Multiple Target Detection For OFDM Radar Based On Convolutional Neural Network

The objective of this paper is to propose a multiple target identification technique for orthogonal frequency division multiplexing (OFDM) radars. First, a 2-D (range & Doppler) periodogram is obtained from the reflected signal through 2-D fast Fourier transform (FFT) of the received OFDM symbols. Usually, the peaks of the periodogram indicates the targets. Conventionally, peak search algorithms are used to find the multiple targets. In this paper, however, a convolutional neural network (CNN) classifier is proposed to identify the targets. The proposed technique does not need any additional information but the 2-D periodogram while the conventional method requires the noise variance as well as the periodogram. The performance is examined through computer simulation. According to the results, if the number of maximum identifiable targets are small, the proposed technique performs well. However, as the number increases, the detection accuracy decreases. In the simulation environments, the proposed method outperforms the conventional one. The proposed OFDM radar technique can be applied to 6G mobile communications to identify the moving targets around the transmitter without additional frequency resource for radar systems.

considered as direct coupling components and removed. The optimal threshold, however, requires the information on signal to noise ratio (SNR) and noise variance, which is difficult to obtain.
In the proposed technique, the number of targets is found via a CNN classifier, one of famous deep learning techniques [10]- [13]. Specifically, the 2-D periodogram is inputted to the proposed CNN and the output is the predicted number of targets. No information other than the periodogram is required. We propose two kinds of CNN inputs. The first one is one 2-D periodogram for the targets, and the second one is two 2-D periodograms. In the latter, one signal is a current 2-D periodogram for the target, and the other is for the direct coupling components only. This periodogram can be obtained only when there is no targets. For example, if the OFDM radar system is equipped in a base station, and it collects the periodogram at dawn, only direct coupling components can exist in the periodogram. The performance of the proposed technique is examined through computer simulation. According to the results, the proposed method is more than 4 dB superior to the conventional method in the SNR range of -20 to 10 dB. If two periodograms are used for the CNN input, over 2 dB further improvement can be achieved.

System and signal model
OFDM radar system model considered in this paper is shown in Figure 1. The m-th transmitted signal vector is denoted by is a complex symbol generated via channel coding and digital modulation of the transmitted information. However, those processing is not important for radar signal processing and omitted here for simplicity. The vector signal is converted into a time domain signal through inverse FFT (IFFT) and transmitted after inserting a CP. The reflected signal from the targets is received and the CP is removed. Then, it is converted into frequency domain signal via FFT. The FFT output is denoted by = [ 0, , 1, , ⋯ −1, ] . and are different due to the time delay and the Doppler frequency of the reflected signal. By comparing and processing and , the targets are identified. (1) Every row of the matrix corresponds to the data on one subcarrier, whereas every column corresponds to the data on one OFDM symbol. It is assumed that the following parameters are known.  The subcarrier space is , and therefore the OFDM symbol duration is = 1/ .  The duration of the CP is .  The sampling rate after the IFFT is and = /  The carrier frequency is While transmitting, the receiver is active to pick up the reflected signal. It is important that the receiver is exactly synchronous to the transmitter, i.e., there must be no time or frequency offset. The received signal can be written as where ( ) , represents the ( , ) -th element of the matrix , and denotes the number of reflecting targets. (ℎ + 1) -th target has a distance ℎ which translates into a delay ℎ (= ℎ / 0 ) where 0 is the speed of light.
,ℎ is the Doppler frequency and ℎ is an unknown phase offset. The attenuation ℎ can be approximated by the point-scatter model [3].
where is the radar cross section. The second summation at the right hand side of (3) represent the direct coupling components, and the number of components is . Direct coupling components are caused by direct coupling between Tx and Rx antennas or circuits. Therefore, the time delays or equivalent distances of the direct coupling components are close to zero. To simulate such direct coupling, the equivalent distances are generated following the Weibull probability density function (PDF): and the equivalent radar cross sections are generated uniformly random. The all direct coupling components have zero Doppler frequency. The matrix ∈ × is white Gaussian noise. To remove the transmitted symbols in , element-wise division is performed to yield.
where ( ) , = (̃) , /( ) , . The radar problem is detection and identification of two sinusoid. The first exponential inside the summation in (5) contains the Doppler frequency and the second exponential has the time delay or distance. The radar cross section can be found from the magnitude. To separate and estimate the sinusoids for the targets, 2-D periodogram (magnitude square of discrete Fourier transform (DFT)) is used: where ∈ × is 2-D periodogram of and DFT size is × . Usually, and are chosen as integer multiples of and to improve estimation resolution.
is a window matrix generated by and are one-dimensional window vectors and we uses the Hanning window. If the target's range and Doppler frequency are limited within certain ranges, only a cropped region of periodogram is useful for target detection. Detecting and identifying targets corresponds to the detection of peaks in the periodogram. If a peak is found at indices (̂,̂), the target distance is ̂= If the subcarrier spacing and the OFDM symbol duration are designed to be small enough, the maximum unambiguous values can cover the target's distance and speed.

Proposed method
This paper focuses on detecting the number of the targets. First, we describe the conventional method and then the proposed method is explained.

Figure 2
Block diagram of conventional target detection As shown in Figure 2, the conventional method find all the local maxima first. Among them, those ones above a certain threshold are selected. In this procedure, only big peaks remain and small peaks are discarded. However, the big direct coupling components still remain and further process is required to remove them. One simple way is to neglect peaks around zero Doppler frequency. After removing direct coupling components, the remaining peaks are considered as the targets. Therefore, the number of targets is the number of remaining peaks.
However, during the zero Doppler removal procedure, the targets whose relative speed is close to zero, may also be discarded and not be detected as targets. This causes detection errors. In addition, since the optimal threshold is a function of SNR and noise variance of the reflected signal, determining optimal threshold in real field applications is rather difficult.

Proposed method
The proposed method predicts the number of target directly from the periodogram through CNN classifier. CNN is a famous deep learning technique that shows excellent performance especially in image classification. As shown in Figure 2, the periodogram can be an image and the radar problem is to find the peaks in the image. Therefore, it is expected that the CNN is very suitable for our radar problem. Figure 3 shows the block diagram of the proposed CNN classifier. The input signal is a 200x200 cropped periodogram. As mentioned previously, if the target's maximum range and speed is limited, we may search only a cropped region. As search range increases, the crop size also increases.

Figure 3 Block diagram of proposed CNN for target detection
The proposed CNN classifier is composed of 6 convolutional layers and 1 fully connected layer. The convolution filter size is 5x5 for every convolutional layer and the channel (or kernel) size is increased from 16 to 256. Each convolution layer also has batch normalization layer, Relu layer and max pooling layer. The last convolution layer's output is connected to a fully connected layer, and the final number of output is + 1. This CNN classifier can detect maximum + 1 targets, and the possible classes are '0' to ' + 1'. '0' means no target exist. The input or output of the CNN can be changed according to the OFDM signals, 2-D DFT size, and the detection range.
If the periodogram for the direct coupling components is available, the detection performance can be further improved. For example, if the radar system is equipped in a base station and is fixed in one place, the direct coupling components can be measured in the early morning when no target exists. To utilize this extra periodogram in the radar problem, we increase the input size of the CNN in Figure 3 to 200 x 200 x 2. Thus, two 200 x 200 periodograms become the inputs of the CNN. Beside the input size, the rest of the CNN structure is the same. Figure 4 shows an example input of this scenario. The left periodogram is from the direct coupling components and the right periodogram is normal periodogram containing both the targets and the direct coupling components.
The proposed CNN classifier does not need SNR estimation nor noise variance estimation, and also, any specific peak search algorithm is not needed. Hence, it is simpler to use in practice than the conventional technique [14][15][16]. The maximum number of target, , is 2, 4, and 8. At each iteration, the number of target is selected randomly from 0 to . For modeling the direct coupling components in (3), the number of direct coupling components is 20 ( ), and the parameters of the Weibull distribution are = 1 and = 1 in (5). Thus, 20 direct coupling components are generated with random effective distances, and in Figure 3, you can see the direct coupling components generated in this way. Due to the characteristic of the Weibull distribution, the effective distances are concentrated near zero.

Training the CNN classifier
For training the CNN classifier in Figure 3, total 50,000 periodograms are generated and used. The reflected target signals have random SNR from -20 dB to +30 dB. The mini batch size is 100 and training is performed for 20 epochs. Therefore, the total number of parameter updates is 10,000. The parameter optimization algorithm is Adam with learning rate 0.001. We will call 'T' for one input CNN (target), and 'T+D' for two input CNN (target + direct coupling). The parameters for each layer are summarized in Table 1 for 'T'. The total number of learnable parameters is 4,374,401+8193* . For 'T+D', since the input size increases to 200 x 200 x 2, the total number of parameters also increases to 4,374,801+8193* . , are 2, 4, and 8. As shown in the figures, as increases convergence time becomes longer. The reason is that as increases, so do the learnable parameters. At the end of the iteration, the losses are close to zero, which indicates that the training is completed well. Comparing 'T' and 'T+D', convergence speed of 'T+D' is slightly faster than 'T'.

Performance comparison
For performance evaluation of the proposed technique, new test signals are generated. For each periodogram, the number of targets is generated randomly from 0 to , but the SNRs of the targets are the same. The SNR is varied from -20 dB to +10 dB with 3 dB step. At each SNR, 10,000 periodograms are generated. The Figures 7  and 8 show the accuracies of the proposed technique for 'T' and 'T+D' respectively. As the SNR increases, the accuracy also improves. = 2 shows the best performance, i.e., the number of maximum targets has a big impact on accuracy. For the case 'T', the accuracy is below 0.9 at best. When = 8, the accuracy is only 0.45 at SNR=10 dB. In contrast, 'T+D' shows much better performance. When = 2, the accuracy at SNR=10 dB shows almost 1. Even for = 4 and = 8, the performance is much better than 'T'. Those results indicate that if the periodogram of the direct coupling components is used, much better target detection performance can be expected.