Design of spectrally compatible waveform with constant modulus for colocated multiple‐input multiple‐output radar

We consider the problem of waveform design for Multiple-Input Multiple-Output (MIMO) radar in the presence of signal-dependent interference embedded in white Gaussian disturbance. We present two sequential optimization procedures to maximize the Signal to Interference plus Noise Ratio (SINR), accounting for a constant modulus constraint as well as a similarity constraint involving a known radar waveform with some desired properties (e.g., in terms of pulse compression and ambiguity). The presented sequential optimization algorithms, based on a relaxation method, yield solutions with good accuracy. Their computational complexity is linear in the number of iterations and trials in the randomized procedure and polynomial in the receive filter length. Finally, we evaluate the proposed techniques, by considering their SINR performance, beam pattern as well as pulse compression property, via numerical simulations.

Joint radar communication systems have been recently proposed for radar and communication sharing spectrum and hardware, to reduce the resource cost of platforms. In this paper, we consider the waveform design problem for a joint multiuser MIMO communication and MIMO radar system. We propose an optimization problem for waveform design, in which the signal-to-interference-plus-noise ratio (SINR) at users and the transmit beam pattern of radar are jointly optimized. To guarantee the efficiency of power amplifiers, the transmit waveform is constrained to be constant modulus. To deal with the non-convex constant modulus constraint, we propose an alternating descend method to solve the problem. The simulation results indicate that under high transmit signal-to-noise ratio (SNR), the communication quality can be guaranteed, along with a reasonable performance loss of radar. Moreover, the performance gap between the constant modulus constraint and the more relaxed per-antenna power constraint, is not significant.

In this paper, a multi-user (MU) satellite Multiple-Input Multiple-Output (MIMO) downlink including a multi-beam GEO satellite and multiple terrestrial users is considered. In order to meet the signal to interference plus noise ratio (SINR) requirements of different users while minimizing the satellite transmit power, the onboard precoding problem is investigated. Zero forcing (ZF) and regularized zero-forcing (RZF) precoding are first adopted and it is found that they can satisfy the SINR constraints by multiplying by a power allocation matrix. The required power allocation matrix is divided into two types: equal power factor schemes and unequal power factor schemes, and they are derived separately, where Karush-Kuhn-Tucker (KKT) conditions are used in RZF unequal power factor scheme and a heuristic algorithm is proposed to optimize the regularization factor in RZF schemes to further reduce the transmit power. Then, a semi-definite programming beamforming (SDPBF) is proposed to jointly optimize precoding and power allocation matrices. The closed-form expressions of the transmit power of the above five precoding schemes are derived and their performance is compared in the simulation part. The research results show that under the same conditions, the performance of RZF is better than that of ZF, the unequal power factor scheme is better than the equal power factor scheme, and SDPBF has the best performance. Besides, it is also found that in addition to changing the precoding method, activating more beams will further reduce the transmit power.

In this paper, we deal with the joint design of transmit waveform and receive filter for airborne multiple-input-multiple-output (MIMO) radar in order to enhance the radar detection performance for a ground target obscured by strong ground clutter. We also assume that the priori knowledge of target including azimuth and normalized Doppler frequency is inaccurate and we use their statistical information to calculate target covariance matrix. In the design stage, we force constant modulus and similarity constraints for waveform at the same time. Moreover, we propose a new iterative procedure to solve the non-convex optimization problem. The aim is to maximize the Signal to Interference plus Noise Ratio (SINR). At the analysis stage, we assess the effectiveness of the proposed algorithm.

This paper considers the design problem of Multiple-Input Multiple-Output (MIMO) radar space-time transmit code (STTC) and space-time receive filter (STRF) for a moving point-like target in the presence of signal-dependent interference. An iterative procedure, whose convergence is analytically proved, is devised to maximize the Signal to Interference plus Noise Ratio (SINR) accounting for both a similarity constraint and constant modulus requirements on the probing waveform. Each iteration of the algorithm, involves the solution of hidden convex problems. Specifically, both a convex problem (whose solution is provided in closed form) and a set of fractional programming problem, that can be globally solved in polynomial time via the Dinkelback's procedure, are solved. The computational complexity is linear in the number of iterations and polynomial with the sizes of the STTC and the STRF. Finally, numerical results are provided to assess the quality of the devised procedure.

Multicell coordinated beamforming (MCBF) has been recognized as a promising approach to enhancing the system throughput and spectrum efficiency of wireless cellular systems. In contrast to the conventional single-cell beamforming (SBF) design, MCBF jointly optimizes the beamforming vectors of cooperative base stations (BSs) (via a central processing unit (CPU)) in order to mitigate the intercell interference. While most of the existing designs assume that the CPU has the perfect knowledge of the channel state information (CSI) of mobile stations (MSs), this paper takes into account the inevitable CSI errors at the CPU, and study the robust MCBF design problem. Specifically, we consider the worst-case robust design formulation that minimizes the weighted sum transmission power of BSs subject to worst-case signal-to-interference-plus-noise ratio (SINR) constraints on MSs. The associated optimization problem is challenging because it involves infinitely many nonconvex SINR constraints. In this paper, we show that the worst-case SINR constraints can be reformulated as linear matrix inequalities, and the approximation method known as semidefinite relation can be used to efficiently handle the worst-case robust MCBF problem. Simulation results show that the proposed robust MCBF design can provide guaranteed SINR performances for the MSs and outperforms the robust SBF design.

We study the minimum latency data broadcast problem under the signal-to-interference-plus-noise-ratio (SINR) model, which is known to capture wireless interference more accurately and realistically than the widely used graph-based models. Previous work mainly involves building a broadcast tree first and then computing interference-aware TDMA schedules for the links on the tree. Observing that the separation of routing and scheduling may lead to unsaturated transmissions in each time slot, we develop a polynomial-time heuristic algorithm, namely PRS, by advocating a parallel way of constructing routing and transmission schedules. Theoretical analysis indicates that PRS generates correct schedules under the SINR constraints. Simulation results demonstrate that PRS outperforms state-of-the-art algorithms in terms of broadcast latency under various network conditions.

In this paper, the Multiple-input Multiple-output(MIMO) radar waveform design under constant modulus constraint is considered. The process of current transmit beampattern design is conducted by approximating the desired transmit beampattern and minimizing the cross-correlation sidelobes. This leads to hard optimization problem due to the nonconvexity of the objective function and constant modulus constraint. In this work, an efficient method is proposed to address those problem based on Majorization-Minimization(MM) method. Finally, we evaluate the performance of the proposed MM-based algorithm via numerical simulations.

This paper considers a quadratic optimization problem in radar discrete-phase waveform design under similarity and constant modulus constraints. A computationally efficient iterative algorithm based on the Alternating Direction Penalty Method (ADPM) framework is proposed. In each iteration, it converts the considered problem into two subproblems with closed-form solutions via an introduced auxiliary variable, while locally increasing the penalty factor involved in the ADPM framework. The proposed algorithm is ensured to converge for any initialization under some mild conditions and avoids the non-convergence problem of the Alternating Direction Method of Multipliers (ADMM) when handling the NP-hard problems. Finally, numerical simulations demonstrate that the proposed algorithm can outperform their counterparts by providing better objective values.

As for the single-channel overlapped signals, in which the modulation parameters of the component signals are identical or similar, it is still a great challenge to extract the component signals. Aiming at this problem, a single-channel blind source separation (SCBSS) algorithm, constrained by constant modulus, is proposed for the overlapped Gaussian minimum shift keying (GMSK) signals and this algorithm also applies to other overlapped signals with constant modulus (CM), such as binary phase shift keying (BPSK) signals and quadrature phase shift keying(QPSK) signals. By tracking the channels of the component signals, the algorithm can effectively estimate their symbol sequences. Simulation results show that the proposed algorithm can work more robustly and reduce the frame error rate (FER), comparing with the competing algorithms.

In this paper, we address the design of optimal waveform for detecting extended target in signal-dependent interference. A two-step waveform design algorithm is proposed to obtain the optimal phase-modulated (PM) waveform with constant modulus. We first obtain the normally called water-filling waveform in frequency domain and subsequently synthesize the corresponding time-domain waveform using the minimum spectral mean-squares error (MSE) as a cost function. The phase gradient algorithm is employed to seek the optimal phase of the PM waveform, which can monotonously decrease the spectral MSE for each iterative step. Simulations demonstrate that the proposed algorithm can obtain asymptotic optimal waveform and its performance outperforms the iterative-estimate algorithm.

Joint design of the transmit and receive weights for coherent FDA radar

When the radar antennas are properly placed so that each antenna falls within the same target beamwidth, the coherent processing can be employed. This paper studies the problem of joint target position and velocity estimation for a coherent passive radar system. The received observation model with direct path influence is developed in frequency domain. Due to the nature of passive processing, the samples of transmitted signals from the illuminators of opportunity are assumed deterministic unknown. The maximum likelihood estimator is presented and the Cramer-Rao bound (CRB) is derived. We show that the direct path signals can help improve the estimation performance. Then, we extend the discussion to the case where the transmitted signals are known to have constant modulus. Again, we show that incorporating the direct path signals in the received observations can have a positive influence on estimating target parameters. Compared with the case of not knowing the constant modulus constraint, the knowledge of constant modulus constraint brings extra performance gain.

In this paper, an optimal waveform design method for target recognition is proposed based on the relative entropy. Since the target recognition can be considered as a hypothesis test procedure, the detection probability could be the cost function to characterize the recognition performance. Then the cost function associated with the relative entropy is maximized to optimize the waveform for improving the recognition performance. The most proposed optimal waveform design methods just only consider the energy constraint. However, only the energy constraint is impractical. In this paper, we do not only consider the total energy limit, but also add the constant modulus constraint from the practice side to design the optimal waveform, since the radar systems commonly require constant modulus waveforms in order to utilize nonlinear power amplifiers. Finally, the simulation results show the effectiveness of the proposed algorithm.

Beampattern synthesis with nulling for sub-arrayed MIMO radar under constant modulus constraints