CC BY
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Visnyk N'l'UU KP1 Seriia Radiolekhnika tiadioaparat.obuduuannia, "2020, Iss. 83, pp. 41—46
Y^K 621.396
Fast Spectrum Sensing Method for Cognitive Radio
Buhaiov M. V.
S. 1'. Korolov Military institute, Zhytomyr, Ukraine E-mai 1: karunen&ukr. ne I.
A key aspect of the functioning of cognitive radio systems is fast and reliable detection of unoccupied channels in cases of dynamic changes of electronic environment. To solve this problem, a fast iterative method based on the coefficient of variation as decisive statistic of the power spectral density (PSD) is proposed. The essence of the method is in comparing the values of the coefficient of variation with the threshold value using the predicted value of the number of signal samples and the method of the golden ratio. The threshold values of the decision statistics were obtained by calculating the vector of PSD. sorting and normalizing it to energy, and calculating the vector of values of the coefficients of variation by sequential removing from the normalized PSD samples with the maximum value. To reduce the number of iterations when calculating the decisive statistics, the predicted value of spectrum occupancy is used. This value is calculated using an empirical formula with the coefficient of variation for the zero iteration as an argument. In practice, the presence of several signals with different powers in the analyzed bandwidth leads to errors in the predicted value of spectrum occupancy. Moreover, the larger the dynamic range and the lower the signal-t.o-noise ratio, the greater this error will be. The predicted value of the spectrum occupancy is a rough estimate of the number of signal samples in the spectrum, and the golden ratio method was applied to find its true value in fast way. Processing gain in reducing the number of iterations for calculating the decisive statistics depends on the spectrum occupancy prediction error and can reach several tens of times. The proposed method can be used to improve existing and develop new cognitive radio systems based on Software Defined Radio (SDR) technology.
Key words: coefficient of variation: iterative method: cognitive radio: golden ratio: spectrum occupancy: threshold
DOI: 10.20535/RADAP. 2020.83.41-46
Introduction
Radio systems based on SDR technologies have become widely used due to providing flexible management of radio frequency spectrum fl 3]. A key-aspect of the functioning of cognitive radio is fast and reliable sensing of unoccupied frequencies in case of dynamically changed electronic environment [4.5]. The solution of this problem is complicated by a priori unknown and time-varying noise variance, number and dynamic range of signals in the analyzed bandwidth. Also, when scanning wide frequency bands, the noise level at different frequencies can change significantly. In addition, nsing of various SDR transceivers, amplifiers and switching antennas requires ongoing estimation of noise power, which in an unknown signal environment is associated with significant difficulties.
In unknown and dynamic signaling environment, estimation of noise variance for threshold calculation will be performed with errors. Increasing the noise variance by only 20% of the estimated leads to an increasing in the probability of false alarm by an
order and even more. In snch conditions, there is a need to develop 3. fest spectrum sensing method with noise-independent characteristics of detection spectrum holes.
1 Review of related works
A significant number of scientific publications is devoted to the radio frequency spectrum sensing in cognitive radio systems. In [6] proposed an adaptive spectrum sensing algorithm for a dynamic signaling environment nsing estimates of noise variance obtained from antoregressive model. However, the proposed threshold adaptation procedure nses slow and complex gradient methods. In [7] for signals detection was proposed calculation the wavelet transform of spectrum and compute the discrete cosine transform from the low- and high-freqnency wavelet coefficients. But it is not specified how the threshold is calculated and whether it depends on the noise level. In [8] proposed threshold adaptation in the frequency domain
using a sot of bandpass filters. But the adaptation algorithm requires knowledge of noise and signal power. In [9] for detection and accurately estimation signals parameters in frequency domain, first calculate the spectrum on a short time window and roughly estimate the occupied frequency bands. In the second stage, using the Goortzol algorithm, accurate estimates of the signal parameters are obtained. However, the threshold value does not adapt to changes of noise variance. In the nmlti-channel method of signal detection proposed in [10]. the noise power is estimated at unoccupied parts of the spectrum, which requires a preliminary analysis of the analyzed frequency band. Limitation of proposed in [11] method for detecting occupied frequency bands is its performance only on signals with a rectangular spectrum. The closest to the proposed method is described in [12]. But the computational complexity of this method increases with increasing spectrum occupancy. Tims, the problem of fast spectrum sensing under conditions of noise variance uncertainty remains unresolved.
2 Purpose and objectives of research
The aim of the article is to provide the possibility of fast and reliable detection of unoccupied spectrum channels for cognitive radio systems in conditions of dynamic change of noise variance.
3 Methodology of spectrum sensing acceleration
To solve the problem of spectrum holes' detection fast iterative method based on decisive statistics is proposed. The Welch method, which is based on the calculation of the Fast Fourier transform (FFT) and has a low variance of spectral estimates, is used to estimate the PSD. This method is based on the division of input sequence of samples of length M into K segments of length N with overlapping L samples, calculation modified periodogram for each segment and averaging of the obtained periodograms.
According to [12]. the coefficient of variation of the PSD samples Q, which has a much smaller variance than the variance of PSD samples themselves, is chosen as the decisive statistics. The essence of the proposed method is to compare the values of the coefficient of variation of the spectrum with the threshold value for each iteration.
The threshold values of the decisive statistics are obtained by calculating the vector of the PSD samples for noise, its sorting and normalization to energy and computing the vector of values of the coefficients of variation by sequential removing from the normalized PSD vector sample with the maximum value.
The length of the coefficients of variation vector is equal to the length of the vector of spectral samples. After processing a large number of noise realizations (determined by the required accuracy of the threshold calculation) for each iteration is calculated the threshold value of the coefficient of variation Qtr [«] for a given probability of false alarm in the frequency-domain PF. It was experimentally found that for a given qnantile of the probability density distribution of the decisive statistics Qtr of the level a is performed the approximate equality P(Qtr[*]) = ! — a~ 1—Pf-
Fig. 1 shows the dependence of the threshold valno of the decisive statistic Qtr via iteration number for Pp = 10-3 and for different values of the FFT window length. At low spectrum occupancy levels, which is equivalent to a small valno of the iteration, the threshold valno of the decisive statistics increases with increasing length of the FFT window.
1 1 /
1 1 1 ;
1 / / r*
/ ✓ / •* • •• - N = 1024
-- N=2043 ---- N = 4096
0 250 500 750 1000 1250 1500 1750 2000 Iteration
Fig. 1. Threshold values of decisive statistics Qtr via iteration
At large N and high bandwidth occupancy 'q described in [12] iterative algorithm requires significant computational resources. To reduce the number of iterations for the calculation of the decisive statistics in the detection of spectrum holes, the predicted valno of spectrum occupancy level (number of signal samples) is nsed. This valno is calculated by the empirical formula using the coefficient of variation of the PSD for zero iteration of decisive statistic Q0. The formula for predicting the spectrum occupancy is obtained by approximating the experimental dependence of the coefficient of variation via spectrum occupancy for the valno of the signal-to-noise ratio (SNR) of 10 dB and the same power of all signals in the sensing bandwidth. For a real signal, the predicted valno of the number of signal samples can be calculated by the following empirical formula:
Jpred « 0.5N (I82e-0'89Q° + 2.15) . (1)
This expression gives an accurate valno of the spectrum occupancy, if the dynamic range of the signals does not exceed 10-12 dB. The dependency of the predicted spectrum occupancy 'q via calculated value of
Qo for zero iteration at SNR 10 dB is shown in Fig. . At other values of SNR there is an ambiguity concerning the predicted spectrum occupancy because Qo can have identical values for high spectrum occupancy and high SNR and low spectrum occupancy and low SNR.
— Empirical data
Qo
Fig. 2. Predicted spectrum occupancy level via Q0
In general case, small values of Q0 indicate high spectrum occupancy or a low occupancy at a low SNR value. Large values of Q0 indicate low occupancy or high occupancy with a significant dynamic range of signals. Therefore, in most cases, the predicted spectrum occupancy valne will be calculated with errors. The error valne increases with increasing dynamic range of the signals in analyzed bandwidth.
In practice, the values of SNR and dynamic range can change significantly, which leads to errors in the predicted valne of the spectrum occupancy. If there are several signals with different powers in bandwidth of the analysis, the predicted valne of the occupancy will be underestimated, and for one signal with less than 10 dB SNR — overestimated. Moreover, the larger the dynamic range and the smaller the SNR, the greater the error in the spectrum occupancy prediction. The valne of error can be estimated by the following expression:
2(Jestim Jpred)
N
lity of false alarm and calculate the vector of threshold values of the decisive statistic Qtr [«], i = 0 ... 0.5N — 1.
2. Calculate the PSD Pxx, its energy-normalized value X and form two auxiliary vectors: a descending array of frequency samples P = sort(X, reverse), which will be followed by signal samples (in case of presence) and then noise, and the array of indices of the vector P—Y = argsort(X, reverse).
3. Calculate the coefficient of variation of the PSD Qo = variation(P).
4. Check if there is signal in given realization of PSD — Q[0] > Qtr [0].
5. If condition 4 is fulfilled, it is necessary to calculate the predicted spectrum occupancy valne, which will correspond to some signal samples number Jpred in the vector P according to ( ).
6. If because of approximation errors and noise influence the calculated value of Jpred is more than 0.5W, it must be replaced by 0.35N, and if less than 0 - by 0.
7. Calculate the new valne of the decisive statistics Q = variation(P[0 : Jpred])-
8. Check the condition Q[Jpred] = Qtr [Jpred] and in case of its validation the vector of values of signal bins can be found as Freq = Y [0 : Jpred]> and the threshold valne will be equal to the minimum valne of the signal bin Threshold=P[ Jpred]• The number of signal samples will be Jestim = Jpred, and the spectrum occupancy level will be 'q = 2N-1Jestim■
9. If condition 8 is not fulfilled, and condition Q[JPred] < Qtr [Jpred] is fulfilled, then the search of Jestim must be performed in the interval [1: Jpred]• To do this, the specified interval is divided into 3 segments in the proportion of the golden ratio. Dividing points have the following coordinates:
Ji = B--
B-A
V
J2 = A+
B - A
(3)
(2)
where Jestim is the estimation of the number of signal samples; Jpred is the predicted value of the signal samples number.
Predicted spectrum occupancy valne is a rough estimate of the number of signal samples in the spectrum, and the golden ratio method was used to reduce time for finding its true value Jestim- Golden ratio method was chosen duo to its' asymptotic effectiveness in realization of minimax strategy of extreme search.
The algorithm of the proposed fast spectrum sensing method is implemented using Python, so when describing further material, the peculiarities of this language are taken into account. The essence of the method is to sequentially perform the following steps.
1. Set the parameters of the Welch periodogram M, K, N, L, type of window function and the probabi-
where A =1, B = Jpred and p «1,618.
For these points, the values of the decisive statistics are calculated and are compared with the threshold values. The division of the segment in the proportion of the golden ratio continues until the difference between the calculated valne of the decisive statistics at a given point and the threshold valne becomes less than certain valne. The point found will correspond to the required number of signal samples Jestim-
10. If conditions 8 and 9 are not fulfilled, the search for the number of signal samples Jestim is performed in the interval f Jpred : 0.35W] similarly to the procedure described in 9.
4 Spectrum sensing performance
The predicted spectrum occupancy valne in the vast majority of cases will deviate from the actual. The occupancy level may be lower than the predicted because of SNR valne below 10 dB or higher duo to the
v
high dynamic range at high occupancy level or higher than 10 dB SNR at low occupancy.
Fig. 3 shows a variant of the underestimated predicted value of the spectrum occupancy duo to the high dynamic range of signals. As can be seen from this figure, the error in predicting the number of signal samples is about 2 times. At Fig. 4 is shown results of proposed method performance for a spectrum occupancy of about 20%. The parameters of the Welch periodogram have the following values: M = 16384, K =16,N = 1024,L = 512, the type of window function — Hamming. The probability of false alarm was chosen as 0.01. As yon can see, the method is suitable to determine occupied channels and signal powers, as well as frequencies that can be used by cognitive radio systems. The dynamic range of signals in this case is at least 30 dB. In general case, the dynamic range of signals, in which the method allows to accurately determine the spectrum holes is limited by the maximum level of the side lobes of the window function.
10 -
- Qtr - 0 "" Jpred Jestim
..... ____
100
200 300 Iteration
400
500
Fig. 3. Underestimated spectrum occupancy
5 Simulation results
Now we compare the speed of spectrum sensing nsing the developed method and the iterative method proposed in f ]. The processing gain G is calculated as the ratio of the number of iterations of decisive statistics computation for the method [12] and the proposed method.
Processing gain depends on several factors: spectrum occupancy and prediction errors, dynamic range and SNR. But duo to the uncertainty of noise, even with the same SNR and spectrum occupancy level for different signal realizations and the same error in the prediction of the occupancy, processing gain in reducing the number of iterations can differ significantly.
Fig. 5 shows the average under the influence of all factors dependence of the processing gain G in reducing the number of iterations via spectrum occupancy prediction error en (calculated according to equation ( )). At low spectrum occupancy of analyzed bandwidth (up to 10%), which corresponds to a value of en less than 0, the average gain is only a few times. This can be explained by a poor approximation of the predicted occupancy at large values of the decisive statistics (Fig. 1). With increasing spectrum occupancy, the gain increases linearly and is several tens of times, although the forecast error modulo does not exceed the forecast error for small occupancy levels.
Fig. 4. Results of proposed method performance
Fig. 5. Processing gain via error of predicted spectrum occupancy
Conclusions
The proposed fast spectrum sensing method allows finding nnoccnpied bands of the radio frequency spectrum under conditions of dynamic change of the electronic environment at unknown noise variation and the dynamic range of signals that can be processed is limited only by the level of the side lobes of the window function. Processing gain in reducing the number of iterations of calculation the decisive statistics depends
on the error of the predicted spectrnm occupancy and can reach several tens of times. The proposed method can be used at improvement of existing and development of new cognitive radio systems based on SDR technology. Prospects for further research in this area are associated with the development and study of similar methods for detecting broadband signals.
References
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[3] Arslan H. (ed.) (2007) Cognitive Radio, Software Defined Radio, and Adaptive Wireless Systems. Springer. 476 p. DOl 10.1007/978-1-4020-5542-3.
[4] Benmammar tí.. Amraoui A.. Krief F. (2013) A Survey on Dynamic Spectrum Access Techniques in Cognitive Radio Networks. International .Journal of Communication Networks and Information Security (1.JCN1S), Institute of Information Technology. Kohat University of Science and Technology, Vol. 5, Iss. 2, pp.68—79.
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Швидкий метод анал!зу радючасто-тного спектра для когштивних радю-систем
Бугайов М. В.
Ключовим аспектом фупкцюпуваппя когштивних радюснстем е швидке та падите визпачеппя вглышх дшяпок частот при дипам1чшй змпп радюелектрошю! обстановки. Для вгцяшеппя дапого завдашш заиропо-повапо швидкий иеративпий метод 1з використаппям коефщ!епта вар1аци спектрально! щглыюста потужпо-ст! (СЩП). CyTiiicTb методу полягае в пор1впяпш зпа-чепь коефкцепта вар!ацп спектра прийпято! реал1зацп з пороговим зпачеппям 1з використаппям прогпозова-пого зпачеппя шлькост! сигпалышх в!дл1к1в та методу золотого перетипу. Порогов! зпачеппя вгцяшуючо! статистики отримапо шляхом розрахупку вектора в!дл1-к!в СЩП. його сортувашш i пормуваш1я до eiiepri'i та розрахупку вектора зпачепь коефщ!еттв вар1аци при посл1довпому в1дкидапш в!д пормовапого вектора СЩП в!дл1ка з максималышм значениям. Для змепшеппя шлькоста 1терацш розрахупку вгцяшуючо! статистики при внявлепш вглышх дшяпок у смуз! частот апал!зу ви-користовуеться прогпозовапе зпачеппя заваптажепост! (шлькост! сигпалышх в!дл1к1в). Дапе зпачеппя розра-ховуеться за емшрпчпою формулою 1з використаппям в якоста аргументу коефкцепта вар!ацп для пульово! 1терацп. На практнц! паявшеть в смуз! частот апал!зу шлькох сигпал1в з р1зпими потужпостями прпзводить до появи помилок прогиозовапого зиачешш заваптаже-iioctl Причому чим бглыннм е дипам1чпий д!апазоп i мепше в1дпошеш1я сигпал-шум. тим бглыною буде дапа помилка. Прогпозовапе зпачешш заваптажепост! е грубою оцшкою шлькост! сигпалышх в!дл1к1в у спектр! i для швидкого пошуку ii icTniuioro зпачеппя застосовапо метод золотого перетипу. Виграш у змепшепш кглькост! 1терацш обчислеппя вгцяшуючо! статистики залежить в!д помилки прогнозу заваптажепост! i може досяга-ти илькох десятшв раз!в. Запропоповапий метод може бути використапий при удоскопалепш 1спуючих та роз-роблеиш пових когштивних радюсистем па основ! SDR технологи.
Клюноог слова: коефщ1епт вар1аци: 1теративпий метод: когштивпе радю: метод золотого перетипу: завап-тажешеть спектра: nopir
Быстрый метод анализа радиочастотного спектра для когнитивных радиосистем
Бугиёв Н. В.
Ключевым аспектом функционирования когнитивных радиосистем является быстрое и падежное определение свободных участков частот при динамическом изменении радиоэлектронной обстановки. Для решения данной задачи предложен быстрый итеративный метод с использованием коэффициента вариации спектральной плотности мощности (СПМ). Сущность метода заключается в сравнении значений коэффициента вариации спектра принятой реализации с пороговым
46
Бугайов М. В.
значением с использованием прогнозируемого значения количества сигнальных отсчетов и метода золотого сечения. Пороговые значения решающей статистики получено путем расчета вектора отсчетов СПМ, его сортировки и нормирования к энергии и расчета вектора значений коэффициентов вариации при последовательном отбрасывании от нормированного вектора СПМ отсчета с максимальным значением. Для уменьшения количества итераций расчета решающей статистики при обнаружении свободных участков в полосе частот анализа используется прогнозируемое значение загруженности (количество сигнальных отсчетов). Данное значение рассчитывается по эмпирической формуле с использованием в качестве аргумента коэффициента вариации для нулевой итерации. На практике наличие в полосе частот анализа нескольких сигналов с разными мощно-
стями приводит к появлению ошибок прогнозируемого значения загруженности. Причем чем больше динамический диапазон и меньше отношение сигнал-шум, тем большей будет данная ошибка. Прогнозируемое значение загруженности является грубой оценкой количества сигнальных отсчетов в спектре и для быстрого поиска ее истинного значения применен метод золотого сечения. Выигрыш в уменьшении количества итераций вычисления решающей статистики зависит от ошибки прогноза загруженности и может достигать нескольких десятков раз. Предложенный метод может быть использован при совершенствовании существующих и разработке новых когнитивных радиосистем на основе SDR технологии.
Ключевые слова: коэффициент вариации; итеративный метод; когнитивное радио; метод золотого сечения; загруженность спектра; порог
