0 Preface
The spectrum splitting of the BOC modulated signal is on both sides of the center frequency point, which is advantageous for avoiding overlap with the spectrum of the center frequency signal, thereby reducing mutual interference between signals to achieve frequency band sharing. In addition, the BOC modulation signal is narrower than the main function of the correlation function of the BPSK modulation signal, and it has higher code tracking accuracy and stronger multipath interference resistance. Due to the uniqueness of BOC modulation, it is favored in the new generation of global satellite navigation systems.
When the BOC modulated signal passes through the navigation satellite transmission channel, the non-ideal characteristics of each device will cause a certain degree of distortion, which will affect the performance of the navigation system. At present, there have been related researches at home and abroad. The literature mainly analyzes several candidate BOC modulation signal characteristics of Galileo. The nonlinear characteristics of BOC modulation are mainly simulated by solid-state power amplifier (SSPA). The BOC modulation mode is analyzed when the input power back-off (IBO) is 0 dB. Correlation loss. The literature mainly analyzes the tracking accuracy of several candidate BOC modulated signals of Galileo affected by linear and nonlinear distortion, and analyzes the power loss and related loss due to the limitation of filter bandwidth. The literature mainly analyzes the distortion effects of on-board high power amplifier on BOC and its derivative signals, and mainly analyzes the joint effects of bandwidth limitation and nonlinear effects.
The influence of nonlinear distortion on the performance of satellite navigation system mainly lies in: causing signal amplitude and phase distortion, causing the constellation diagram to be compressed and deflected, causing the receiver's decision detection to be greatly affected, causing in-band distortion; generating a large amount of intermodulation distortion and harmony. Wave distortion, adjacent channel interference (ACI) generated by signal spectrum spreading, produces out-of-band distortion. Therefore, research on nonlinear compensation of satellite navigation channels is particularly important. However, most of the current domestic and international researches only on the impact of non-ideal satellite channels on BOC signals, but little research has been done to eliminate this effect.
Adaptive digital predistortion is one of the best methods to compensate for nonlinear distortion. It achieves linearization by constructing the inverse of nonlinear distortion in front of nonlinear devices. As the information rate increases, the signal bandwidth increases, and the navigation channel not only has nonlinear characteristics, but also its memory effect becomes more and more obvious. For nonlinear distortion with memory effect, if the traditional memoryless predistortion technique is still used, the nonlinear compensation mechanism may be invalid or not effective. Therefore, the linear compensation technique for studying nonlinear distortion of memory is of great significance.
In this paper, the predistortion simulation analysis of BOC signal is carried out, and the navigation satellite transmission channel is modeled equivalently. The transmitter channel is equivalent to Wiener-Hammerstein model, and a direct learning structure based on this model is designed. Adapting to the LMS pre-distortion scheme, it can be seen from the simulation results that the pre-distortion scheme can well eliminate the distortion effect of the navigation channel on the BOC signal.
1 Navigation transmit channel model
According to the existing domestic and international navigation satellite transmission channel models, an equivalent simplified model of the navigation satellite transmission channel can be summarized and summarized in Figure 1.
As shown in Figure 1, both the pre-filter and the post-filter use a linear FIR filter, and the high-power amplifier uses a traveling wave tube power amplifier (TWTA) model. The AM/AM conversion of the traveling wave tube high power amplifier is characterized by amplitude nonlinear distortion, and the AM/PM conversion is represented by phase nonlinear distortion. It can usually be simulated by the memoryless Saleh amplitude-phase model, namely:
When considering the prefilter, TWTA, and post filter, the memory effect can't be ignored. At this time, the navigation transmit channel can be equivalent to the memory Wiener-Hammerstein model, that is, the linear time invariant system (LTI_1). A linear time-invariant system (LTI_2) is connected in series with a memoryless nonlinear model (NL), which is often used to describe high-power amplifiers in satellite communications. Its structure is shown in Figure 2.
Each of these modules is represented by a mathematical expression:
The mathematical expression for the Wiener-Hammerstein model that combines each module is:
Where: K represents the polynomial order of the power amplifier model; L represents the memory depth of the power amplifier.
2 predistortion scheme
The predistortion method is usually divided into look-up table pre-distortion and polynomial pre-distortion. Because polynomial pre-distortion saves RAM memory cells and the convergence speed is fast, this paper chooses polynomial pre-distortion method. The polynomial-based predistortion has two kinds of direct learning structure and indirect learning structure. The structure of the direct learning structure is simple, and the algorithm can achieve better predistortion effect after convergence. The predistorter parameters are not affected by the noise of the output of the power amplifier nonlinear system. The effect can directly update the parameters of the predistorter. But first need to set the PA model, estimate the nonlinear transfer function of the amplifier according to the model, and then find the inverse function as the transfer function of the predistorter. According to the description of the first part of the navigation transmission channel model, the main part of the navigation transmission channel can be equivalent to the memory Wiener-Hammerstein model, which is consistent with the condition that the required model is required in the direct learning structure, so the direct learning structure is adopted in this paper.
Figure 3 is a predistortion block diagram based on the direct learning structure. In this structure, x(n) is the input signal at time n, and y(n) is the output signal of the power amplifier. The expected response of the whole system is d(n). ), the linear magnification in the graph is G. When e(n) = d(n) - y(n), when the algorithm converges to e(n) = 0, the output of the amplifier is linear of the input signal, and there is y(n) = G*x(n).
The navigation transmission channel established in this paper is a memory nonlinear channel. To compensate for nonlinearity, its inverse characteristic should also have a memory effect. Predistortion based on memory polynomial can usually compensate for the nonlinear model with memory effect. The memory polynomial model is as follows:
Where: K is the order of the memory polynomial, and the compensation effect is related to the order of the polynomial. To a certain extent, the higher the order, the better the compensation effect, but at the same time, the complexity of the algorithm is increased. For the same input signal, the predistortion polynomial is the most The choice of the best order is related to the power amplifier model. Q is the depth of memory. The greater the memory depth, the more obvious the predistortion effect is. The better the linearity of the power amplifier is, but the difficulty is too large. It is necessary to select the appropriate one according to actual needs.
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