This paper gives an overview on the research status, developments, and achievements of subarrayed array processing for the multifunction phased array radar. We address some issues concerning subarrayed adaptive beamforming, subarrayed fast-time space-time adaptive processing, subarray-based sidelobe reduction of sum and difference beam, subarrayed adapted monopulse, subarrayed superresolution direction finding, subarray configuration optimization in ECCM (electronic counter-countermeasure), and subarrayed array processing for MIMO-PAR. In this review, several viewpoints relevant to subarrayed array processing are pointed out and the achieved results are demonstrated by numerical examples.

PAR (phased array radar) and especially MFPAR (multifunction PAR) often adopt a subarrayed antenna array. SASP (subarrayed array signal processing) is one of the key technologies in modern PARs and plays a key role in the MFPAR.

In this paper we consider the modern MFPAR with an element number of the order of 1000 (assume that the subarrays are compact and nonoverlapping) and with amplitude tapering (e.g., Taylor weighting) applied at the elements for low sidelobes. And the steering into the look direction is done by phase shifting at the elements. Assume the MFPAR with many modes of operation (e.g., search, track, and high resolution) and all processing to be performed digitally with the subarray outputs.

The key technologies and issues of SASP include subarray weighting for quiescent pattern synthesis and PSL (peak sidelobe) reduction, subarrayed adaptive interference suppression with subarrayed ABF (adaptive beamforming) or ASLB (adaptive sidelobe blanking), subarrayed adaptive detection, subarrayed parameter estimation, for instance, adaptive monopulse and superresolution direction finding, optimization of subarray configuration, and an expansion of the SASP, that is, application in MIMO- (multiple-input multiple-output-) PAR, and so forth.

Nickel is the pioneer and trailblazer in the field of the SASP. Since the 1990s, he has firstly systematically performed a series of thorough researches which theoretically and technically lay the solid foundation of the SASP. His research achievements represent the development level of SASP technology [

Similarly, Farina with different coauthors has given creative and pioneering contributions to the following aspects, including subarrayed weighting for SLC [

SASP possesses a good application prospect for millimeter wave PAR seeker, airborne multifunction radar, and space-borne early-warning radar. A famous and outstanding example is the tri-national X-band AMSAR project for a future European airborne radar [

This paper summarizes the research achievements in the field of SASP including the study results of the author. The relevant issues focus on subarrayed ABF, subarrayed fast-time STAP, subarrayed PSL reduction for sum and difference beam, PSL reduction for subarrayed beam scanning, subarrayed adapted monopulse, subarrayed superresolution direction finding, subarray optimization for ECCM (electronic counter-countermeasure), and the SASP for MIMO-PAR.

In this review, viewpoints and innovative ways are presented which are relevant to the SASP. For the proposed algorithms we give examples.

In this section we investigate subarrayed ABF and adaptive interference suppression. Actually, the adaptive weighting is implemented at subarray level. The subarrayed ABF has three configurations, that is, DSW (direct subarray weighting), SLC (sidelobe canceller), and GSLC (generalized SLC) types [

Configurations of subarrayed ABF.

DSW

Subarrayed SLC

Subarrayed GSLC

The limitation of DSW configuration is that it requires an estimation of the interference-plus-noise covariance matrix. The matrix is necessary for the estimation of adaptive weights. The limitation of the subarrayed SLC configuration is that equipment with auxiliary antennas and auxiliary channels is required, as indicated in Figure

This section is devoted to the DSW and GSLC configurations.

First consider the subarrayed optimum BF (optimum adaptive filter [

The shortcoming of the subarrayed SMI is that the sidelobe level of adapted pattern is increased remarkably compared with quiescent pattern with tapering weighting due to subarrayed weighting (assuming the subarray transformation matrix

Suppose that we have an array with

On the other hand, the subarrayed SMI has only asymptotically a good performance. In practice, we have to draw on a variety of techniques to provide robust performance in the case of small sample size. The improved versions of subarrayed SMI comprise the subarrayed LSMI (load sample matrix inversion), the subarrayed LMI (lean matrix inversion), and so forth. The subarrayed LSMI and the subarrayed LMI are the extensions of LSMI [

Quiescent pattern control approaches are another kind of the improved versions of subarrayed optimum ABF. The approaches preserve the desired quiescent pattern in the absence of jammer. Therefore, they make system automatically converge to the nonadapting mode. Thus the conversion problem between the two working modes of the subarrayed ABF is resolved [

The pattern control approaches include normalization method, MOD (mismatched optimum detector), and SSP (subspace projection). Therein, the starting point of the normalization method [

The MOD [

The SSP [

Table

Performance contrast of quiescent pattern control approaches.

Suitability for overlapped subarrays | Computational burden | |
---|---|---|

MOD | Suitable | Very small |

Normalization method | Nonsuitable | Large |

SSP | Suitable | Very heavy |

Following we present an improvement of quiescent pattern control approaches. For the pattern control, the PSL reduction capability is at the cost of degradation of adaptation. This results in an output SINR loss. On the other hand, for the subarrayed optimum ABF, the anti-jamming capability is optimum. In order to compromise PSL and adaptation capability, we put forward the methods combining subarrayed optimum ABF and quiescent pattern control. The adaptive weight is

The combined method unifies subarrayed optimum ABF and quiescent pattern control, both of which are two extreme cases of the combined method. The combined method improves the flexibility of the PSL reduction for adaptive pattern and makes the trade-off between PSL and SINR according to real requirements. When we want to obtain better PSL reduction capability, we can choose higher value of

The above-mentioned quiescent pattern control method and the combining method can be extended into subarrayed fast-time STAP, as will be shown in Section

In the subarrayed GSLC, the blocking matrix in auxiliary channel (Figure

Let

The adaptive patterns and output SINR obtained by Householder transform-based GSLC are the same as that of the optimum ABF-based DSW [

Adaptive patterns with I/Q errors.

Amplitude errors

Phase errors

The subarrayed GSLC with Householder transform is valid no matter it is with amplitude errors or phase errors, which is insensitive to phase errors even.

For the broadband array, additional time delays at subarray outputs are adopted in order to compensate phase difference of internal subarray of each frequency component. The look direction is controlled by subarray time-delay and phase shifter together for whole working bandwidth.

The adaptive weights of subarrayed broadband ABF can be obtained through broadband steering vector method. This method controls the look direction for each frequency of working bandwidth and realizes gain condition constraints, that is, makes the gain for each frequency to be equal. Assume bandwidth of all jammers is

Assume that a ULA consisting of 99 elements is partitioned into 25 nonuniform subarrays; the relative bandwidth is

Adapted pattern obtained with subarrayed broadband ABF.

In the recent twenty years, extensive and thorough research on slow-time STAP used for clutter mitigation in airborne radar has been carried out [

In the presence of broadband jammers, subarrayed ABF would form broad adaptive nulls, which consumes spatial degrees of freedom and distorts the beam shape as indicated in Figure

The subarrayed ABF methods presented in Section

To give an example, suppose a UPA (uniform planar array) with

Adaptive patterns in the case of broadband jammer (cut patterns in azimuth plane).

On the other hand, for broad array, similar to subarrayed broadband ABF, the subarrayed fast-time STAP should adopt time delays at subarray outputs to compensate phase difference. This is subarrayed fast-time STAP with broadband steering vector method [

We give the simulation results, in which the parameters of array are set the same as Figure

Adaptive pattern by broadband steering vector-based subarrayed fast-time STAP.

The optimum adaptive weights of subarrayed fast-time STAP can be determined by the LCMV criterion [

The adaptive pattern in the case of broadband SLJ is given in Figure

Comparison of combined subarrayed fast-time STAP with the optimum one.

The sidelobe reduction of patterns is the basic task for the PAR systems. In this section, we deal with subarray weighting-based algorithms for the PSL reduction of sum and difference beam. The goal is to obtain a trade-off between hardware complexity and achievable sidelobe level.

One function of subarray weighting is to reduce the PSL of both the sum and the difference beam simultaneously for a monopulse PAR, in which digital subarray weighting substitutes the analog element amplitude weighting. Accordingly, hardware cost and complexity are greatly reduced.

In this section, two techniques are presented as follows.

This approach completely substitutes the element weighting adopting subarray weighting (for instance, a Taylor and Bayliss weighting for sum and difference beam, resp.). We assume that no amplitude weighting at element level is possible. The two schemes for determining subarray weights are as follows.

The analytical approach includes two ways, namely, weight approximation and pattern approximation. The former makes the subarray weight to approximate the Taylor or Bayliss weight in LMS (least mean square) sense, while the latter makes the patterns obtained with the subarray weights approximate to that obtained by the Taylor or Bayliss weight in LMS sense [

The weight approximation-based subarray weights are determined by

Sum beam:

Difference beam:

Take the sum beam for example, the pattern approximation-based subarray weights are determined by

Assume a ULA with 30 omnidirectional elements with

Subarrayed weighting-based quiescent patterns.

Sum beam

Difference beam

Note the subarray weighting-based PSL reduction capability cannot be the same as that with element weighting, which is a price required for reducing the hardware cost. This approach is more suitable for the difference beam which is used for target tracking.

This approach optimizes the subarray weights using GA. The GA could achieve global optimum solution which is unconstrained by issues related solution.

Here, fitness function has a great influence to PSL reduction capability. We choose two kinds of fitness functions: (1) the weight approximation-based fitness function, that is,

Adopting

In order to overcome the limitation of two approaches mentioned above, we present an improved GA, that is, partition genetic process into two stages whose process is as below. The first stage is used for the preliminary optimization using

There is a UPA containing

Sum patterns: improved GA.

Table

The PLSs of sum beam with several approaches.

Without weighing | Conventional GA |
Conventional GA |
Improved GA | |
---|---|---|---|---|

PSL (dB) | −13.43 | −26.18 | −27.70 | −27.77 |

The scheme generates sum and difference channels simultaneously only using an analog weighting. In order to determine the analog weights, it is assumed that the supposed interferences locate within the sidelobe area of sum and difference beams [

The literature [

The division of planar array into four quadrants.

Construction of sum and difference channels.

Assume coordinate of

It should be pointed out that the PSL reduction effect with only analog weighting approach is determined by the selected design parameters, such as JNR and spatial distribution of supposed interferences.

Assume that a UPA consists of

Patterns obtained by only analog weighting.

Sum beam

Double difference beam

Patterns obtained by analog and digital weighting (with weight approximation approach).

Sum beam

Double difference beam

In fact the PSL reduction capabilities of weight approximation- and pattern approximation-based subarray weighting are quite close.

The look direction is usually controlled by phase shifters for PAR. However further subarrayed digital beam scanning may be required for forming multiple beams and many other applications which are used for a limited sector of look directions around the presteered direction.

Typically with subarrayed scanning, the PSL will increase rapidly with the scanning direction departing from the original look direction. The larger the scan angle is, the greater the PSL increase is [

In this section, we discuss the PSL reduction approaches for subarrayed beam scanning, namely, beam clusters created at subarray level.

With subarrayed scanning, the resulting pattern is composed of the pattern of each subarray. Each subarray pattern has a high PSL which contributes to a high PSL of the array pattern. If pattern of each subarray would be superimposed properly in the main beam and has a low PSL, the PSL of the array pattern could be reduced effectively.

Therefore, one can post-process the subarray outputs using a weighting network, consequently creating new subarrays with the patterns with similar shape within the main beam and with PSLs as low as possible. The starting point is to make the new subarray patterns to approximate the desired one.

The natural form of desired subarray pattern is the ISP (ideal subarray pattern) which is constant within the mainlobe and zero else [

As an example, assume that a UPA consists of

By using the ISP based on rectangular projection, we give an example for reducing the sidelobes in Figure

Subarray patterns obtained by ISP.

Rectangular projection method

Circular projection method

Figure

Array patterns with beam scanning obtained by ISP method (azimuth cut).

Non-weighing network

Rectangular projection method

Circular projection method

It is seen from above-mentioned examples that the PSL reduction capability with ISP is not satisfied. For the reason, we adopt GSP- (Gaussian subarray pattern-) based approach [

The result obtained with the GSP approach is shown in Figure

Array patterns with beam scanning obtained by GSP (azimuth cut).

In order to ensure the accuracy of angle estimation of monopulse PAR in jammer environments, we should adopt subarrayed adaptive monopulse technique. The subarrayed ABF can improve SINR and detection capability. However, under circumstances of MLJ (mainlobe jamming) the adaptive null will distort the main beam of pattern greatly, thus leading to serious deviation of the angle estimation. Thereby, the subarrayed adaptive monopulse should be applied.

Existing approaches usually take the adaptive patterns into account to avoid the degradation of monopulse performance near the null. For example, one can use LMS-based target direction search to determine adaptively the weights of optimum difference beam [

The reined subarrayed adaptive monopulse methods with higher monopulse property have been suggested, for example, the approximative maximum-likelihood angle estimators [

The realization process of the two-stage subarrayed adaptive monopulse is as follows: firstly, the subarrayed ABF is used to suppress the SLJ, while maintaining the mainlobe shape; secondly, the MLJ is suppressed, while maintaining the monopulse performance; that is, the jammers are canceled with nulls along one direction (elevation or azimuth) and undistorted monopulse ratio along the orthogonal direction (azimuth or elevation) is preserved. The two-stage subarrayed adaptive monopulse requires four channels, in which the delta-delta channel is used as an auxiliary channel for the mainlobe cancellation.

However, the method possesses two limitations: (1) after the first-stage processing, the PSLs of patterns increase greatly, and (2) the monopulse performance is undesirable, for there exists serious distortion in deviation of the look direction for adaptive monopulse ratio; the reason is that the MLM (mainlobe maintaining) effect is not ideal. Therefore, in the first-stage processing, subarrayed optimum ABF is substituted by MOD; consequently, the monopulse performance would be improved greatly [

Suppose a rectangular UPA with

Next we illustrate the simulation results taking the elevation direction as an example. Figure

Adaptive patterns of elevation sum beam obtained by first-stage adaptive processing.

Figure

Elevation monopulse ratio obtained by two-stage adaptive processing.

Since the subarrayed optimum ABF combined with MLM is used in the first-stage processing, the monopulse ratio deviated from the look direction shows serious distortion. Undoubtedly, the MOD combined with MLM is an appropriate choice to enhance adaptive monopulse ratio, for its similarity to quiescent monopulse ratio and the small distortion when deviated from the look direction. And the relative error of adaptive monopulse ratio with improved two-stage monopulse (MOD+MLM for first-stage processing) is only 3.49% compared with quiescent monopulse ratio when the elevation is −2.7°, while the conventional two-stage monopulse (subarrayed optimum ABF+MLM for the first-stage processing) is as much as 69.70%. So, improved method monopulse reduces error of monopulse ratio greatly compared with conventional method. The numerical results demonstrate that, in the range of 3 dB bandwidth of patterns, for the improved method monopulse, the relative error of adaptive monopulse ratio is less 1% and even reaches 0.01% compared with quiescent monopulse ratio.

Two-stage subarrayed adaptive monopulse integrates several techniques, including subarrayed ABF, MLM, quiescent pattern control, and four-channel MJC. The SLJ and MLJ are suppressed, respectively, so it is unnecessary to design the sophisticated monopulse techniques to match the mainlobe of patterns.

For the wideband MLJs, the SLC type STAP can be used to form both sum and difference beam. If auxiliary array is separated from the main array by distances that are sufficiently large, the array can place narrow nulls on the MLJ while maintaining peak gain on a closely spaced target [

To address angle superresolution issues, a variety of methods have been developed. This paper only focuses on subarrayed superresolution. In this section, two types of the approaches are described: the first refers to the narrowband superresolution; the second approach presents the broadband superresolution [

The subarrayed superresolution direction finding could be achieved by extending the conventional superresolution algorithms into the subarray level. However, this kind of algorithms has to calibrate the whole array manifold. But for the active calibration technique the realization is very complicated and costly, while for the self-calibrate solutions there are limitations, for example, difficulty of implementation; high computational burden (some algorithms are many times more than original superresolution algorithms even); the convergence problems for some iterative algorithms; the performances are limited in the case of a lot of array position errors; some are only effective for specific errors of one or two kinds only [

Thus, simplified array manifolds can be used. The essence of these methods is to treat the whole array as a superarray and each subarray as a superelement. The idea is to approximate the patterns at subarray outputs by those of superelements located at the subarray centres [

These methods can eliminate uncertain information in sidelobe area. The available region of direction finding of them is within 3 dB beamwidth of patterns around the center of the look direction. However, combined with beam scanning by element phase shifting, superresolution can be achieved in any possible direction, that is, make the superresolution be carried out repeatedly by changing look direction. The advantage is suppressing sidelobe sources in complicated situation such as multipathway reflection; consequently, number of sources and dimension of parameter estimation are reduced and the process of superresolution is simplified [

The available direction finding area of direct simplified array manifold-based subarrayed superresolution is fixed which cannot be adjusted and the sidelobe sources cannot be suppressed completely. Changing subarray patterns can overcome the limitations, but it is unable to be achieved by restructuring the subarray structure. The subarray structure is an optimized result based on various factors and hardware is fixed. Therefore, we post-process the subarray outputs by introducing a weighting network which constructs required new subarray patterns. This kind of methods improved the flexibility of array processing greatly and the optimization of subarrays for different purpose and distinct processing tasks can be achieved based the same hardware [

Compared with the method based direct simplified array manifold, the ISP and GSP methods can adjust the available region of direction estimation and suppress sidelobe sources better [

The subarrayed superresolution approaches presented in the Section

The subarrayed ISSM (incoherent signal subspace method), subarrayed CSST (coherent signal subspace transform), and subarrayed WAVES (weighted average of signal subspace) translate broadband problems into a subband processing. All these algorithms need to make delay-weighing for outputs of subbands. The subarrayed ISSM only averages the direction finding results of each subband obtained by subarrayed MUSIC. The subarrayed CSST and subarrayed WAVES should choose the suitable focusing transformation matrix and therefore need to preestimate source direction. If the preestimated direction is erroneous, the direction finding performance will be degraded. The subarrayed WAVES determines a joint space from all subspaces of subband covariance matrix, which is only one representative optimum signal subspace [

The broadband superresolution based on subarray time delay does not need any subband processing. Accordingly, it has less calculation which is easy to be implemented but needs a focusing transform. For the simplified array manifold-based approaches, they have better performance if the preestimated target direction is near the look direction; otherwise the performance would be degraded rapidly.

The narrowband subarrayed superresolution can be extended to the space-time superresolution (such as the subarrayed space-time MUSIC). Through compensating the phase using a subarray delay network, this kind of algorithms reduces the frequency-angle ambiguities. Then use the space-time steering vector to calculate the space-time covariance matrix and extract the dominant signal subspace [

To give an example, suppose a UPA with

Two targets are deemed to be separable if their peak values of spatial spectrum both are greater than the value in the central direction of targets. Namely, targets are resolvable if the following two conditions are both met:

Figure

Contrast of performances of three broadband subarrayed superresolution algorithms.

Probability of resolution versus azimuth difference of two targets

Probability of resolution versus SNRs

The s.t.d of direction finding

For the PAR equipped with ABF, the optimization of subarray configuration is a key problem and challenge in the field of the SASP.

For its obvious influence on the performance of PAR, the optimization of subarray configuration can bring much improvement of the system performances such as sidelobe level, detection capability, accuracy of angle estimation, ECCM capability (anti-MLJ), and so forth. The subarray division is a system design problem; the optimized result has to take into account various factors. However, different capabilities may be contradictory mutually.

There are different solutions to this contradiction. In this section we briefly overview the MOEA (multiobjective evolutionary algorithm) procedure working on this issue. MOEA might make an optimal trade-off between above-mentioned capabilities.

The objective functions in the MOEA could be the mean

On the other hand, several issues should be considered on engineering realization: for example, all the subarrays are nonoverlapped and array is the fully filled, subarray configuration is relatively regular, and all elements inside a subarray are relatively concentrative (subarray’s shapes should not be disjointed). Therefore, multiple constraints should be set during the process of genetic optimization.

The process of optimizing subarray is quite complicated for the great amount of elements in a PAR and the large searching space. Thus we can adopt the improved GA to make optimizing with a characteristic of adaptive crossover combination, which is based on the adaptive crossover operator; this will result in remarkable enhancement on convergence speed of optimization and calculation efficiency [

Suppose a UPA with

We optimize the five objective functions simultaneously based on the MOEA. Hereinto, the first objective function is the PSL of adapted sum pattern in

Optimized results based on MOEA.

First objective function: sum adapted pattern in

Second objective function: sum adapted pattern in

On the other hand, for the PAR with subarrayed ABF, the ideal optimum subarray configuration should keep system’s performances be optimal for various interference environments interference environments. But this is impossible to realize in principle.

Historically, the SASP techniques are mainly used for the PAR systems. In this section, we discuss the concept of the SASP suitable for MIMO-PAR system. Creating this technique is an impetus following from previous sections.

The MIMO structure is impracticable when the array is composed of hundreds or thousands of elements due to the huge quantity of independent transmitting signals and transmitting and receiving channels. Hardware cost and algorithmic complexity will exceed the acceptable level.

Therefore, we present the subarrayed MIMO-PAR. It is an extension of the subarrayed PAR. The MIMO-PAR is the combination of MIMO radar and PAR: the array is divided into several subarrays; inside each subarray a coherent signal is transmitted, working as PAR mode; orthogonal signals are transmitted between subarrays to form a MIMO system. The MIMO-PAR presented in this paper adopts Tx/Rx array modules, and transmitting and receiving arrays have the same subarray configuration, while both at the transmitting and receiving ends the SASP techniques are be applied.

The features of MIMO-PAR are listed as follows.

It maintains advantages of MIMO radar as well as the characteristics of PAR (such as the coherent processing gain).

Compared with MIMO radar, the MIMO-PAR reduces the cost and complexity of the hardware (the number of the transmitting and receiving channels) and the computational burden greatly. For example, the dimension of optimization algorithms for designing transmitting signals is reduced to subarray number, while it is the same as the element number in MIMO. Typically element number has an order of magnitude from several hundreds to several thousands and subarray number is only a few dozens of magnitude.

Hardware cost and algorithm complexity can be flexibly controlled by adjusting the number of the subarrays. The ability of coherent processing (SNR) and the characteristics of waveform diversity (angle resolution) can be compromised by adjusting the subarray structure and subarray number.

Compared with MIMO radar, the transmitting signals of different subarrays can be combined with independent beam look directions to improve the capability of beam control, producing more flexible transmitting beam patterns, thus improving the flexibility of object tracking.

The characteristics with further advantages over MIMO radar, such as lower PSL of total pattern, can be achieved by design of the weighting of subarrayed transmitting/receiving BF. Moreover, MIMO-PAR can enhance the anti-jamming capability and generate higher output SINR under strong interference, and realize low PSL without expense of mainlobe gain loss.

The performance of the system can be enhanced by optimizing the structure of subarray, such as transmitting diversity, SNR, PSL of total pattern, the performance of transmitting beam, and the ECCM capability.

The exiting research achievements related to receiving SASP for PAR can be generalized to the MIMO-PAR. This is a promising direction of further studies.

The configuration of MIMO-PAR with Tx/Rx modules can be easily made compatible with existing subarrayed PAR.

The research topics are as follows.

Assume a UPA of Tx/Rx community with 960 omnidirectional elements on a rectangular grid at half wavelength spacing. The array is divided into

PSLs of total pattern for different radar models (dB).

Radar model | PAR | MIMO | MIMO-PAR |
---|---|---|---|

PSLs in |
−15.00 | −24.66 | −26.56 |

PSLs in |
−15.16 | −25.26 | −26.95 |

Total patterns of PAR, MIMO, and MIMO-PAR.

The rectangle transmitting beam pattern can be used to radiate the maximum transmitting energy to interesting areas, so as to improve the exploring ability. As a result, a rectangle transmitting beam pattern can be synthesized from cross-correlation matrix of transmit signals [

The transmitting beam control includes two scenarios. (1) Each subarray has different beam directions to form a broad transmitting beam (for radar search mode). (2) Each subarray has the same beam direction to focus on transmitting beam (for tracking mode).

Aiming at a UPA, Figure

Transmit beam patterns based on synthesis of subarray transmitted signal.

The performance evaluation of transmitted signal includes (1) orthogonality and (2) range resolution and multiple-target resolution (pulse compressing performance). On the other hand, the orthogonality degrades with increase of the subarray number.

In the MIMO-PAR, when the element number and subarray number are fixed, the subarray structure has a significant impact on the system performance. Then the subarray structure has to be optimized. While in the MOEA method, the following constraints can be chosen as objective functions: (1) the waveform diversity capability, (2) the coherent processing gain, (3) the PSL of the total pattern in elevation direction, (4) the PSL of the total pattern in azimuth direction, and (5) the RMSE of the transmitting beam pattern and the rectangular pattern.

In this paper, we describe some aspects of the SASP. From these investigations, we draw the concluding remarks as follows.

For the SASP the achievable capabilities in application are constrained by some hardware factors, for example, channel errors.

The amalgamation as well as integration of multiple SASP techniques is a trend, such as the combination of subarrayed ABF, adaptive monopulse, and superresolution. Consequently, the performance of the SASP could be improved.

The subarray optimization is still a complicated and hard problem, compared with the algorithms.

The extension of the SASP into MIMO-PAR could promote and deepen development of the SASP.

Furthermore, we point out the problems to be dealt with. The challenging works are in the following areas.

The more thorough study of subarray optimization should be carried out. It is important for improving capabilities of system (including ECCM).

The SASP for anti-MLJs is still a hard research topic.

The SASP techniques for the thinned arrays should be further developed.

At present, the research focuses mainly on the planar arrays which are only suitable for small angle of view (for instance, ±45°). The SASP should be extended to the conformal arrays (e.g., seekers).

Adaptive beamforming

Analogue-to-digital conversion

Adaptive sidelobe blanking

Beam forming

Constrained adaptive pattern synthesis

Coherent signal subspace transform

Cramer-Rao Bound

Direct subarray weighting

Electronic counter-countermeasure

Genetic algorithm

Generalized sidelobe canceller

Gaussian subarray pattern

Ideal subarray pattern

Incoherent signal subspace method

Jammer-to-noise ratio

Linearly constrained minimum variance

Lean matrix inversion

Least mean square

Load sample matrix inversion

Multifunction phased array radar

Multiple-input multiple-output

Mainlobe jamming

Mainlobe maintaining

Mismatched optimum detector

Multiobjective evolutionary algorithm

Phased array radar

Peak sidelobe level

Subarrayed array signal processing

Signal-to-interference-plus-noise ratio

Sidelobe canceller

Sidelobe jamming

Sample matrix inverse

Signal-to-noise ratio

Subspace projection

Space-time adaptive processing

Uniform linear array

Uniform planar array

Weighted average of signal subspace.

The author declares that there is no conflict of interests regarding the publication of this paper.

The author would like to thank Dr. Ulrich Nickel of Fraunhofer FKIE, Germany, for his insightful comments and useful discussions. This work has been partially supported by “the Fundamental Research Funds for the Central Universities” (Grant no. HIT.NSRIF.201152), the ASFC (Aeronautical Science Foundation of China, no. 20132077016), and the SAST Foundation (no. SAST201339).