Realization of discrete frequency coded radar signal based on DSP

Abstract: The discrete frequency coded sequence set is a set of orthogonal coded waveform sequences with good autocorrelation and cross-correlation. Its signal can improve the target search, tracking and recognition capabilities of the mesh multi-radar system. In order to design this signal, it is necessary to solve the NP-hard combinatorial optimization problem. Considering the speed limit of DSP and the real-time requirements of signal generation, a simple and effective local search algorithm is adopted, and the target algorithm and waveform output are completed using TI's TMS320F28335 and BB's DAC7724, and a waveform that meets the requirements is obtained.

Keywords: Discrete frequency coded sequence; Local search algorithm; Digital signal processor; Digital/analog conversion

0 Introduction
With the rapid development of information fusion technology, the target search capability, tracking and identification capability of mesh multi-radar system have been greatly improved, and thus it has been more widely used due to its high performance. However, in order to avoid self-interference and detection confusion, the signal of the mesh radar system needs special design. If the waveform transmitted by the system belongs to a set of orthogonal coded waveforms, and any waveform in this waveform set has an autocorrelation that approximates the impulse function, and there is no cross-correlation between any two waveforms, the system can switch between single-base, dual-base and multi-base according to real-time needs, thereby achieving stronger target detection, tracking and identification capabilities than traditional radar systems.

Orthogonal frequency coding is also a frequency hopping technology that can suppress multipath interference during signal transmission, improve the signal-to-noise ratio, and prevent radar signals from being intercepted, thereby improving the safety of radar stations. At the same time, diversity transmission of signals also ensures the recoverability of signals and solves the attenuation problem.

Digital signal processor (DSP) has powerful computing and processing capabilities, and has the advantages of fast data transmission speed and parallel processing of multiple instructions. Using TI's DSP chip TMS3-20F28335 as the control core and BB's 12-bit digital/analog converter DAC7724 as the execution unit, it can output arbitrary waveforms according to the corresponding mathematical function description.

1 Design of discrete frequency coded radar signal
Assume that there are L radar sites in a multi-radar system, that is, there are L frequency hopping sequences, each of which contains N continuous sub-pulses with a duration of tb. The coded signal can be expressed as:

Where: is the coding frequency of the sub-pulse; tb is the duration of the sub-pulse. For the frequency hopping sequence l, its frequency coding sequence is taken as {n1△f, n2△f, ..., nN△f), where: 0≤ni≤N-1, generally △f=1/tb. The frequency coding sequence can also be further represented by a coefficient sequence, that is, {n1, n2, ..., nN}.
Ideally, the autocorrelation function and cross-correlation function of the signal should meet the following conditions:
Autocorrelation function of sl:


The goal of signal design is to achieve the autocorrelation and cross-correlation characteristics described in equations (3) and (4). The energy function E is used to represent the sum of the sidelobe energy of the autocorrelation function of each frequency hopping sequence and the energy of the cross-correlation function between all different frequency hopping sequences, that is:

make E minimum. This is an NP-hard problem, similar to the TSP problem (traveling salesman problem). No polynomial time algorithm has been found so far, so it is necessary to use some heuristic algorithms that may not necessarily reach the optimal solution to find an approximate optimal solution.

2 Local search algorithm

2.1 Algorithm idea
Search for a new solution in the neighborhood of the solution. If the energy value of the new solution decreases, accept the new solution and continue searching in the neighborhood of the new solution; otherwise, discard the new solution and search again. In this way, the energy minimum point will be searched along the direction of energy decrease.

2.2 Algorithm Flow
The local search algorithm flow chart is shown in Figure 1.

2.3 Implementation Technical Issues
(1) Neighborhood Construction
For each row of the frequency-coded sequence set F, two elements are randomly selected and their positions are swapped to obtain a new sequence. All such sequences constitute the 2-opt neighborhood of the original sequence. The neighborhood here is not the neighborhood in the sense of Euclidean distance, but the neighborhood in the sense of Hamming distance.

(2) Program termination condition
Considering the overall running time, a maximum number of runs can be set so that the loop will terminate after executing to a certain extent.

2.4 Analysis of advantages and disadvantages
The local search algorithm only reflects the principle of concentration, but does not have a diffusion strategy. It is a greedy algorithm and has the risk of falling into a local optimal solution; but it has a fast convergence speed and high efficiency, which can greatly reduce the requirements for DSP speed and has high practical value.

2.5 Matlab algorithm simulation results
The simulation results are shown in Table 1.

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2.6 Result Analysis
Figure 2 shows that in the process of running the local search algorithm, the value of the objective function E shows an obvious decreasing trend, so the algorithm successfully converges.

Figure 3 shows that for each frequency sequence obtained, the autocorrelation function of the corresponding waveform is similar to the impulse function, which enables the radar to have a higher range resolution.

Figure 4 shows that for every two frequency sequences obtained, the cross-correlation functions of the corresponding waveforms are close to zero, which can reduce the interference between radars.

3 Waveform generation

3.1 Chip Introduction
The TMS320F28335 (TI) 32-bit floating-point digital signal processor (DSP) chip has a 32-bit DSP core processor with an operating frequency of 150 MHz and adopts a Harvard bus structure. The program read bus has 22 address lines and 32 data lines, and the data read and write buses are both 32 bits.
DAC7724 is a 4-channel, 12-bit resolution, ±10 V signal range, 10μs settling time, and ±15 V power supply D/A converter. The ideal relationship between the input digital quantity and the output analog quantity is as follows:

Where: N is the digital input; VOUT is the analog output; VREFL is the low reference voltage; VREFH is the high reference voltage.

3.2 Software Design
3.2.1 Design Ideas
First, execute the local search algorithm to obtain the frequency coding sequence array n[L, N]; then start timer 0 and set an infinite loop to wait for interrupts; in the interrupt service subroutine, send the amplitude of the signal s at each moment to the DAC output.

3.2.2 Design process
In the interrupt service subroutine, the number of waveform frequencies can be controlled by the DIP switch, that is, one, two or all frequencies can be selected from the N frequencies in the frequency encoding array to achieve real-time conversion between single base, dual base and multi-base. The design process is shown in Figure 5.

3.2.3 Specific implementation of waveform output
The waveform output in the interrupt service subroutine is relatively complex and needs to be explained in detail.
(1) Determine the interrupt cycle prd_isr of TIMER0;
(2) Determine the number of points output within a pulse width tb = num = tb/prd_isr;
(3) When the number of interrupts count < NUM, the waveform frequency remains unchanged, and the signal value is as follows:

perform D/A conversion on its value and output it from the i-th channel, with count increasing by 1 each time it is converted; when the number of interrupts count > num, count is reset to zero, and j is increased by 1, switching to the next frequency.

3.3 Result waveforms
The result waveforms of multi-base, dual-base and single-base when N=7 are shown in Figures 6 to 8.

3.4 Result Analysis
The frequencies of the waveforms in Figures 6 to 8 are encoded according to the obtained frequency code n[i][j](0≤i

4 Conclusions
The local search algorithm is verified by using Matlab, and the simulation results are given. The results show that the discrete frequency coded sequence set obtained has good autocorrelation and cross-correlation; then the waveform generation system is realized by DSP, and the results obtained meet the expected design requirements.
This paper gives the actual generation method of discrete frequency coded radar signals, which has a high reference value for practical applications.