Page 54 - Fall_DTF

Lncalizatiun with Aliased Sparse Arrays
3) Multiplicative processor A n 5 -. Ina "l‘hV_e'-f,5._I"°':~'.',_"".9__°_,'-'I,__"9 __---z
W‘ PI‘ ‘II r,i"u'|i.,nin-‘i i‘ ’|i"i ii], Iifli.-ii" ‘I‘f
xi. arm' XA .. '«( .3 E -70 | A - I
3% W E ‘D IHIIIH W ‘I llllll H In
Q9
sum-my B Xu H >'i(““’ 5 5" . . . I . . .
ms and W“) ’ g 30 \EA|u)( EIE(u)l —|P,Miuu — P_n(1uH— . |PM1uHI‘!‘
':lT
b) Min processor .iI I I .oI: 0 I as I I IV
.. ariav X4 K .L J SA( > e:9°S“'fi
iii and‘ é’ ljw D ‘ mrsmpana M=2. N=3 with unilorm tape-rir_>q ‘
|E|.s.,.<..i s
W; V} ., r’ -,, .r
., ,, x.. ,, Yul J sum.) 1 ‘?° ' . pl: '='-.. . - - , il. ~ '=’
Sn“u”...i.“m 1:‘ gm ..I‘,,, ’. i..,- ’-;j.«' ,..p,i-..,,
é ” W1" ‘H3 3‘ ,. in nu,
Figu1e3. Black diagrams for the multiplicative (a) and min (b)pr0— 2 so Q i W t; 4;; I‘ flu
cessors. Input to lwth pmeesseis is narrowband far each suliarray. E3: 80 W... ..iEA.n,i Batu)! —lP,,_,,4uI\ — Pwnn » - IP,_<un ,
Output uf eueh prueessur is an estimate afthe puwerpropuguting .,-,.m , .1,. , U... , , H" , .,,. I I...“
with directional cosine ii, The multiplicative pracessar inezudes un 4 en: 0 as 1
ubsaluie value ufrei time averaging to guuiuniee that Sm“(uD) is pasi— WW4"?
tiveforpluttingpurpuses. See text for discussion. [1 .3 ‘l E"‘:".',_"’°“’ ”=2- "=3 ‘"'l‘'‘ °°"""’°"""'V"""’
§ 20
£3 -to ‘= 5 2 5 2 .5 .
pattern of the min processor is the minimum of the subarray B-Q
ower atterns: P u) = min B u 1, B u) 2 . I so
P P ......( [l A( ll l a( l 1 g 80 ‘BANK EB(u)\ _[pMiuu _ Pwiun - - |PM1uH
Figure 2b compares the multiplicative and min power llllnmimllinnt finlmllliriinllinl
. 4 In 5 n o 4 1
patterns for the 7, 9 coprime array to the power pattern of i.:CGSWl
3 63js=“s°r UM Th? P10‘ {W's swim key PMS “b°'_" Figure 4. Camparison ofbeam and power patterns for three canfigw
Coimme may PF°C955m8- FKSL the mm 1059 05 the mull“ rations: unifarmly weightedM = 7, N = 9 unextendedeaprime array
plicative and min processors for coprime factors M and N (u), anifurmly weighted M = 2, N = 3 coprime array extended tn
has the same width as the ULA processor for an MN-sensor match the aperture nf the 7, 9 coprime array (b), and Dolph—Chel7y—
U1A_ Second_ there are no gmfing lobes in pmmw) and pmw) ehewweighted extended 2. 3 coprime array (5). Each plot shows the
because the Pmdm and min operations on me subway be_ patterns an a lagscale; absolute Value 15 used to uveidpieuzems with
. . _ _ negative sidelabes in the multiplicative pattern. The 63—sensar ULA
ampattems elinunate them. Thi.rd, the sidelobes of the mul- . .
pattern 15 included on each plat.
tiplicative and min processors are higher than for the ULA
processor with the same resolution. Finally, although the min
Power Patter“ is 8““r"‘meed to be P°5ifiVev this is H0‘ ‘me for lowers the sidelobes. Adding sensors increases the aperture,
the m“1fiPfiC“l-We P3“em- The Presence °f negalive 5idel°be5 thus increasing the resolution. If the desire is to constrain
in the P,,,,,k('4) is ‘he 19350“ ‘he m‘-‘MP1-icafive P0We1' es‘-lmate the array to the aperture spanned by the 63-sensor ULA and
is H0‘ P°5ifiVe defi-‘me? 599 Adhikflli and Buck (2017) ‘I01 3 lower the sidelobe levels, then the solution is to use lower
discussion of this important but subtle issue. Coprirng factors‘
Trading sparaity for sidelobe control Figure 2a shows an M = 2, N = 3 extended coprime-array
. . . that matches the aperture of the 7, 9 design. hi the basic 2, 3
Figure 2b shows that a coprime array with M + N — 1 = 15 _ _ _
. . . design, subarray A has 2 sensors with 3d spacing and subar-
sensors has the same main lobe width as a ULA with MN _ _ _
_ . . ray B has 3 sensors with 2d spacing. The extended design
— 63 sensors. Although the coprime array requires fewer _ _ _ _ _
. . . . . . . concatenates multiple copies of this basic design to span the
sensors, the cost of sparsity is a significant increase in sid- mu f (h 7 9 _
elobes. Applications requiring lower sidelobes must sacrifice ape e 0 E ‘ Copnme army
some sparsity. Adhikari et al. (2014) show that extending Figure 4, a and b, compares the patterns for the unextended
e co rime arra erio ic re eatin eac su arra , arra an t e exten e , esi . atterns are s own
th p" ybyp'd'a]lyp'g hb y79 ydh dd23d'gnP h
52 1 AI:i'.iuII:l:I Tbday 1 Fuuzois