may vary slightly from the text contained in the explanatory note. More detailed information of the research of the receiver detection based on j-correlation signal processing can be obtained after December 2011 from the author of this work only with the written permission scientific leader.
