Xue Yao, Yu Liu, Zaichen Zhang, Xianxiang Yu, Guolong Cui

Abstract: This paper develops a new transmit beamforming for an integrated mechanical and electrical scanning dual-function radar-communication (DFRC) system. Differing from the related some works using beampattern sidelobe level to communication, we exploit the fact that transmit beamforming weight vector u k in direction θ and weight vector in direction - θ can achieve the same spatial power distribution, and formulate a new transmit beamforming vector design problem accounting for some extra sidelobe level constraints. By doing so, the number of the transmit beamforming weight vectors and the computing demand in the multi-user communication (MUC) scenario can be reduced. Finally, the numerical examples are designed to verify the effectiveness of the proposed design strategy in comparison with the existing method.

Keywords: dual-function radar-communication; transmit beamforming method; multi-user communication

1 Introduction

There have been increasing demands for systems with both communication and radar sensing capabilities, on emerging platforms such as unmanned aerials vehicles and smart cars [1,2]. At present, the research on the pre-mentioned study territory can be classified into two categories: 1)radar-communication coexistence (RCC). It spurred innovation in developing two separate systems that allow the coexistence of radar and communication systems. The two separate systems operate in the same frequency bandwidth while preventing or minimizing mutual interference. 2) dual-function radar-communication. Instead of using two separate systems, it is possible to develop a system which shares hardware and signal processing modules. In this way, reduced cost, smaller size, lighter weight and better spectrum efficiency can be achieved.

A comprehensive review of RCC techniques has been provided in [3]. It classified the RCC techniques into three categories: 1) radar centric spectrum sharing (RCSS)[4,5], 2) communication-centric spectrum sharing (CCSS)[6-8], 3) coordinated design spectrum sharing (CDSS)[9-10].

In general, the DFRC techniques can be classified into the following categories: 1) information theory for the DFRC [11,12], 2) temporal and spectral processing [13-23], 3) spatial processing [24-35], 4) index modulation [36-39].Herein, we consider the third technique which is the spatial processing.

Currently, multiple input multiple output(MIMO) radar and MIMO communication have drawn much attention. Multiple antennas provide higher degrees of spatial freedom. The similarity between the two technologies provides possibility for the combination of MIMO radar and MIMO communication. In [24,25], an array probing signal is designed to synthesize radar and communication waveforms towards different directions. However, the method in [24,25] only considered waveform synthesis at the main beam direction but cannot suppress the sidelobe of the radar transmit beampattern. The work in [26] extended the method of [24,25] to designing the array probing signal to match the radar transmit beam pattern and minimize the interference power at communication receivers. However, the techniques in [24-26] only minimize the interference power, do not consider the signal-to-interference-plus-noise ratio (SINR) at each user, which is the quantity dictating the communications rate. In [27] the authors studied transmit beamforming in DFRC systems with multiple receivers, in which the communication waveform was utilized as a radar transmit waveform. In such a dual-function system, the available degrees of freedom for the MIMO radar waveform was equal to the number of communication users. This resulted MIMO radar cannot utilize its full degrees of freedom when the number of users was smaller than the number of antennas. In [28] the authors designed a transmit beamforming to optimize both the radar transmit beampattern and the SINR at the communication users. Unlike [27],they precoded individual communication and radar waveforms jointly, allowing to extend the MIMO radar waveform degrees of freedom to its maximal value.

In [29-31] the authors studied methods to design range-angle-dependent beampatterns using frequency diverse array (FDA).

Sidelobe manipulation methods are studied in [32-35]. A method for information embedding using distinct sidelobe levels (SLLs) towards the intended communication receiver has been reported in [33]. During each radar pulse, the communication receiver detects the SLL and interprets the associated information symbol. It is difficult to design multiple transmit power distribution patterns with the same mainlobe using time modulated arrays. This difficulty is attributed to the fact that the optimization criterion involved in the design is highly nonlinear and computationally demanding. Another method using waveform diversity in tandem with sidelobe control was reported in [34]. Multiple simultaneously transmitted orthogonal waveforms were used for embedding a sequence of several bits during each radar pulse. Two weight vectors were designed to achieve two transmit spatial power distribution patterns, which have the same main radar beam,but differ in sidelobe levels towards the intended communication receivers. Although the proposed technique claimed that it was able to deliver information to multiple communication directions outside the mainlobe of the radar. It can only transmit the same communication information to multiple communication directions. The weight vectors design realized broadcast communication(BC) rather than MUC. The result is attributed to the fact that the optimization criterion involved in the transmit beamforming design is only two different cases. In [35] the authors extended the BC to MUC by providing a new transmit beamforming method. It means that the proposed system can transmit different communication symbols to multiple communication directions. The same signaling strategies in [34] and[33] were adopted. If N users locate at arbitrary directions within the sidelobe legion,JMUC=2Ntransmit beamforming weight vectors should be designed by using the signaling strategies in [34]and=2NLB weight vectors should be designed by using the signaling strategy in [33](during each radar pulse repetition time, the communication information symbol of LBbits is transmitted).

In order to take full advantages of the low cost of mechanical scanning and the flexibility of electrical scanning, special attention was paid to concepts mechanically moving the complete antenna and electronically scanning the beam with fixed antenna [40-42].

In this paper, a new computionally efficient method is proposed for appropriately designing the transmit beamforming weight vectors needed in MUC which is applicable to a DFRC system.Based on the fact that the transmit beamforming weight vector ukin direction θ and weight vector u*kin direction -θ can achieve the same spatial power distribution, a new transmit beamforming vector design problem accounting for some extra sidelobe level constraints is formulated. By doing so, the number of the transmit beamforming weight vectors and the computing demand in the MUC scenario can be reduced.The same signaling strategies in [34] and [33] are adopted.

The paper is organized as follows. The signal model is provided in Section 2. The new transmit beamforming method is presented in Section 3. Supporting simulation results are presented in Section 4. Conclusions are drawn in Section 5.

2 Signal Model

In this section, we develop a DFRC signal model for MUC scenario using transmit beamforming weight vectors.

As shown in Fig. 1, we consider a DFRC system equipped with one dual-function transmit array, one rotating table, one radar receive array and multiple (more than one) communication receive arrays. The transmit array consists ofMttransmit antennas. The radar receive array consists of Mrreceive antennas. The rotating table can move the transmit array and radar receive array mechanically. Without loss of generality,we assume that both the radar transmit and receive arrays are closely spaced to each other such that a target located in the far-field would be at the same spatial angle with respect to both arrays. The primary function of the DFRC system is the radar operation. It means the communication function as a secondary task without affecting the primary function. The transmit array is used to focus the transmit power within the main beam where the radar operation takes place. The Mt×Pmatrix of the baseband representation of the signals at the input of the transmit antennas is given by

Fig. 1 MUC scenario

3 Transmit Beamforming Method

In this section, we introduce the computationally efficient transmit beamforming method in MUC scenario. Initially, we review the existing weight vectors designs in [35]. Subsequently, a new computionally efficient method is proposed for appropriately designing the transmit beamforming weight vectors needed for implementing the DFRC system.

3.1 Existing Weight Vectors uk Design in MUC Scenario

For the general case when the radar operation takes place in a spatial sector θ =[θmin,θmax], one way to design the transmit beamforming weight vectors ukis to minimize the root-mean square error (RMSE) between a desired transmit power radiation pattern and the actual one under the constraints that the sidelobes be bounded by certain pre-defined levels. This can be formulated as the following optimization problem. The formulation described in Eq. (4) design each transmit beamforming weight vector separately and, therefore, enable design of an arbitrary number of transmit beamforming weight vectors.

3.2 Computationally Efficient Weight Vectorsuk Design

Because the proposed weight vectors design method in [35] is highly computationally demanding. Based on the well-knowed fact that the weight vector ukin direction θ and the weight vector u*in direction -θ can achieve the same spatial power distribution, a new transmit beamforming vector design problem accounting for some extra sidelobe level constraints is formulated. By doing so, the number of the transmit beamforming weight vectors and the computing demand in the MUC scenario can be reduced.Note that both the solution u to optimization problem (6) and it’s complex conjugate u*will be used. Because mainbeam of the proposed method must be located symmetrically along the normal, the low cost of mechanical scanning and the flexibility of electrical scanning are considered. Furthermore, an electro-mechanical beam is designed in the DFRC system. The rotating table can change the direction of the mainbeam.

4 Simulation Results

We consider a uniform linear transmit array consisting of Mt=10 antennas spaced half wavelength apart. In addition to the radar operation within the mainbeam [ -10°,10°]. In all simulation example, we confirmed MUC.

4.1 Example 1: Existing Weight Vectors Design in MUC Scenario

We assume that the radar operation requires the power level emitted in the sidelobe areas to be at least 20 dB lower than mainlobe. We further assume that, during each radar pulse repetition time, the communication information symbol of LB=2bits is transmitted towards the two communication receivers located in directions θ1=-50°and θ2=30°. For the sake of presentation, the existing weight vectors design in MUC scenario [35] is shortened to EX-WVD.

If we adopt the signaling strategy in [34],JMUC=22=4transmit weight vectors are designed by solving optimization problem (4)4 times. The parameters==0.01(-20) dB or==10-4(-40) dB. The SLL is 0 .01 that represents the transmitted information bit is1 and the SLL is 10-4that represents the transmitted information bit is 0. There are 22=4 permutations for transmitting a information bit to two communication receivers. Fig. 2 shows the transmit power distribution patterns associated with all transmit weight vectors versus angle. We observe that, as expected, all transmit weight vectors have almost the same pattern within the mainbeam, which implies that the radar operation will not be affected if the waveform is radiated via either transmitbeam. Note that, the beam patterns be marked black are similar to the transmit power distribution patterns metioned in[34]. The same information bits will transmitted to the multiple communication receivers.

Fig. 2 Beampatterns associated with EX-WVD using signaling strategy in [34]

Fig. 3 Beampatterns associated with EX-WVD using signaling strategy in [33] (c1:00)

Fig. 4 Beampatterns associated with EX-WVD using signaling strategy in [33] (c1:01)

Fig. 5 Beampatterns associated with EX-WVD using signaling strategy in [33] (c1:10)

Fig. 6 Beampatterns associated with EX-WVD using signaling strategy in [33] (c1:11)

4.2 Example 2: Computationally Efficient Weight Vectors Design in MUC Scenario

In this example, the optimization problem (6) is solved to obtain the transmit weight vectors.Compared with example 1, we only solve the optimization problem half times to get all the transmit weight vectors. Similar to example 1, we assume that main radar operation takes place within the sector θ =[-10°,10°], and two communication receivers are located in directionsθ1=-50°and θ2=30°, and the power level transmitted in the sidelobe areas is at least 20 dB lower than mainlobe. For the sake of presentation, computationally efficient weight vectors design in MUC scenario is shortened to CE-WVD.

Fig. 7 Beampatterns associated with CE-WVD using signaling strategy in [34]

We observe that, the beampatterns associated with designed transmit weight vectors and their complex conjugate are symmetic about normal.

Fig. 8 Beampatterns associated with CE-WVD using signaling strategy in [33] (c1:00)

Fig. 9 Beampatterns associated with CE-WVD using signaling strategy in [33] (c1:01)

Fig. 10 Beampatterns associated with CE-WVD using signaling strategy in [33] (c1:10)

Fig. 11 Beampatterns associated with CE-WVD using signaling strategy in [33] (c1:11)

The red ones represent the designed beampatterns and the blue ones represent the beampatterns associated with the complex conjugate of designed weight vectors.

We also observe that, the beampatterns shown in Fig. 8 and Fig. 11 are symmetic about normal. The same situation between the beampatterns shown in Fig. 9 and Fig. 10.

The CPU (Inter Core i5-6200U@2.3GHz and RAM 8GHz) time of all the pre-metioned methods is shown in Tab. 1.

Tab. 1 Computation complexity of two methods

4.3 Example 3: BER Performance

In this example, we use the setup in Example 1 and Example 2 to investigate the performance of the proposed computationally efficient transmit beamforming mehtod. The bit error ratio (BER)criteria is adopted. Two independent sequences of 106symbols (two bits each) unencoded are transmitted to two communication receivers. Both communication receivers are assumed to be equipped with 10 receive antennas arranged in a uniform linear transmit array where the positions of elements are half wavelength apart. The BERs versus the signal-to-noise ratio (SNR) for the proposed transmit beamforming method and the existing method is shown in Fig. 12.

Fig. 12 BER versus SNR

Clearly, the performance of proposed transmit beamforming method is similar with the existing transmit beamforming method. Note that the computation cost of the proposed method is smaller than existing one. The two signaling strategies in [34] achieve superior BER performance as compared to the signaling strategy in [33].

4.4 Example 4: Probability of Intercept

In this example, we test the security of the communication process and show that the proposed transmit beamforming method prevents communications interception from directions other than the intended ones. To this end, we calculate the BERs versus transmission angle for all methods tested. We use the same set up as in Example 3,except that the SNR is fixed at 0 dB.

Fig. 13 depicts the BERs versus angle for the communication receiver 1 located inθ1=-50°, which shows that the BER assumes high values for directions other than the intended communication directions in all cases. This means that the proposed transmit beamforming method has inherent security against information interception from directions other than the communication directions.

Fig. 13 BER versus angle (c1)

The performance of proposed transmit beamforming method is similar with the existing transmit beamforming method. Note that the computation cost of the proposed method is smaller than existing one. It can be also confirmed from the figure that the two signaling strategies methods in [34] have a better BER towards the communication directions as compared to the signaling strategy method of [33]. Fig. 14 depicts the BER versus angle for the communication receiver 2 located in θ2=30°, the similar conclusions can be obtained.

Fig. 14 BER versus angle(c2)

4.5 Example 5: DOA Estimation Performance

This example evaluates the DOA estimation performance of the radar operation. We assume two targets located in the far-field at angles 3°and 5°, respectively. The target reflection coefficients are assumed to be constant during each radar pulse, but change from pulse to pulse and are drawn from a normal distribution. The number of radar receiver array elements is Mr=50. The number of pulses is 1 00. The MUSIC algorithm is used to perform DOA estimation for the proposed two transmit weight vectors design methods. The two targets are assume to be resolved provided

is satisfied [43]. The RMSE and the probability of target resolution are averaged over 1000 independent runs. Figs. 15-16 show the RMSE versus SNR and the probability of target resolution versus SNR, respectively. We can observe that the two signaling stragies in [34] outperform the signaling stragy in [33]. We also observe that the performance of proposed transmit beamforming method is similar with the existing transmit beamforming method. Note that the computation cost of the proposed method is smaller than existing one.

Fig. 15 RMSE versus SNR

Fig. 16 Probability of target resolution versus SNR

5 Conclusion

A new computationally efficient transmit beamforming design method for MUC was introduced,which utilized sidelobe control of the transmit beamforming in tandem with waveform diversity in a DFRC system. Based on the fact that transmit beamforming weight vector ukin directionθ and weight vector u*kin direction -θ can achieve the same spatial power distribution, a new transmit beamforming vector design problem accounting for some extra sidelobe level constraints was formulated. By doing so, the number of the transmit beamforming weight vectors and the computing demand in the MUC scenario can be reduced without a poor performance. The communication performance was investigated by the BER versus SNR and the probability of intercept, simulation results show that the performance of this computationally efficient weight vectors design method is basically the same with the common weight vectors design method in MUC.The radar operation is basically unaffected because the transmit power distribution patterns with the same mainlobe in this paper. As an extension of the proposed transmit beamforming design method, it is of interest to study the signaling strategy with quadrature amplitude modulation(QAM).