In Electronic Infomation Category: F | on May 04,2011

Abstract: In order to solve the boot of the FM carrier frequency difference between the transmitter antenna array pattern synthesis of the impact, where the maximum use of the DFT spectrum and **BA6858FP datasheet** and the spectral coefficients of two adjacent real (or imaginary part) the interpolation of each transmitter estimates the carrier frequency, and **BA6858FP price** and then proposes an effective compensation method to reduce the frequency difference caused by the instantaneous phase of the integrated effect pattern. Experimental results show that: the frequency estimation accuracy of this method is high, this method can effectively solve the frequency difference of the antenna array pattern synthesis of.

** 0 Introduction **

** Deterioration in the terms in the communications, environment, topography is not conducive to communication, you can consider the use of smart antenna technology to form a multiple antenna array transmitter and BA6858FP suppliers and machine work, compared with a single Department of transmitters, transmitting more power, direction stronger, more conducive to communication. Is the carrier frequency offset of the transmitter antenna pattern on the impact of simulation analysis, the maximum line and then using DFT spectral coefficients of two adjacent real (or imaginary part) for interpolating the frequency estimates Then digital oscillator frequency offset correction, and through the MATLAB / SIMULINK simulation results show that this method is feasible, and achieved good results. **

** 1 Principle **

** 1.1 system diagram This experimental system **

** smart antenna technology is the use of multiple FM transmitter into a single uniform linear array, in order to ensure that the communication conditions deteriorate communication normally. However, after the transmitter power, the transmitter carrier frequency will be different, this will after the antenna pattern synthesis of a serious impact, thereby affecting the enhancement of communication capabilities. This paper presents the first accurate estimate of each carrier frequency, and then use digital oscillator of frequency correction, the FM transmitter output signal of the same carrier frequency in order to obtain a better pattern. Simulation system block diagram shown in Figure 1. **

** **

** Figure 1 a simple simulation system The experiment required five **

** FM transmitter to form a uniform linear array to the first FM transmitter carrier frequency output signal as a reference, using the discrete Fourier transform (DFT, Discrete Fourier Transform), the maximum line and two lines adjacent real coefficients (or imaginary part) for interpolating the frequency estimates, then the FM frequency correction until the same carrier frequency output signal. Among them, the reference signal for the antenna through the bottom of the coupler and add a matching circuit, and then estimate the signal into the frequency value of port operations. **

** 1.2 linear array model **

** The transmitter antenna of the study will form a uniform linear array, which is a simple array structure, all equally spaced array elements arranged in a straight line. Assuming the position of array elements in (xm, ym), m = 1,2, ... ..., N, with the origin as a reference point, , said azimuth (y-axis incident angle signal, that is, with the array of normals angle), shown in Figure 2. Figure 2 for the array element spacing d (typically half the incident wavelength of the signal) to the left of the array element as a reference point, is the incident plane wave on the array azimuth. **

** **

** uniform linear array in Figure 2 indicate **

** The direction of the array can be photo: **

** **

** Equation (1): for the wave number; d for the array element spacing; 0 for the azimuth. **

** The FM transmitter output signal of each array element as an incentive to get directions photo: **

** **

** Which, sn (t) is the n-way transmitter output signal, and its expression is: **

** **

** Transmitters use a certain type of crystal as a standard frequency source, the maximum frequency error is 30 Hz, that the stability of the crystal by the radio carrier frequency difference caused by the phase difference generated by changing over time, that : **

** **

** This will have serious implications for pattern synthesis, therefore, must first frequency estimation, and then make the appropriate phase compensation to reduce the synthesis of the impact pattern. **

** 1.3 FFT-based frequency estimation and frequency correction **

** Maximum use of line and its adjacent DFT spectrum coefficients of the real part of two (or imaginary) in interpolated frequency estimate. **

** Set signal sinusoidal signal, expressed as: **

** **

** Equation (5): x (n) is unknown discrete real sinusoidal signal, a, f0, are the amplitude, frequency, and phase; fs is sampling frequency. **

** DFT-based spectral analysis method, with fast operation (using the fast Fourier transform (FFT, Fast Fourier Transform)), of the sinusoidal signal has a significant SNR gain and have the advantages of algorithm parameters is not sensitive, best performance is a comprehensive approach, it has been widely used. But because of the picket fence effect, when the sampling frequency is not an integer multiple of frequency resolution of DFT, the sinusoidal signal spectrum leak, even without noise, the true frequency of the signal is still down in the main lobe between the two discrete FFT spectrum, resulting in frequency estimates can not meet the required precision. Therefore, interpolation is introduced to improve the accuracy of frequency estimation. **

** X (n) N-point discrete-time signal Fourier transform (DFT) is denoted by X (k), in view of the symmetry of real DFT sequence, ignoring the negative frequency part of the spectrum, namely: **

** **

** Equation (6) T = N / fs is the sampling length. Mk is the corresponding **

** assume X (k) to obtain the serial number when the maximum value, then the equation (6) f0T can be expressed as km + , [-0.5,0.5], which are: **

** **

** Whichever is greater when the N, the equation (7) can be expressed as: **

** **

** (8) for the general sine wave signal DFT coefficients of expression. **

** According to equation (8) can be amplitude km line: **

** Two adjacent lines **

** km (km +1 and km -1 at) amplitude is approximately: **

** **

** According to equation (8), (9) and (10) can be derived by the following two equations: **

** **

** From (9), type (10) and (11) can be seen in X (km), X (km +1) and X (km -1) the real and imaginary parts of the size and angle + ((N -1) / N) Ц associated, when cos [ + ((N-1) / N) Ц] than sin [ + ((N -1) / N) Ц] hours, the real part will smaller than the imaginary part. To reduce noise, when the real part is large, by (12) is given, otherwise from (13) is given. **

** calculation steps given below: **

** request sequence x (n) of the FFT, by sequence X (k); find X (k) to obtain the maximum number of values ??mk; If Re [X (km)]> Im [X ( km)], in accordance with (12) calculated value, or according to equation (13) calculated the value of . **

** The frequency estimation is: **

** **

** This method SNR 24 dB, the average estimation error is slightly larger than the Rife estimation, and when SNR 45 dB, the signal frequency estimation performance close to the CRLB. **

** 1.4 phase compensation **

** To the first reference output signal of the transmitter, the frequency estimation algorithm for the frequency of the signal received from various quarters the value of fn, write fn = f1-fn signals for the i-frequency signals with the first difference. To f2 = f1-f2 example: **

** Order: **

** **

** With this signal and audio signal as a modulated signal is loaded into the transmitter input, the resulting output signal is: **

** **

** At this point, assuming that 1 = 2, then there is: **

** **

** By the derivation we can see that the frequency difference to compensate for the phase difference caused by the impact of pattern synthesis, phase compensation to achieve the purpose. Similarly we can find the rest from various quarters **

** signal and reference signal frequency difference, and then make the appropriate phase compensation. **

** 2 Simulation results **

** The experimental simulation using SIMULINK platform. Experiment, using five transmitters, audio frequency of 300 Hz, amplitude 2, the carrier frequency center frequency f0 = 10 MHz, the error range of 30 Hz. Let azimuth = / 6, the FM transmitter are 10 MHz carrier frequency, its orientation shown in Figure 3, this time, the main lobe gain of 16.25 dB. **

** **

** Figure 3, the same carrier frequency in the direction map **

** And when the carrier frequency varies, fi = 107 + [-20, -15,15,20,30] Hz, its direction is shown in Figure 4, this time, the main lobe gain of only 13.3 dB, and the sidelobe level has reached 12.1 dB, significantly reduced power main lobe. By SIMULINK simulation, that the transmitter carrier frequency deviation in the range of 6 Hz, the resulting array pattern is acceptable. **

** **

** Figure 4 contains the frequency of each pattern with Time **

** The signal to noise ratio SNR = 45 dB, the use of frequency estimation algorithms presented here operate on, got an estimate of the frequency ^ if = 1e7 + [-18.5, -15.6,14.8,21.3,28.8] Hz, and then The first signals of carrier frequency offset correction for the reference to obtain the pattern shown in Figure 5, we can see, basically consistent with Figure 3, reached a phase compensation purposes. **

** **

** Figure 5, the phase compensation **

** 3 Conclusion Here the maximum use of DFT **

** line and two lines adjacent real coefficients (or imaginary) in interpolated frequency estimate. This interpolation algorithm when the first few lines of the DFT coefficients of the real and imaginary parts of the size of the comparison, greater than the imaginary part of the real use of real time interpolation, which in turn is used to interpolate the imaginary part, thereby reducing the noise impact and improve the estimation accuracy. Theoretical analysis and simulation results show the effectiveness of the algorithm, and then use digital oscillator frequency offset correction of the carrier frequency so that each transmitter is basically the same carrier frequency, has been relatively good array pattern, experimental simulation shows that this method is feasible. **

** Using FFT spectral main lobe of the two largest FFT-based interpolation can improve the accuracy of frequency estimation, but the practical application of precision can be achieved by the noise is much lower than the results obtained under ideal conditions. In addition, this offset correction is only in simulation stage, no engineering practice, there may be theoretical simulation and practical differences, such as: the acquisition of the reference signal, ie, sampling frequency, the actual situation of the subsidiary circuit is required that the coupler and the matching circuit, the circuit is more complex, but also on the additional interference caused by signal sampling; In addition, frequency estimation, the SNR of 45 dB when there will be to achieve higher accuracy. Therefore, the need for practical engineering operations, in order to further verify the feasibility of the method. **

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