1002:
used in the beamspace. Post
Doppler methods may also be used on the full antenna element input as well to reduce the data in this dimension only. A popular example is displaced phase center antenna (DPCA), which is a form of data-independent STAP in the beamspace, pre-Doppler. The goal is to perform beamforming such that the beam appears stationary as the airborne radar is in motion over discrete time periods so the clutter appears without Doppler. However, phase errors can cause significant degradation since the algorithm is not adaptive to the returned data. Many other methods may be used to reduce the rank of the interference covariance matrix, and so all methods in the reduced rank category can be thought of as simplifying the covariance matrix to be inverted:
101:. Thus, a notch filter at the zero-Doppler bin can be used. Airborne platforms with ownship motion experience relative ground clutter motion dependent on the angle, resulting in angle-Doppler coupling at the input. In this case, 1D filtering is not sufficient, since clutter can overlap the desired target's Doppler from multiple directions. The resulting interference is typically called a "clutter ridge," since it forms a line in the angle-Doppler domain. Narrowband jamming signals are also a source of interference, and exhibit significant spatial correlation. Thus receiver noise and interference must be considered, and detection processors must attempt to maximize the
521:. Other difficulties arise when the interference covariance matrix is ill-conditioned, making the inversion numerically unstable. In general, this adaptive filtering must be performed for each of the unambiguous range bins in the system, for each target of interest (angle-Doppler coordinates), making for a massive computational burden. Steering losses can occur when true target returns do not fall exactly on one of the points in our 2-D angle-Doppler plane that we've sampled with our steering vector
259:. Unfortunately, in practice, this is oversimplified, as the interference to be overcome by steering the nulls shown is not deterministic, but statistical in nature. This is what requires STAP to be an adaptive technique. Note that even in this idealized example, in general, we must steer over the 2-D angle-Doppler plane at discrete points to detect potential targets (moving the location of the 2-D sinc main lobe shown in the figure), and do so for each of the range bins in our system.
1341:
using principal component techniques or diagonal-loading SMI (where a small magnitude, random diagonal matrix is added to attempt to stabilize the matrix prior to inverting). This modeling has an added benefit of decorrelating interference subspace leakage (ISL), and is resistant to internal clutter motion (ICM). The principal component method firsts applies
2273:
562:
sometimes called the data-independent variation. The data-dependent variation estimates the interference covariance matrix from the data. In MIMO communications systems, this can be done via a training sequence. The clairvoyant detector is given when the covariance matrix is known perfectly and defined as:
561:
uses the estimated (sample) interference covariance matrix in place of the actual interference covariance matrix. This is because the actual interference covariance matrix is not known in practice. If it is known by some means, then it need not be estimated, and the optimal weights are fixed. This is
1141:
adaptive filter problem). By performing fixed
Doppler processing, the adaptive filters become spatial only. Since the target response is already steered to a specified angle-Doppler location, the dimensionality can be reduced by pre-processing multiple Doppler bins and angles surrounding this point.
966:
must be estimated using data samples, the number of samples required to achieve a particular error is heavily dependent on the dimensionality of the interference covariance matrix. As a result, for high dimensional systems, this may require an unachievable number of unambiguous range cells. Further,
2290:
radar STAP techniques. New algorithms and formulations are required that depart from the standard technique due to the large rank of the jammer-clutter subspace created by MIMO radar virtual arrays, which typically involves exploiting the block diagonal structure of the MIMO interference covariance
203:
filter, with a standard 1-D FIR filter for each channel (steered spatial channels from an electronically steered array or individual elements), and the taps of these 1-D FIR filters corresponding to multiple returns (spaced at PRI time). Having degrees of freedom in both the spatial domain and time
1340:
There are also model based methods that attempt to force or exploit the structure of the covariance interference matrix. The more generally applicable of these methods is the covariance taper matrix structure. The goal is to compactly model the interference, at which point it can then be processed
1001:
Reduced rank methods aim to overcome the computational burdens of the direct method by reducing the dimensionality of the data or the rank of the interference covariance matrix. This can be accomplished by forming beams and performing STAP on the beamspace. Both pre and post
Doppler methods can be
1947:
More restrictive examples involve modeling the interference to force
Toeplitz structures, and can greatly reduce the computational complexity associated with the processing by exploiting this structure. However, these methods can suffer due to model-mismatch, or the computational savings may be
1145:
Since these methods reduce the data dimensionality, they are inherently sub-optimal. There are a number of techniques to compare the performance of reduced-rank methods and estimated direct methods to clairvoyant STAP (direct with perfect knowledge of interference covariance matrix and target
1753:
can be complicated, depending on the complexity of the underlying model attempting to emulate the interference environment. The reader is encouraged to see for more information on this particular subject. Once this taper is sufficiently modeled, it may also be applied to the more simple SMI
1943:
is the identity matrix of the appropriate size. It should be seen that this is meant to improve the standard SMI method where SMI uses a smaller number of range bins in its average than the standard SMI technique. Since fewer samples are used in the training data, the matrix often requires
262:
The basic functional diagram is shown to the right. For each antenna, a down conversion and analog-to-digital conversion step is typically completed. Then, a 1-D FIR filter with PRI length delay elements is used for each steered antenna channel. The lexicographically ordered weights
1497:
939:
range cell. Therefore, space-time snapshots surrounding the desired range cell are averaged. Note that the desired range cell space-time snapshot is typically excluded (as well as a number of additional cells, or "guard cells") to prevent whitening of the statistics.
2170:
1332:. Note in general this quantity is statistical and the expectation must be taken to find the average SINR loss. The clairvoyant SINR loss may also be calculated by taking the ratio of the optimal SINR to the system SNR, indicating the loss due to interference.
117:
1266:
1855:
2128:
943:
The main problem with direct methods is the great computational complexity associated with the estimation and inversion of matrices formed from many degrees of freedom (large number of elements and or pulses). In addition, for methods where
124:
STAP is essentially filtering in the space-time domain. This means that we are filtering over multiple dimensions, and multi-dimensional signal processing techniques must be employed. The goal is to find the optimal space-time weights in
1142:
In addition to reducing the dimensionality of the adaptive processor, this in turn reduces the number of required training data frames when estimating the interference covariance matrix since this quantity is dimension dependent.
878:
1039:
657:
1350:
420:
2268:{\displaystyle \mathbf {\widetilde {W}} \approx \left(\mathbf {\widetilde {Z}} \mathbf {\widetilde {Z}} ^{\mathrm {T} }\right)\mathbf {\widetilde {Z}} \mathbf {\widetilde {S}} ^{\mathrm {T} }}
1901:
2163:
2061:
2032:
2003:
1151:
1731:
475:
1759:
2068:
1526:
964:
519:
372:
1073:
350:
1297:
1139:
1639:
1921:
1330:
442:
1613:
1556:
937:
773:
716:
320:
are the degrees of freedom to be solved in the STAP problem. That is, STAP aims to find the optimal weights for the antenna array. It can be shown, that for a given
318:
237:
1583:
907:
743:
686:
288:
2361:
2387:
991:
2332:
146:
2408:
2309:
1965:
1941:
1751:
1699:
1679:
1659:
1113:
1093:
539:
497:
257:
186:
166:
85:
The theory of STAP was first published by
Lawrence E. Brennan and Irving S. Reed in the early 1970s. At the time of publication, both Brennan and Reed were at
967:
these adjacent data cells must contain stationary statistics as a function of range which is rarely a good assumption for the large number of cells required (
780:
499:
is a space-time snap-shot of the input data. The main difficulty of STAP is solving for and inverting the typically unknown interference covariance matrix,
20:
193:
102:
1948:
undone by the problem of model fitting (such as the nonlinear problem of fitting to a
Toeplitz or block-Toeplitz matrix) and order estimation.
557:
The optimum solution is using all degrees of freedom by processing the adaptive filter on the antenna elements. For adaptive direct methods,
204:
domain is crucial, as clutter can be correlated in time and space, while jammers tend to be correlated spatially (along a specific bearing).
54:, etc.). Through careful application of STAP, it is possible to achieve order-of-magnitude sensitivity improvements in target detection.
1007:
567:
239:. This is an idealized example of a steering pattern, where the response of the array has been steered to the ideal target response,
2766:
2751:
2736:
2704:
2651:
2630:
2598:
2568:
2547:
1492:{\displaystyle \mathbf {{\widetilde {R}}_{PC-CMT}} =\left(\sum _{m=0}^{P-1}\lambda _{m}v_{m}v_{m}^{H}\right)\circ T+\sigma _{n}^{2}}
2796:
196:. Thus, the goal is to suppress noise, clutter, jammers, etc., while keeping the desired radar return. It can be thought of as a
1345:
to estimate the dominant eigenvalues and eigenvectors, and then applies a covariance taper and adds an estimated noise floor:
46:
to aid in target detection. Radar signal processing benefits from STAP in areas where interference is a problem (i.e. ground
2291:
matrix to break the large matrix inversion problem into smaller ones. In comparison with SIMO radar systems, which will have
2287:
1973:
86:
379:
1969:
1342:
2776:
IEEE Aerospace and
Electronic Systems Magazine – Special Tutorials Issue, Vol. 19, No. 1, January 2004, pp. 19–35.
2478:
IEEE Aerospace and
Electronic Systems Magazine – Special Tutorials Issue, Vol. 19, No. 1, January 2004, pp. 19–35.
1862:
549:
The various approaches can be broken down by processing taxonomy, or by simplifying the data space / data sources.
189:
73:
of the interference environment, an adaptive STAP weight vector is formed. This weight vector is applied to the
35:
2423:
2139:
2037:
2008:
98:
775:
range cell consisting of the statistics from interfering noise, clutter, and jammers is estimated as follows:
558:
200:
1261:{\displaystyle L_{s,2}={\frac {{\mbox{SINR}}{\Bigr |}_{W={\hat {W}}}}{{\mbox{SINR}}{\Bigr |}_{W=W_{opt}}}}}
1979:
1968:
can formulate STAP solutions. Frequency-selective channel compensation can be used to extend traditional
1850:{\displaystyle \mathbf {{\widetilde {R}}_{SMI-CMT}} =\mathbf {{\widetilde {R}}_{SMI}} \circ T+\delta I}
2123:{\displaystyle \mathbf {\hat {S}} =\mathbf {\widetilde {W}} ^{\mathrm {T} }\mathbf {\widetilde {Z}} }
1704:
449:
2672:
IEE Colloquium on Space-Time
Adaptive Processing (Ref. No. 1998/241), April 1998, pp. 2/1–2/6.
108:
While primarily developed for radar, STAP techniques have applications for communications systems.
74:
66:
2389:
degrees of freedom, allowing for much greater adaptive spatial resolution for clutter mitigation.
1504:
947:
502:
355:
19:
2133:
1046:
323:
1273:
97:
For ground-based radar, cluttered returns tend to be at DC, making them easily discriminated by
1118:
89:(TSC). While it was formally introduced in 1973, it has theoretical roots dating back to 1959.
2762:
2747:
2732:
2700:
2647:
2626:
2594:
2564:
2543:
2413:
1618:
1906:
1302:
427:
2398:
1588:
1531:
912:
748:
691:
293:
210:
1561:
885:
721:
664:
266:
2337:
47:
2473:
2366:
970:
2314:
128:
2294:
1926:
1736:
1684:
1664:
1644:
1098:
1078:
873:{\displaystyle \mathbf {{\hat {R}}_{k}} ={\frac {1}{P}}\sum _{m=0}^{P-1}x_{m}x_{m}^{H}}
524:
482:
242:
171:
151:
58:
2790:
2780:
51:
2418:
444:
is a scalar that does not affect the SINR. The optimal detector input is given by:
62:
116:
65:
antenna with multiple spatial channels. Coupling multiple spatial channels with
2403:
1270:
where we've taken the ratio of the SINR evaluated with the sub-optimal weights
2283:
197:
70:
43:
1903:
is the typical SMI estimated matrix seen in the approximate direct method,
2165:, the estimated optimal weighting matrix (STAP coefficients) is given by:
168:
is the number of antenna elements (our spatial degrees of freedom) and
1733:
is the estimated noise floor. The estimation of the covariance taper
1146:
steering vector), mostly based around SINR loss. One such example is
1956:
Despite nearly 40 years of existence, STAP has modern applications.
207:
A simple, trivial example of STAP is shown in the first figure, for
39:
1034:{\displaystyle \mathbf {R} \Rightarrow \mathbf {\widetilde {R}} }
652:{\displaystyle \mathbf {R_{k}} ={\mbox{E}}\left{\Bigr |}_{H_{0}}}
2005:
at a MIMO receiver, we can linearly weight our space-time input
993:
for 3 dB SINR degradation from optimal, clairvoyant STAP).
909:
is the training data obtained from the input processor for the
2681:
Van Trees, H. L., Optimum Array
Processing, Wiley, NY, 2002.
2623:
Adaptive Wireless Communications: MIMO Channels and Networks
374:, the optimal weights maximizing the SINR are calculated as
2286:
to improve spatial resolution for clutter, using modified
69:
waveforms lends to the name "space-time." Applying the
1043:
Post-Doppler methods decompose the STAP problem from an
2585:
2583:
2581:
2579:
2577:
1976:
systems using STAP. To estimate the transmitted signal
23:
Doppler-Bearing response of a 2-dimensional beam-former
1641:
implies element-by-element multiplication of matrices
1216:
1178:
745:. For SMI, the interference covariance matrix for the
587:
415:{\displaystyle \mathbf {W} =\kappa \mathbf {R} ^{-1}s}
2781:
Radar Basics – Part 4: Space-time adaptive processing
2369:
2340:
2317:
2297:
2173:
2142:
2071:
2040:
2011:
1982:
1929:
1909:
1865:
1762:
1739:
1707:
1687:
1667:
1647:
1621:
1591:
1564:
1534:
1507:
1353:
1305:
1276:
1154:
1121:
1101:
1081:
1049:
1010:
973:
950:
915:
888:
783:
751:
724:
694:
667:
570:
527:
505:
485:
452:
430:
382:
358:
326:
296:
269:
245:
213:
174:
154:
131:
192:
taps (our time degrees of freedom), to maximize the
718:range cell under the interference only hypothesis,
2670:Space-Time Adaptive Processing for Airborne Radar,
2381:
2355:
2326:
2303:
2267:
2157:
2122:
2055:
2026:
1997:
1935:
1915:
1895:
1849:
1745:
1725:
1693:
1673:
1653:
1633:
1607:
1577:
1550:
1520:
1491:
1324:
1291:
1260:
1133:
1107:
1087:
1067:
1033:
985:
958:
931:
901:
872:
767:
737:
710:
680:
651:
533:
513:
491:
469:
436:
414:
366:
344:
312:
282:
251:
231:
180:
160:
140:
120:Top-level diagram for the STAP 2-D adaptive filter
2078:
1989:
1896:{\displaystyle \mathbf {{\widetilde {R}}_{SMI}} }
1225:
1187:
792:
631:
2646:, Prentice-Hall Signal Processing Series, 1984.
2617:
2615:
2613:
2611:
2609:
2607:
1299:and the SINR evaluated with the optimal weights
42:systems. It involves adaptive array processing
1944:stabilization in the form of diagonal loading.
2759:Applications of Space-Time Adaptive Processing
2559:Richards, M.A., Scheer, J.A., and Holm, W.A.,
2534:
2532:
2530:
2528:
2526:
2524:
2522:
2520:
2518:
2516:
2514:
2512:
2510:
2508:
2506:
2504:
2467:
2465:
2463:
2461:
2459:
1701:is the estimated covariance matrix taper, and
2502:
2500:
2498:
2496:
2494:
2492:
2490:
2488:
2486:
2484:
2457:
2455:
2453:
2451:
2449:
2447:
2445:
2443:
2441:
2439:
1966:multiple-input multiple-output communications
688:is the space-time snapshot statistic for the
194:signal-to-interference and noise ratio (SINR)
103:signal-to-interference and noise ratio (SINR)
8:
2744:Principles of Space-Time Adaptive Processing
2664:
2662:
2660:
2334:receive degrees of freedom, for a total of
2644:Multidimensional Digital Signal Processing
2691:
2689:
2687:
2368:
2339:
2316:
2296:
2258:
2257:
2246:
2245:
2233:
2232:
2220:
2219:
2208:
2207:
2195:
2194:
2175:
2174:
2172:
2158:{\displaystyle \mathbf {\widetilde {S}} }
2144:
2143:
2141:
2109:
2108:
2101:
2100:
2089:
2088:
2073:
2072:
2070:
2056:{\displaystyle \mathbf {\widetilde {W}} }
2042:
2041:
2039:
2027:{\displaystyle \mathbf {\widetilde {Z}} }
2013:
2012:
2010:
1984:
1983:
1981:
1928:
1908:
1880:
1869:
1868:
1866:
1864:
1819:
1808:
1807:
1805:
1777:
1766:
1765:
1763:
1761:
1738:
1717:
1712:
1706:
1686:
1666:
1646:
1620:
1596:
1590:
1569:
1563:
1539:
1533:
1512:
1506:
1483:
1478:
1454:
1449:
1439:
1429:
1413:
1402:
1368:
1357:
1356:
1354:
1352:
1310:
1304:
1278:
1277:
1275:
1241:
1230:
1224:
1223:
1215:
1200:
1199:
1192:
1186:
1185:
1177:
1174:
1159:
1153:
1120:
1100:
1080:
1048:
1020:
1019:
1011:
1009:
972:
951:
949:
920:
914:
893:
887:
864:
859:
849:
833:
822:
808:
798:
787:
786:
784:
782:
756:
750:
729:
723:
699:
693:
672:
666:
641:
636:
630:
629:
617:
612:
602:
586:
576:
571:
569:
526:
506:
504:
484:
459:
451:
429:
400:
395:
383:
381:
359:
357:
325:
301:
295:
274:
268:
244:
212:
173:
153:
130:
16:Signal processing technique used in radar
2729:Space-Time Adaptive Processing for Radar
2540:Space-Time Adaptive Processing for Radar
115:
18:
2591:Fundamentals of Radar Signal Processing
2435:
2136:. Using STAP with a training sequence
1095:individual adaptive filters of length
7:
2724:, IEEE AES-9, pp. 237–252, 1973
2625:, Cambridge University Press, 2013.
1923:is the diagonal loading factor, and
2642:Dudgeon, D.E. and Mersereau, R.M.,
1998:{\displaystyle \mathbf {\hat {S}} }
2259:
2221:
2102:
14:
2731:, Artech House Publishers, 2003.
2621:Bliss, D.W. and Govindasamy, S.,
2542:, Artech House Publishers, 2003.
2311:transmit degrees of freedom, and
1615:eigenvector estimated using PCA,
2251:
2248:
2238:
2235:
2213:
2210:
2200:
2197:
2180:
2177:
2149:
2146:
2114:
2111:
2094:
2091:
2075:
2047:
2044:
2018:
2015:
1986:
1887:
1884:
1881:
1874:
1871:
1826:
1823:
1820:
1813:
1810:
1796:
1793:
1790:
1787:
1784:
1781:
1778:
1771:
1768:
1558:eigenvalue estimated using PCA,
1384:
1381:
1378:
1375:
1372:
1369:
1362:
1359:
1025:
1022:
1012:
952:
799:
789:
577:
573:
507:
460:
396:
384:
360:
352:interference covariance matrix,
57:STAP involves a two-dimensional
38:technique most commonly used in
2699:, John Wiley & Sons, 2009.
2593:, McGraw-Hill Education, 2014.
1726:{\displaystyle \sigma _{n}^{2}}
470:{\displaystyle y=\mathbf {W} x}
190:pulse-repetition interval (PRI)
77:samples received by the radar.
1754:adaptation of CMT as follows:
1283:
1205:
1075:adaptive filtering problem to
1016:
99:Moving Target Indication (MTI)
87:Technology Service Corporation
28:Space-time adaptive processing
1:
2720:Brennan, L.E. and I.S. Reed,
559:Sample Matrix Inversion (SMI)
201:finite-impulse response (FIR)
2697:MIMO Radar Signal Processing
2563:, SciTech Publishing, 2010.
1521:{\displaystyle \lambda _{m}}
1343:principal component analysis
959:{\displaystyle \mathbf {R} }
514:{\displaystyle \mathbf {R} }
367:{\displaystyle \mathbf {R} }
2282:STAP has been extended for
1068:{\displaystyle MN\times MN}
345:{\displaystyle MN\times MN}
93:Motivation and applications
2813:
2561:Principles of Modern Radar
2363:, MIMO radar systems have
1292:{\displaystyle {\hat {W}}}
148:-dimensional space, where
1964:For dispersive channels,
1134:{\displaystyle N\times N}
2761:, IEE Publishing, 2004.
2746:, IEE Publishing, 2002.
2722:Theory of Adaptive Radar
2424:Synthetic aperture radar
2134:mean squared error (MSE)
1634:{\displaystyle A\circ B}
2797:Radar signal processing
2695:Li, J. and Stoica, P.,
1916:{\displaystyle \delta }
1325:{\displaystyle W_{opt}}
437:{\displaystyle \kappa }
2383:
2357:
2328:
2305:
2269:
2159:
2124:
2057:
2034:with weighting matrix
2028:
1999:
1937:
1917:
1897:
1851:
1747:
1727:
1695:
1675:
1655:
1635:
1609:
1608:{\displaystyle m^{th}}
1579:
1552:
1551:{\displaystyle m^{th}}
1522:
1493:
1424:
1326:
1293:
1262:
1135:
1109:
1089:
1069:
1035:
987:
960:
933:
932:{\displaystyle m^{th}}
903:
874:
844:
769:
768:{\displaystyle k^{th}}
739:
712:
711:{\displaystyle k^{th}}
682:
653:
535:
515:
493:
471:
438:
416:
368:
346:
314:
313:{\displaystyle W_{NM}}
284:
253:
233:
232:{\displaystyle N=M=10}
182:
162:
142:
121:
24:
2384:
2358:
2329:
2306:
2270:
2160:
2125:
2058:
2029:
2000:
1938:
1918:
1898:
1852:
1748:
1728:
1696:
1676:
1656:
1636:
1610:
1580:
1578:{\displaystyle v_{m}}
1553:
1523:
1494:
1398:
1327:
1294:
1263:
1136:
1110:
1090:
1070:
1036:
988:
961:
934:
904:
902:{\displaystyle x_{m}}
875:
818:
770:
740:
738:{\displaystyle H_{0}}
713:
683:
681:{\displaystyle x_{k}}
654:
536:
516:
494:
472:
439:
417:
369:
347:
315:
285:
283:{\displaystyle W_{1}}
254:
234:
183:
163:
143:
119:
22:
2783:, EETimes, 6/28/2011
2367:
2356:{\displaystyle M+NL}
2338:
2315:
2295:
2171:
2140:
2069:
2038:
2009:
1980:
1927:
1907:
1863:
1760:
1737:
1705:
1685:
1665:
1645:
1619:
1589:
1562:
1532:
1505:
1351:
1303:
1274:
1152:
1119:
1099:
1079:
1047:
1008:
997:Reduced rank methods
971:
948:
913:
886:
781:
749:
722:
692:
665:
568:
525:
503:
483:
450:
428:
380:
356:
324:
294:
267:
243:
211:
172:
152:
129:
2382:{\displaystyle MNL}
1960:MIMO communications
1952:Modern applications
1722:
1488:
1459:
1336:Model based methods
986:{\displaystyle 2NM}
869:
622:
2379:
2353:
2327:{\displaystyle NL}
2324:
2301:
2265:
2155:
2120:
2053:
2024:
1995:
1933:
1913:
1893:
1847:
1743:
1723:
1708:
1691:
1671:
1651:
1631:
1605:
1585:is the associated
1575:
1548:
1518:
1489:
1474:
1445:
1322:
1289:
1258:
1220:
1182:
1131:
1105:
1085:
1065:
1031:
983:
956:
929:
899:
870:
855:
765:
735:
708:
678:
649:
608:
591:
531:
511:
489:
467:
434:
412:
364:
342:
310:
280:
249:
229:
178:
158:
141:{\displaystyle NM}
138:
122:
61:technique using a
25:
2414:Multistatic radar
2304:{\displaystyle M}
2254:
2241:
2216:
2203:
2183:
2152:
2117:
2097:
2081:
2050:
2021:
1992:
1936:{\displaystyle I}
1877:
1816:
1774:
1746:{\displaystyle T}
1694:{\displaystyle T}
1674:{\displaystyle B}
1654:{\displaystyle A}
1365:
1286:
1256:
1219:
1208:
1181:
1108:{\displaystyle N}
1088:{\displaystyle M}
1028:
816:
795:
590:
534:{\displaystyle s}
492:{\displaystyle x}
252:{\displaystyle s}
188:is the number of
181:{\displaystyle M}
161:{\displaystyle N}
36:signal processing
2804:
2779:Michael Parker,
2774:A STAP Overview,
2757:Klemm, Richard,
2742:Klemm, Richard,
2708:
2693:
2682:
2679:
2673:
2666:
2655:
2640:
2634:
2619:
2602:
2589:Richards, M.A.,
2587:
2572:
2557:
2551:
2536:
2479:
2469:
2399:Array processing
2388:
2386:
2385:
2380:
2362:
2360:
2359:
2354:
2333:
2331:
2330:
2325:
2310:
2308:
2307:
2302:
2274:
2272:
2271:
2266:
2264:
2263:
2262:
2256:
2255:
2247:
2243:
2242:
2234:
2231:
2227:
2226:
2225:
2224:
2218:
2217:
2209:
2205:
2204:
2196:
2185:
2184:
2176:
2164:
2162:
2161:
2156:
2154:
2153:
2145:
2132:to minimize the
2129:
2127:
2126:
2121:
2119:
2118:
2110:
2107:
2106:
2105:
2099:
2098:
2090:
2083:
2082:
2074:
2062:
2060:
2059:
2054:
2052:
2051:
2043:
2033:
2031:
2030:
2025:
2023:
2022:
2014:
2004:
2002:
2001:
1996:
1994:
1993:
1985:
1942:
1940:
1939:
1934:
1922:
1920:
1919:
1914:
1902:
1900:
1899:
1894:
1892:
1891:
1890:
1879:
1878:
1870:
1856:
1854:
1853:
1848:
1831:
1830:
1829:
1818:
1817:
1809:
1801:
1800:
1799:
1776:
1775:
1767:
1752:
1750:
1749:
1744:
1732:
1730:
1729:
1724:
1721:
1716:
1700:
1698:
1697:
1692:
1680:
1678:
1677:
1672:
1660:
1658:
1657:
1652:
1640:
1638:
1637:
1632:
1614:
1612:
1611:
1606:
1604:
1603:
1584:
1582:
1581:
1576:
1574:
1573:
1557:
1555:
1554:
1549:
1547:
1546:
1527:
1525:
1524:
1519:
1517:
1516:
1498:
1496:
1495:
1490:
1487:
1482:
1464:
1460:
1458:
1453:
1444:
1443:
1434:
1433:
1423:
1412:
1389:
1388:
1387:
1367:
1366:
1358:
1331:
1329:
1328:
1323:
1321:
1320:
1298:
1296:
1295:
1290:
1288:
1287:
1279:
1267:
1265:
1264:
1259:
1257:
1255:
1254:
1253:
1252:
1251:
1229:
1228:
1221:
1217:
1213:
1212:
1211:
1210:
1209:
1201:
1191:
1190:
1183:
1179:
1175:
1170:
1169:
1140:
1138:
1137:
1132:
1114:
1112:
1111:
1106:
1094:
1092:
1091:
1086:
1074:
1072:
1071:
1066:
1040:
1038:
1037:
1032:
1030:
1029:
1021:
1015:
992:
990:
989:
984:
965:
963:
962:
957:
955:
938:
936:
935:
930:
928:
927:
908:
906:
905:
900:
898:
897:
879:
877:
876:
871:
868:
863:
854:
853:
843:
832:
817:
809:
804:
803:
802:
797:
796:
788:
774:
772:
771:
766:
764:
763:
744:
742:
741:
736:
734:
733:
717:
715:
714:
709:
707:
706:
687:
685:
684:
679:
677:
676:
658:
656:
655:
650:
648:
647:
646:
645:
635:
634:
627:
623:
621:
616:
607:
606:
592:
588:
582:
581:
580:
540:
538:
537:
532:
520:
518:
517:
512:
510:
498:
496:
495:
490:
476:
474:
473:
468:
463:
443:
441:
440:
435:
421:
419:
418:
413:
408:
407:
399:
387:
373:
371:
370:
365:
363:
351:
349:
348:
343:
319:
317:
316:
311:
309:
308:
289:
287:
286:
281:
279:
278:
258:
256:
255:
250:
238:
236:
235:
230:
187:
185:
184:
179:
167:
165:
164:
159:
147:
145:
144:
139:
2812:
2811:
2807:
2806:
2805:
2803:
2802:
2801:
2787:
2786:
2717:
2715:Further reading
2712:
2711:
2694:
2685:
2680:
2676:
2667:
2658:
2641:
2637:
2620:
2605:
2588:
2575:
2558:
2554:
2537:
2482:
2474:A STAP Overview
2470:
2437:
2432:
2395:
2365:
2364:
2336:
2335:
2313:
2312:
2293:
2292:
2280:
2244:
2206:
2193:
2189:
2169:
2168:
2138:
2137:
2087:
2067:
2066:
2036:
2035:
2007:
2006:
1978:
1977:
1972:techniques for
1962:
1954:
1925:
1924:
1905:
1904:
1867:
1861:
1860:
1806:
1764:
1758:
1757:
1735:
1734:
1703:
1702:
1683:
1682:
1663:
1662:
1643:
1642:
1617:
1616:
1592:
1587:
1586:
1565:
1560:
1559:
1535:
1530:
1529:
1508:
1503:
1502:
1435:
1425:
1397:
1393:
1355:
1349:
1348:
1338:
1306:
1301:
1300:
1272:
1271:
1237:
1222:
1214:
1184:
1176:
1155:
1150:
1149:
1117:
1116:
1097:
1096:
1077:
1076:
1045:
1044:
1006:
1005:
999:
969:
968:
946:
945:
916:
911:
910:
889:
884:
883:
845:
785:
779:
778:
752:
747:
746:
725:
720:
719:
695:
690:
689:
668:
663:
662:
637:
628:
598:
597:
593:
572:
566:
565:
555:
547:
523:
522:
501:
500:
481:
480:
448:
447:
426:
425:
394:
378:
377:
354:
353:
322:
321:
297:
292:
291:
270:
265:
264:
241:
240:
209:
208:
170:
169:
150:
149:
127:
126:
114:
95:
83:
17:
12:
11:
5:
2810:
2808:
2800:
2799:
2789:
2788:
2785:
2784:
2777:
2772:Melvin, W.L.,
2770:
2755:
2740:
2727:Guerci, J.R.,
2725:
2716:
2713:
2710:
2709:
2683:
2674:
2656:
2635:
2603:
2573:
2552:
2538:Guerci, J.R.,
2480:
2471:Melvin, W.L.,
2434:
2433:
2431:
2428:
2427:
2426:
2421:
2416:
2411:
2406:
2401:
2394:
2391:
2378:
2375:
2372:
2352:
2349:
2346:
2343:
2323:
2320:
2300:
2279:
2276:
2261:
2253:
2250:
2240:
2237:
2230:
2223:
2215:
2212:
2202:
2199:
2192:
2188:
2182:
2179:
2151:
2148:
2116:
2113:
2104:
2096:
2093:
2086:
2080:
2077:
2049:
2046:
2020:
2017:
1991:
1988:
1961:
1958:
1953:
1950:
1932:
1912:
1889:
1886:
1883:
1876:
1873:
1846:
1843:
1840:
1837:
1834:
1828:
1825:
1822:
1815:
1812:
1804:
1798:
1795:
1792:
1789:
1786:
1783:
1780:
1773:
1770:
1742:
1720:
1715:
1711:
1690:
1670:
1650:
1630:
1627:
1624:
1602:
1599:
1595:
1572:
1568:
1545:
1542:
1538:
1515:
1511:
1486:
1481:
1477:
1473:
1470:
1467:
1463:
1457:
1452:
1448:
1442:
1438:
1432:
1428:
1422:
1419:
1416:
1411:
1408:
1405:
1401:
1396:
1392:
1386:
1383:
1380:
1377:
1374:
1371:
1364:
1361:
1337:
1334:
1319:
1316:
1313:
1309:
1285:
1282:
1250:
1247:
1244:
1240:
1236:
1233:
1227:
1207:
1204:
1198:
1195:
1189:
1173:
1168:
1165:
1162:
1158:
1130:
1127:
1124:
1104:
1084:
1064:
1061:
1058:
1055:
1052:
1027:
1024:
1018:
1014:
998:
995:
982:
979:
976:
954:
926:
923:
919:
896:
892:
867:
862:
858:
852:
848:
842:
839:
836:
831:
828:
825:
821:
815:
812:
807:
801:
794:
791:
762:
759:
755:
732:
728:
705:
702:
698:
675:
671:
644:
640:
633:
626:
620:
615:
611:
605:
601:
596:
585:
579:
575:
554:
553:Direct methods
551:
546:
543:
530:
509:
488:
466:
462:
458:
455:
433:
411:
406:
403:
398:
393:
390:
386:
362:
341:
338:
335:
332:
329:
307:
304:
300:
277:
273:
248:
228:
225:
222:
219:
216:
177:
157:
137:
134:
113:
110:
94:
91:
82:
79:
15:
13:
10:
9:
6:
4:
3:
2:
2809:
2798:
2795:
2794:
2792:
2782:
2778:
2775:
2771:
2768:
2767:0-85296-924-4
2764:
2760:
2756:
2753:
2752:0-85296-172-3
2749:
2745:
2741:
2738:
2737:1-58053-377-9
2734:
2730:
2726:
2723:
2719:
2718:
2714:
2706:
2705:0-47017-898-1
2702:
2698:
2692:
2690:
2688:
2684:
2678:
2675:
2671:
2665:
2663:
2661:
2657:
2653:
2652:0-13604-959-1
2649:
2645:
2639:
2636:
2632:
2631:1-10703-320-9
2628:
2624:
2618:
2616:
2614:
2612:
2610:
2608:
2604:
2600:
2599:0-07179-832-3
2596:
2592:
2586:
2584:
2582:
2580:
2578:
2574:
2570:
2569:1-89112-152-9
2566:
2562:
2556:
2553:
2549:
2548:1-58053-377-9
2545:
2541:
2535:
2533:
2531:
2529:
2527:
2525:
2523:
2521:
2519:
2517:
2515:
2513:
2511:
2509:
2507:
2505:
2503:
2501:
2499:
2497:
2495:
2493:
2491:
2489:
2487:
2485:
2481:
2477:
2475:
2468:
2466:
2464:
2462:
2460:
2458:
2456:
2454:
2452:
2450:
2448:
2446:
2444:
2442:
2440:
2436:
2429:
2425:
2422:
2420:
2417:
2415:
2412:
2410:
2407:
2405:
2402:
2400:
2397:
2396:
2392:
2390:
2376:
2373:
2370:
2350:
2347:
2344:
2341:
2321:
2318:
2298:
2289:
2285:
2277:
2275:
2228:
2190:
2186:
2166:
2135:
2130:
2084:
2064:
1975:
1971:
1967:
1959:
1957:
1951:
1949:
1945:
1930:
1910:
1857:
1844:
1841:
1838:
1835:
1832:
1802:
1755:
1740:
1718:
1713:
1709:
1688:
1668:
1648:
1628:
1625:
1622:
1600:
1597:
1593:
1570:
1566:
1543:
1540:
1536:
1513:
1509:
1499:
1484:
1479:
1475:
1471:
1468:
1465:
1461:
1455:
1450:
1446:
1440:
1436:
1430:
1426:
1420:
1417:
1414:
1409:
1406:
1403:
1399:
1394:
1390:
1346:
1344:
1335:
1333:
1317:
1314:
1311:
1307:
1280:
1268:
1248:
1245:
1242:
1238:
1234:
1231:
1202:
1196:
1193:
1171:
1166:
1163:
1160:
1156:
1147:
1143:
1128:
1125:
1122:
1102:
1082:
1062:
1059:
1056:
1053:
1050:
1041:
1003:
996:
994:
980:
977:
974:
941:
924:
921:
917:
894:
890:
880:
865:
860:
856:
850:
846:
840:
837:
834:
829:
826:
823:
819:
813:
810:
805:
776:
760:
757:
753:
730:
726:
703:
700:
696:
673:
669:
659:
642:
638:
624:
618:
613:
609:
603:
599:
594:
583:
563:
560:
552:
550:
544:
542:
528:
486:
477:
464:
456:
453:
445:
431:
422:
409:
404:
401:
391:
388:
375:
339:
336:
333:
330:
327:
305:
302:
298:
275:
271:
260:
246:
226:
223:
220:
217:
214:
205:
202:
199:
195:
191:
175:
155:
135:
132:
118:
111:
109:
106:
104:
100:
92:
90:
88:
80:
78:
76:
72:
68:
67:pulse-Doppler
64:
60:
55:
53:
49:
45:
41:
37:
33:
29:
21:
2773:
2758:
2743:
2728:
2721:
2696:
2677:
2669:
2643:
2638:
2622:
2590:
2560:
2555:
2539:
2472:
2419:Phased array
2281:
2167:
2131:
2065:
1970:equalization
1963:
1955:
1946:
1858:
1756:
1500:
1347:
1339:
1269:
1148:
1144:
1042:
1004:
1000:
942:
881:
777:
660:
564:
556:
548:
478:
446:
423:
376:
261:
206:
123:
112:Basic theory
107:
96:
84:
63:phased-array
56:
31:
27:
26:
2404:Beamforming
2063:as follows
2668:Ward, J.,
2430:References
2284:MIMO radar
2278:MIMO radar
545:Approaches
71:statistics
44:algorithms
2252:~
2239:~
2214:~
2201:~
2187:≈
2181:~
2150:~
2115:~
2095:~
2079:^
2048:~
2019:~
1990:^
1911:δ
1875:~
1842:δ
1833:∘
1814:~
1788:−
1772:~
1710:σ
1626:∘
1510:λ
1476:σ
1466:∘
1427:λ
1418:−
1400:∑
1376:−
1363:~
1284:^
1206:^
1126:×
1057:×
1026:~
1017:⇒
838:−
820:∑
793:^
432:κ
402:−
392:κ
334:×
59:filtering
2791:Category
2393:See also
75:coherent
1528:is the
81:History
52:jamming
48:clutter
34:) is a
2765:
2750:
2735:
2703:
2650:
2629:
2597:
2567:
2546:
1859:where
1501:where
882:where
661:where
479:where
424:where
40:radar
2763:ISBN
2748:ISBN
2733:ISBN
2701:ISBN
2648:ISBN
2627:ISBN
2595:ISBN
2565:ISBN
2544:ISBN
2409:MIMO
2288:SIMO
1974:SISO
1661:and
1218:SINR
1180:SINR
1115:(an
32:STAP
290:to
198:2-D
2793::
2686:^
2659:^
2606:^
2576:^
2483:^
2438:^
1681:,
541:.
227:10
105:.
50:,
2769:.
2754:.
2739:.
2707:.
2654:.
2633:.
2601:.
2571:.
2550:.
2476:,
2377:L
2374:N
2371:M
2351:L
2348:N
2345:+
2342:M
2322:L
2319:N
2299:M
2260:T
2249:S
2236:Z
2229:)
2222:T
2211:Z
2198:Z
2191:(
2178:W
2147:S
2112:Z
2103:T
2092:W
2085:=
2076:S
2045:W
2016:Z
1987:S
1931:I
1888:I
1885:M
1882:S
1872:R
1845:I
1839:+
1836:T
1827:I
1824:M
1821:S
1811:R
1803:=
1797:T
1794:M
1791:C
1785:I
1782:M
1779:S
1769:R
1741:T
1719:2
1714:n
1689:T
1669:B
1649:A
1629:B
1623:A
1601:h
1598:t
1594:m
1571:m
1567:v
1544:h
1541:t
1537:m
1514:m
1485:2
1480:n
1472:+
1469:T
1462:)
1456:H
1451:m
1447:v
1441:m
1437:v
1431:m
1421:1
1415:P
1410:0
1407:=
1404:m
1395:(
1391:=
1385:T
1382:M
1379:C
1373:C
1370:P
1360:R
1318:t
1315:p
1312:o
1308:W
1281:W
1249:t
1246:p
1243:o
1239:W
1235:=
1232:W
1226:|
1203:W
1197:=
1194:W
1188:|
1172:=
1167:2
1164:,
1161:s
1157:L
1129:N
1123:N
1103:N
1083:M
1063:N
1060:M
1054:N
1051:M
1023:R
1013:R
981:M
978:N
975:2
953:R
925:h
922:t
918:m
895:m
891:x
866:H
861:m
857:x
851:m
847:x
841:1
835:P
830:0
827:=
824:m
814:P
811:1
806:=
800:k
790:R
761:h
758:t
754:k
731:0
727:H
704:h
701:t
697:k
674:k
670:x
643:0
639:H
632:|
625:]
619:H
614:k
610:x
604:k
600:x
595:[
589:E
584:=
578:k
574:R
529:s
508:R
487:x
465:x
461:W
457:=
454:y
410:s
405:1
397:R
389:=
385:W
361:R
340:N
337:M
331:N
328:M
306:M
303:N
299:W
276:1
272:W
247:s
224:=
221:M
218:=
215:N
176:M
156:N
136:M
133:N
30:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.