Location-Based Hybrid Precoding Schemes and QoS-Aware Power Allocation for Radar-Aided UAV–UGV Cooperative Systems

Unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) complement each other, promising a variety of benefits for unmanned cooperative systems. When infrastructures for communication are unavailable, such as disaster relief and patrol mission in sparsely populated areas, UGVs can be controlled to go to the esignated areas with the aid of a UAV. Specifically, the UAV hovers over the UGVs, sending commands to the UGVs and obtaining location information from the UGVs. In this paper, we consider integrating millimeter wave communication and UAV–UGV cooperative system. For high mobile unmanned cooperative systems, we develop two joint radar-aided hybrid precoding schemes, which are suitable for a fully connected (FC) hybrid precoding structure and partially connected (PC) hybrid precoding, respectively. Specifically, an effective hybrid precoding scheme is first proposed by using location information to jointly design hybrid precoding and power allocation. Moreover, we also derive the radar parameter estimation problem Cramér-Rao lower bound (CRLB). In order to ensure the minimum quality-of-service (QoS) of UGVs, we propose a QoS-aware power allocation scheme based on the difference-of-two-convex-function (D.C.) programming. Finally, a heuristic hybrid precoding design algorithm, where the analog precoding matrix is usually implemented by low-resolution phase shifters (PSs), is proposed based on antenna dynamic grouping and radar parameter acquisition, with the aim of maximizing the sum-rate of the UAV–UGV cooperative systems. Extensive computer simulation results indicated the validity of the proposed radar-aided location-based hybrid precoding schemes in the UAV–UGV heterogeneous cooperative system.


I. INTRODUCTION
Research on unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs), which aim at meeting diverse emerging application requirements while solving various problems in case of emergency such as communication failure, rescue effort, and post-disaster reconstruction, has The associate editor coordinating the review of this manuscript and approving it for publication was Hasan S. Mir. recently received extensive attention from both academia and industry [1], [2]. However, due to many indeterminate factors involved in emergency distinctive needs, the separate division of labor between UAV and UGV unavoidably reveals its own insufficiencies [3]. To realize their full potential, UAVs and UGVs can cooperate with each other and complement each other's strengths. Specifically, UAV equipped with a wideangle camera can be rapidly deployed to a designated area and search for targets in a wide range, but the small payload VOLUME 10, 2022 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ and high power consumption limit its capabilities for many applications. On the contrary, UGV with a limited field of view can approach the desired location to accomplish complex missions due to its large payload. However, it is difficult to control from a macroscopic point of view. To address the shortcomings of the above homogeneous system, the UAV-UGV heterogeneous cooperative systems have aroused significant attention [4]. Despite the UAV-UGV cooperative system's potential prospects, substantial research work is needed to actualize the advantages offered by the heterogeneous cooperative system. To satisfy the requirement for exceedingly high data rates and low delays, millimeter wave (mmWave), as one of the most crucial characteristics of 5G mobile networks, is projected to enable ultra-wideband connection with extremely high stability and low delay to improve data rates [5]. Nevertheless, in the mmWave band, the signal suffers from severe propagation loss and and rain-attenuation [6]. Fortunately, more antennas can be deployed in the same size space as compared to conventional communication, because of the shorter wavelength of the mmWave band. Large-scale antenna array can realize highly directional beamforming while compensating for the serious path loss of the mmWave signals by the generated beamforming gain [7]. Consequently, the integration of mmWave wireless communication and the UAV-UGV cooperative system could satisfy the requirement of high data rate transmission in the future. The challenge of combining mmWave massive MIMO systems and UGV-UAV cooperative systems is to design efficient beamforming techniques to reduce the cost and power consumption while weighing system hardware limitations and system performance [8].
Beamforming with multiple data streams, namely precoding, is typically utilized to further enhance the spectral efficiency (SE) of millimeter wave systems. While the principle of precoding is independent of carrier frequency, signal processing in mmWave communication systems is constrained by a number of practical limitations. For instance, fully digital precoding (FDP) is generally used in traditional MIMO systems, which needs one private radio frequency (RF) chain (incorporating expensive digital-to-analog converter) perantenna elements [9]. Although FDP can guarantee the best performance of mmWave MIMO systems, it is unrealistic from the perspectives of cost and energy consumption in the millimeter-wave band [10]. One approach to solve the aforementioned involves the use of hybrid precoding (HP) solutions. Specifically, a low-dimensional digital precoder is used at the baseband to ensure the performance of the system, and then a few RF chains are used to connect the high dimensional analog precoder (analog domain) controlled by a phase shifter (PS) network to reduce the hardware cost. Two typical HP schemes have been extensively studied for mmWave MIMO systems. Depending on the connection method, the existing HP schemes can be split into fully-connected hybrid precoding (FC-HP) architecture as shown in Fig. 4(a) and partially-connected hybrid precoding (PC-HP) architecture as depicted in Fig. 4(b). For the FC-HP architecture, each RF chain is linked to all antennas via PSs. A low complexity hybrid precoding algorithm on the basis of orthogonal matching pursuit (OMP) was developed by using the sparsity of the millimeter wave channel [11]. However, the behavior of the algorithm is unsatisfactory when the amount of RF chains is fewer than twice of the number of data streams. At the same time, for multiuser mmWave systems, a low-complexity HBF method named phased-ZF (PZF) was presented in [12], which designed an analog precoder by extracting the phase of the conjugate transpose of the cascaded downlink channel and designed a digital precoder through a zero-forcing (ZF) algorithm on the effective channel. The difference with the above problem is that it assumes that the amount of RF chains is the same as the amount of data streams.
However, there is also a problem in FC-HP structures. In order to achieve accurate phase control in RF domain, each RF chain needs to be linked to all antenna elements through PSs. The presence of a significant large number of phase shifters will cause huge power consumption. This has caused a variety of research into the PC-HP structure, so as to offer a compromise between performance and power consumption. Compared with the FC structure, the main difference is that each RF chain of the PC structure can only be attached to a subgroup of antenna elements. The PC-HP architecture was first proposed in [13]. Moreover, a low complexity HP algorithm according to successive interference cancellation (SIC) was developed, and the complexity of this algorithm is only about 10% of the OMP algorithm in [11]. In [14], both FC and PC precoding structures are considered. The hybrid precoding problem is divided into two sub-problems of digital precoding and analog precoding, and the principle of alternating minimization (AltMin) is used to alternately optimize the digital precoder and analog precoder, whereas the algorithm requires the digital and analog precoder to be updated in each iteration, resulting in significant computational complexity. The abovementioned hybrid precoder design usually assumes employment of highresolution PSs, which requires complex hardware design and has heavy power consumption at mmWave systems. To solve this problem, several works have studied the design of a hybrid precoder with low-resolution PSs for FC-HP architecture and PC-HP architecture [15]- [17].
High-speed mobility (HSM) is another challenging issue that arises in UAV-UGV cooperative systems. Despite the fact that the mmWave has been extensively utilized in static scenes, using it in mobile networks, in which the transmitting/receiving nodes are likely to move, and the channel might have complicated structures, is a significant challenge [18]. To the best of our knowledge, research on precoding design for HSM problems in the mmWave Multi-User Multiple-Input Single-Output (MU-MISO) communication systems is still in its early stages. Furthermore, power allocation and precoding are two approaches for effective cochannel interference management, thereby improving multiuser wireless network performance [19]. However, because joint hybrid precoding and power allocation optimization are frequently 50948 VOLUME 10, 2022 tricky, most known studies dissociate this coupled problem into two separate subproblems. At the same time, the concept of integrated sensing and communication (ISAC) is put forward in the literature [20], which can make full use of spectrum resources by jointly designing a communication system and radar system. Mobile networks are changing from pure communication networks to networks with combined communication and radar abilities. By using traditional radar's tracking, localization and object recognition functions, perception information obtained by radar can be used to assist communication and establish a more stable and effective communication link.
As a result of the aforementioned observations, we propose a location-based hybrid precoding strategy for the mmWave MU-MISO system under radar-aided UAV-UGV cooperative systems. Specifically, two main schemes are developed in this paper. First, based on the motion parameters acquired by radar, an HP scheme with an FC structure is designed, with joint precoding and power allocation to optimize the sum-rate while guaranteeing the quality-of-service (QoS) requirement of each UGV at the same time. In addition, the Cramér-Rao lower bound (CRLB) of the motion parameters estimation problem is deduced. Second, with the aid of a radar system, an HP algorithm with a PC structure is proposed to optimize the sum-rate by dynamically grouping antennas. The major contributions of our work are summarized as follows: • For the proposed UAV-UGV cooperative system, a radar-aided mmWave communication strategy is presented, in which one UAV can serve several UGVs.
• With the assistance of the radar system, an efficient hybrid precoding scheme is developed for FC structure and PC structure, respectively, to optimize the sum-rate performance of the UAV-UGV cooperative system.
• Taking advantage of radar positioning, firstly, the nonconvex joint hybrid precoding and power allocation optimization problems involved in the FC structure hybrid precoding scheme are modeled as a difference-of-twoconvex-function (D.C.) programming problem, so as to optimize the sum-rate while meeting the minimum QoS requirements.
• For the purpose of reducing system power consumption, we further present a novel heuristic hybrid precoding algorithm based on a dynamic antenna grouping for PC architecture. Due to the use of motion parameters obtained by radar, the proposed algorithm complexity is further reduced.
• In terms of positioning error, the positioning accuracy is evaluated using the upper bound of positioning error The remainder of this paper is laid out as follows: In Section II, we present the system model of the proposed radar-aided UAV-UGV cooperative system. Section III describes the signal processing of the radar system. In Section IV and Section V, the detailed description of our proposed radar-aided FC-based and PC-based hybrid precoding scheme is given, respectively. Section VI provides the extensive simulations results. A detailed conclusion of our paper is given in Section VII.
Notation: Throughout this paper, we will use the following notation: Uppercase boldface letters represent matrices and lowercase boldface letters denote vectors. I N represents the N × N identity matrix. A represents the L2-norm of A. a p stands for the p-norm of a. |A| denotes the determinant of A, while |A| represents the cardinality of set A.â denotes the estimator of a, and Re{a} represents the real part of a, in whichâ and a may be a scalar, vector, or matrix. A T represents the transpose of A, and A H denotes the conjugate transpose of A. Lastly, ∇f (x) denotes the gradient of function f (a). The inner product of a and b is represented as

II. SYSTEM MODEL
In this section, we describe a radar-aided hybrid precoding system and channel model that takes user mobility and largescale fading into account.

A. SYSTEM OVERVIEW
The schematic diagram is illustrated in Fig. 2, in which a UAV loaded with a mmWave base station (BS) and monostatic radar hovers over UGVs. Specifically, for the communication function of the UAV, the UAV-BS has N t transmit antennas and Z RF chains, which send Z data streams to Z UGVs with a single antenna for receiving communication VOLUME 10, 2022 information, respectively. In addition, the number of RF chains is normally much smaller than the amount of antennas in the actual system, i.e., Z N t . In order to enable the radar sensing capability of the UAV, the monostatic radar loaded on the UAV is set up separately with N r receiving antennas in addition to sharing N t transmitting antennas of the UAV-BS [21]. Further, in the proposed system, due to the limitation of the RF chain, the maximum number of transmission streams is limited to Z . We assume that each scheduled UGV only allocates one data stream for transmission. s ∈ R Z represents the vector of transmitted symbols.
To establish connectivity, the UAV first periodically scans the space until it is recognized by UGVs. In addition, we suppose a UAV communicates with Z UGVs and simultaneously locates them with radar. The z-th UGV's and UAV's horizontal positions is defined as Consider a multiuser mmWave downlink MISO system where a UAV-BS with N t antennas communicates to Z singleantenna UGVs. Each antenna of the UAV-BS is marked separately as 1, 2, . . . , N t , and T = {1, 2, . . . , N t }. Each of the Z UGVs is labeled, respectively, as 1, 2, . . . , Z , and U = {1, 2, . . . , Z }.

B. LARGE-SCALE FADING
The z-th UGV's horizontal distance from the UAV is defined as We utilize a Low Altitude Platform (LAP) that was established in [22]. The air-to-ground (ATG) path loss between the z-th UGV and the UAV could be expressed in dB as where with a and b representing the Sigmoid-curve (S-curve) parameters, and η LoS and η NLoS separately denote the excessive path loss in the conditions of line-of-sight (LoS) and non-line-of-sight (NLoS). h is the height of the UAV, f is the system frequency, and d z is the practical distance between the z-th UGV and UAV. c is the velocity of light.

C. COMMUNICATION CHANNEL MODEL
We consider a high path-loss propagation setting with a finite amount of scatters, assuming that each scatter contributes just one propagation path. For this reason, we utilize Saleh-Valenzuela (SV) channel model, as illustrated in [12]. Eventually, the z-th user's channel vector H z can be formulated as where L z is the amount of all propagation paths and α z,l is the complex gain of the l-th scattering cluster, whereas θ z,l is its angle of departure (AOD). Eventually, the vector a t (θ) denotes the normalized transmit array response vector.
Although the algorithms and results deduced in the rest of this paper are effective in any antenna array configuration, in this paper, we assume that an M -element uniform linear array (ULA) is utilized at UAV-BS. The transmit array response vector a t (θ) can be defined as where k = 2π λ represents the wavenumber of the signal, and d denotes the inter-antenna space.

D. HYBRID PRECODING
In our proposed hybrid precoding system, let µ := (µ 1 , µ 2 , . . . , µ z ) T represent the transmitted power vector, each component µ z of which denotes the transmitted power of z-th UGV, σ 2 z represents the noise power. Observing the comparable expressions in [12], we are committed to the design of digital and analog precoders. Firstly, the transmitted symbols of Z UGV are precoded by a digital precoding matrix It is worth noting that the amplitude and phase adjustment is workable for the digital precoder F; however, due to hardware constraints, phase modification can only be performed on the analog precoder V. Consequently, each element of V is normalized to meet the v i,j = 1 where v i,j represents the magnitude of the (i, j)th entry of V . Moreover, analog precoding is performed through the use of low-resolution PS in practical implementation, each with quantized phases controlled by B bits. Each entry of the analog precoder can be represented V and F are related through the power constraints,i.e., VF 2 F = Z . Let y = [y 1 , y 2 , . . . , y Z ] T represent the received signal of Z UGVs, and the received signal vector of the z-th UGV can be defined as where s z , z = 1, . . . ., Z , represents the transmit symbol of the z-th UGV. All transmit symbols are individual across the UGVs, E[ss H ] = P Z I Z where P denotes total transmit power of the UAV-BS. H z , z = 1, . . . , Z , denotes the channel between the the z-th UGV and UAV. n z stands for the complex Gaussian noise (i.i.d.), which is presumed to be circularly symmetric Gaussian with variance σ 2 z .
To simplify the subsequent symbolic representation, we denoted by g H z the effective analog precoding gain of the z-th UGV,i.e., Furthermore, the signal-to-interference-plus-noise ratio (SINR) of the z-th UGV can be defined as The resulting achievable rate of z-th UGV is represented as Finally, the sum-rate of the proposed UAV-UGV cooperative system can be calculated as

III. SIGNAL PRECODING AND DECODING OF THE RADAR SYSTEM
In this section, a radar system for the auxiliary mmWave communication system to acquire angle parameters is elaborated.

A. RADAR PRECODING SYSTEM
In order to determine the status of the UGV, the monostatic radar transmits a multibeam signal s(t) ∈ C Z , i.e., where s z (t) denotes the signal pointing to the z-th UGV. We suppose the radar signal s z (t) is emitted by using an uniform steering vector a(φ z ), which is formulated by where φ z is the angle of the z-th UGV in the targeted direction of the UAV. The receive uniform steering vector can then be represented in the same manner. The emitted signal is reflected back by Z UGV. Then, the roundtrip echo is captured by the sensing detector. From the UAV perspective, the channel for z-th UGV and UAV will be modeled as where G a = √ N t N r denotes the antenna array gain. b(θ z ) represents the received uniform steering vector, meeting b(θ z ) = a(θ z ), because θ z is the practical angle of the UAV designated to the z-th UGV. Additionally, the parameters γ z , ω z , and β z represent the time delay, Doppler spread, and reflection damping coefficient related to z-th UGV, respectively.
Eventually, the received echo r(t) ∈ C N r is defined as whereñ(t) represents the complex Gaussian noise vector, and P is a precoding matrix whose z-th column is represented as Considering the characteristics of the large mmWave MIMO system, the array response vectors a(θ) for various angles θ are asymptotically orthogonal [23], i.e., Benefiting from this, the UAV can identify the echoes reflected back from different UGVs, i.e., r(t) = [r 1 (t), · · · , r Z (t)] H . More specifically, after receiving all the reflected signals from the UGVs, the UAV will perform matched filtering with a group of emitted signals, and finally, the received echo from the z-th UGV can be denoted as: where δT represents the frame duration. γ and ω represent the time delay and Doppler shift, respectively. Further, it is worth noting that after matched filtering the estimates of the signaling delay and Doppler shift associated with the corresponding UGVs can be derived, denoted asγ z andω z , respectively. Moreover, the filtered complex Gaussian noise vector can be expressed as When the corresponding delay and Doppler shift are estimated, a sample of the echo signal from the z-th UGV can be derived by where p z represents the allocated transmit power to the z-th UGV, and G t denotes the signal-to-noise ratio (SNR) gain derived after matched filtering, which is the same as the energy of the emitted signal.

B. CRLB OF THE TIME DELAY IN SIGNAL PROPAGATION
We suppose that the radar-equipped UAV emits signals to search for UGVs. Once detected, the signals return within a short time period. The discrete signal N samples received are denoted bŷ s = s( T − τ ) + n , for = 0, 1, · · · , N − 1, (20) where T represents the frame duration of the -th and ( + 1)-th discrete samples. The emitted signal VOLUME 10, 2022 s( T − τ ) suffers a time delay τ before it is received by the UGV. n denotes the complex Gaussian noise.
For a given received signalŝ = {ŝ } =0,1,··· ,N −1 , its posteriori probability is defined by The maximum a posteriori (MAP) estimation expressed aŝ For the sake of simplification, we consider using logarithmic probability for maximum likelihood (ML) estimation: where p(ŝ|τ ) represents the multiple Gaussian distribution as follows By analyzing Equation (24), the ML estimation problem (23) can be equated to the problem of minimizing the Euclid's distance between the emitted signal and the echo signal as follows: Since |s( T − τ )| 2 denotes the constant associated with τ , the estimation ofτ is represented bŷ In the actual situation, the higher the signal sampling frequency, the smaller the variation of the time delay. Therefore, the mean value of N samples can be used to approximate the time delay, i.e.,τ avg = 1 N N −1 =0 τ . Then, we examine the CRLB of the time delay with complex Gaussian noise. Through the observation ofŝ, the CRLB of the time delay estimation can be expressed as [25] VAR(τ avg ) ≥ σ 2 According to the analysis of Equation (28), the CRLB is affected by noise power. The positioning accuracy can be enhanced by improving the SNR. Observing Equation (2), the function related to the distance between the UAV and UGV can be used to measure the positioning accuracy.

IV. RADAR-AIDED FC-BASED HYBRID PRECODING SCHEME
In this section, first, we discuss the FC-based hybrid precoding design for the radar-aided UAV-UGV cooperative systems. Then, the sum rate of the UAV-UGV cooperative system is jointly optimized by D.C. programming, combined with FC-based hybrid precoding and power allocation.

A. OPTIMAL ANGLE ESTIMATION
Based on the received signal in Equation (19), the monostatic radar carried on a UAV has the ability to infer the angle parameters and reflection coefficients [26]. The reflection damping coefficient β z is given by where ζ denotes the radar cross section (RCS) [27], and d z represents the roundtrip distance from the z-th UGV. The delay of the radar echo γ z can be calculated by where c is the signal propagation speed. Further, the estimate of β z can be easily derived aŝ Substituting Equation (31) into Equation (19) and using standard mathematical manipulation, we obtain (32) whereθ z is the predicted angle. Then, our goal is to maximize the likelihood function p(r z |θ z ). To determine the number of the transmit antennas, we can use N t discrete angles to represent the possible values of θ z , expressed as = π N t , 2π N t , · · ·, π . To simplify the estimation process, of maximum likelihood function p(r z |θ z ) by selecting the values approximate to the predicted angleθ z in the set .
Eventually, from the viewpoint of ML estimation, the likelihood maximization of the likelihood function can be calculated as follows: By solving the above equation, we can obtain the optimal estimated angleθ z , for z = 1, .., Z . Furthermore, these optimal angles will be used to construct the analog precoding matrix in mmWave MIMO systems with FC-HP structures.

B. ANALOG PRECODER DESIGN
The measurement scenario is shown in Fig. 3. At the i-th moment, we use p U i ∈ R 2 with altitude h represent the position of UAV and p G i ∈ R 2 to denote the positon of UGV. Further, it is assumed that the height of the UAV is constant during the flight. The linear motion is assumed over the estimation period for both UAV and UGV [28]. From location p U i , the UAV moves in a linear trajectory with known velocity v U i ∈ R 2 . Then, the returned pilot is received at another location p U j . According to the Nyquist sampling theorem, we assume that the channel is sampled by the pilot at a rate not less than twice the maximum Doppler shift, i.e., 1 T p ≥ 2f D , where T p denotes the time spacing between two adjacent pilots, and f D is the maximum Doppler frequency. Using this assumption, the signal information can be fully transmitted between the UAV and UGV. The propagation speed of beam is a constant c.
We denote the distance between a UGV and a UAV by d ug i at the i-th instant, i.e., The ideal roundtrip distance traveled is given by Assuming the UAV is moving in a linear trajectory, the position of the UAV at the j-th instant is represented by where v U i =ṗ U i is the unknown linear velocity of the UGV. When the echo signal is received, the UGV's position at the j-th instant is Once the location parameter at the i-th moment p is acquired, the predicted actual angle θ z,i of the z-th UGV at i-th moment with respect to UAV is denoted as We assume that the speed of the UGV remains constant for a certain time, and the predicted position at the j-th moment is represented asp where v G z,i is the speed of the z-th UGV at the i-th moment. According to the ML estimation theory shown in Equation (33), the optimal angleθ z can be found by maximizing the likelihood function p(r i |θ z ).
Based on the channel model adopted in [12], the analog precoding matrix of the FC-HP structure can be denoted by where each element is designed as

C. DIGITAL PRECODER DESIGN
In the Section IV-B, the analog precoder can be obtained by taking advantage of the positioning information acquired by the radar system. Next, in order to eliminate interference between different UGVs, a digital precoder can be constructed. In simple terms, the digital precoding matrix is designed into the pseudo inverse of the effective channel using the block zero-forcing (BZF) algorithm [12]: where G represents the effective channel, i.e., G = [g 1 , g 2 , · · · , g Z ] H . In order to meet the standardization constraint, i.e., V · f z = 1, we perform power standardization for each f z originating from F = f 1 , f 2 , · · · , f Z , each element is defined as

D. QoS-AWARE POWER ALLOCATION SCHEME
In this section, we propose a QoS-aware power allocation scheme using the D.C. programming method for given precoders and UGV locations. The large path loss in the channel between the UAV and the UGV results in the dominance of large scale fading. By estimating and predicting the UGV position parameters, we can derive the received power as follows where L dB z is the path loss calculated using Equation (2). Taking into account the large scale fading between the UAV and the UGV caused by the distance, finally, according to Equation (10), the achievable rate of the z-th UGV is reformulated as VOLUME 10, 2022 where µ z = 10 µ dB z 10 , p z = 10 p dB z 10 , and L z = 10 L dB z 10 . Due to the need to safeguard the QoS requirements of UGVs, the sum-rate optimization problem is defined as: where C 1 represents the power constraint limited by P, and C 2 guarantees the each UGV's QoS at the lowest required data rate λ.
According to the steps in [29], the sum-rate maximization problem will be remodeled as the D.C. programming problem shown below: where From observations based on Equation (47), f (µ) and g(µ) are both concave with respect to µ, i.e., Equation (47) denotes the D.C. functions. For z = 1,2,. . . ,Z, we assume that e z ∈ R Z is e z (z) = 0, z = 1,2,. . . ,Z and e z (i) = 1 ln 2·L i · |g H z f i | 2 , i = z. Finally, ∇g(µ) represents the gradient of g(µ), as shown below Selecting a feasible solution µ (0) , the optimal solution µ (n+1) is generated as the optimum solution of the problem (47) in the n-th iteration: The above problems can be easily solved by CVX. The running complexity of Formula (49) is O(Z 3 ) in each iterative process, as mentioned in [29]. Because g(µ) is a concave function, its gradient g(µ) is also a super gradient [30], so it has the following properties: Furthermore, since µ (n+1) is also a solution of Equation (49), it meets the following equation ≥ f (µ (n) ) − g(µ (n) ). (51c) Consequently, it is easy to see the conclusion that the (n+1)-th solution is invariably superior to the (n)-th solution. The criterion for the termination of the iteration is when |f (µ (n+1) ) − g(µ (n+1) ) − (f (µ (n) ) − g(µ (n) ))| ≤ meets a predetermined threshold > 0. In Section VI, we observe that the proposed scheme can quickly converge to the approximate global optimal solution. Its convergence and monotonicity can be seen in Fig. 6.

V. RADAR-AIDED PC-BASED HYBRID PRECODING SCHEME
In this section, a novel hybrid precoding scheme is presented, as shown in Fig. 4. Specifically, with the aid of radar systems, we consider a hybrid precoding design for the UAV-UGV cooperative system in a more practical scenario, where the FC structure design used in Section III will no longer be appropriate. For this reason, instead of the infinite precision PS with FC structure design, we use a hybrid precoding design with finite precision PS and PC structures.

A. PROPOSED DYNAMICALLY CONNECTED HYBRID PRECODING SCHEME
In this part, we address the issue of designing hybrid digital/analog precodes for the PC-HP structure in Fig. 4. Specifically, all transmitting antennas are grouped according to Algorithm 1 proposed in this section. Then, each RF chain is dynamically connected to disjoined antenna groups through a dynamic connection network. Thus, each entry of the analog precoder V is designed as 2 B n = 0, 1, . . . , 2 B − 1 . Meanwhile, the analog precoder includes only one nonzero element in each row to ensure that distinct subarrays do not overlap, i.e., V (i, :) 0 = 1, i = 1, . . . , N t . In particular, it is noted that unlike the weighting sum-rate maximization problems considered in the previous section, this section assumes uniform power allocation, focusing on the process of designing the hybrid digital/analog precoder and no longer considering the power allocation problem. Thus, Equation (9) is for t = 1, 2, . . . , N t do 15: if t ∈ U z then 16: n 0 = arg min The problem of designing hybrid digital/analog precodes with B bits quantized PSs for the PC-HBF Structure is designed as By analyzing Equation (53), we find that the sum-rate maximization problem corresponds to maximizing the SINR of each UGV. Whereas, directly maximizing SINR per UGV needs the joint design of digital and analog precoders, which is not feasible due to the high computational complexity. Inspired by the findings in [31], [32], in which a two-stage dynamically connected (DC) hybrid precoding scheme was used to solve the above optimization problem, we use the angle parameters obtained by the radar system to directly design the analog precoder, which further reduces the complexity of this PC hybrid precoding scheme. Specifically, first, the transmitting antennas are dynamically grouped, and then the analog precoder is designed in combination with the angle parameters obtained by the radar system to directly maximize |H z v z | without considering the inter-UGV interferences. Secondly, in order to eliminate interference between different UGVs, the digital precoding matrix is created using the effective channel matrix. The digital precoding matrix is calculated according to the effective channel to eliminate the interference between different UGVs.

B. ANTENNA DYNAMIC GROUPING ALGORITHM
According to the above analysis, first, the hybrid precoder design problem in Equation (53) is equivalent to max Z z=1 |H z v z |. However, maximizing Z z=1 |H z v z | is in turn equivalent to maximizing each term in the summation. Thus, the optimization problem we need to solve can be formulated as arg max where U z refers to the group of transmitting antennas linked to the z-th RF chain. |U z | represents the cardinality of the set U z . C 1 ensures that the antenna in U z is exclusively linked to the z-th RF chain, and the RF chain resources will not be wasted because |U z | = 0. C 2 guarantees that each antenna is linked with at least one RF chain. In addition, it is necessary to additionally satisfy the condition U z ∩ U z = ∅, for z = z , to ensure that each antenna element is linked to only one RF chain. Finally, the proposed Algorithm 1 can solve the above optimization problem, as shown above. In summary, the hybrid precoding algorithm based on a dynamic antenna grouping (DAG) starts by grouping the antennas. It then appends Steps 5 to 12 to ensure user fairness while not wasting RF resources. It is worth pointing out that Steps 2 to 12 are a heuristic method, but its complexity is very low. Steps 13 to 20 use the angle parameters obtained through the radar system to directly design the quantized analog precoding matrix V , and the method of acquisition of the angle parameters is described in Section IV. Finally, step 21 designs the digital precoding matrix F by using the BZF algorithm.

VI. SIMULATION RESULTS
This section shows several numerical results obtained through computer simulations to verify the performance of the novel radar-aided location-based hybrid precoding schemes. From Fig. 5 to Fig. 7, we presumed that the UAV-BS was equipped with a ULA of 64 transmit antennas (i.e., N t = 64). In the simulation of the last three pictures, we considered VOLUME 10, 2022  a UAV-BS equipped with a ULA of 128 transmit antennas (i.e., N t = 128). In both cases, the amount of UGVs was four (i.e., Z = 4), and each was equipped with a single-antenna.The total transmit power is constrained by P = 10 mW and the initial point µ (0) is set to [0.25, 0.25, 0.25, 0.25] mW. The amount of propagation paths was given as L z = 10, and σ 2 z = −10 dBm for each UGV. The AoDs were uniformly distributed over [0, 2π]. We calculated the average value of over 100 times for each computer experiment.
In Fig. 5, the spectral efficiency of the conventional hybrid precoding schemes and the proposed radar-aided hybrid precoding scheme are compared. The line ''Single User'' corresponds to the algorithm proposed in [11] represents a UAV communicating with a UGV. Therefore, the user interference can be completely ignored. The radar-aided hybrid precoding scheme as reported in [34] with uniform power distribution is represented by the ''Uniform Power Allocation'' curve. The curves labeled ''Uniform Power Allocation'' and ''D.C. Power Allocation'' were found to perform similarly where  the line labeled ''D.C. Power Allocation'' represents the algorithm proposed in this paper. The sum-rate, on the other hand, was significantly reduced when location information was not used, as shown on the ''ZF without Localization'' curve corresponds to the schemes reported in [12]. The cause of this is that the UAV can't accurately distribute the beam to the UGVs. Eventually, the algorithm corresponding to a line labeled ''CCP without Localization'' is the one reported in [35]. Fig. 6 depicts the proposed D.C. power allocation scheme's convergence behavior under two SNR values of −4 dB and 15 dB, respectively. Fig. 6 reveals the monotonicity and convergence of the proposed scheme under two SNR values.
Next, we verify the QoS for each UGV by setting λ = 2 bps/Hz, λ = 4 bps/Hz and λ = 6 bps/Hz, respectively. Inspection of Fig. 7 shows the CDF of the UGV's rate and the proposed ''D.C. Power Allocation'' scheme can meet the minimum QoS for each UGV at each set threshold (i.e., 2, 4, 6 bps/Hz). By comparison, when setting λ = 4 bps/Hz, approximately 10% and 12% of UGVs cannot meet the QoS  required through the ''uniform power allocation'' scheme and ''ZF without Localization'' scheme. Fig. 8 depicts the spectral efficiency versus SNR present in the proposed PC-hybrid precoding scheme based on the dynamic antenna grouping (DAG-PC-hybrid precoding) in different quantized phase controls. From Fig. 8, we notice that with the improvement of PS resolution, the behavior of the DAG-PC-hybrid precoding scheme is better. Fig. 9 depicts the spectral efficiency versus the amount of antennas of proposed radar-aided PC-based hybrid precoding schemes. Under the given situation, we set the number of user to Z = 4 and SNR = 10 dB. From Fig. 9, we can also expect that with the growth of number of antennas N t , the behavior of sum-rate will be enhanced by providing more diversity and precoding gain. Fig. 10 depicts the spectral efficiency versus SNR of the proposed radar-aided hybrid precoding schemes, in which the PS is quantized to 1 bit and 2 bit, respectively. In order to compare the schemes better, we also added two schemes: a traditional fully-digital-zero-forcing (FD-ZF) precoding scheme [12] and a traditional PC-hybrid precoding scheme [33]. It can be observed from Fig. 10 that the DAG-PC-hybrid precoding scheme always has better behavior than the PC-hybrid precoding scheme. Specifically, the curve ''FC-hybrid precoding, B = 1'' and ''DAG-PA-hybrid precoding, B = 2'' have comparable performance.

VII. CONCLUSION
In our work, we developed two novel location-based hybrid precoding schemes for a radar-aided UAV-UGV heterogeneous cooperative system. On the basis of radar-assisted communications, we decomposed the hybrid precoders design problem into two sub-problems, namely localization and communication. First, the specific location of the UGV was detected by the radar loaded on the UAV. Then, using the location information obtained from the UGVs, locationbased precoding was accomplished. Next, two radar-aided hybrid precoding schemes were designed. In the first scheme, with the assistance of the radar system, the joint design of hybrid precoding and power allocation was proposed to maximize the sum-rate based on D.C. programming. The latter scheme mainly considered more practical scenes. Using phase shifters with limited precision, a heuristic algorithm based on antenna dynamic grouping was designed to maximize the sum-rate. Finally, we used a computer simulation to validate the efficacy of our proposed novel location-based hybrid precoding schemes for the radar-aided UAV-UGV cooperative systems.