Cost Equation for the SKA

 

Sander Weinreb, Caltech/JPL,  sweinreb@caltech.edu

Larry D’Addario, NRAO and SETI Institute, ldaddario@astro.berkeley.edu

 

July 7, 2001

 

1.   General form of spreadsheet

 

2.   Performance and cost parameters

 

3.   Results: Cost vs antenna diameter and other parameters

 

4.   Front-end model

 

5.   Signal processing model

 

                       

 

Text Box: SKA Cost Equation Spread Sheet Rows are for input or computed parameters such as cost coefficients or performance parameters Columns are for varying antenna diameters Sheets are for varying major parameters such as cryogenic temperature or era of electronics costs. Output of the program is the total cost and cost of each subsystem. The Aeff/Tsys is constrained at 20,000 by computing the number of antennas needed for each station. Parameters – There are 14 performance parameters and 19 cost parameters listed on the next page Models – Details are in the equations in the spreadsheet. Antenna cost is 0.1*D^3 K$.

 

 

 

 


 



 

 




Front-End Cost and Performance  Model

 

Cooler Type

Physical Temp

Cooler

Cost, K$

Noise @

10 GHz

Noise @

50 GHz

Noise @

F GHz

None

300

1

40

200

4*F

Peltier

180

3

24

120

2.4*F

Pulse or Klemenko

60

6

10

50

1.0*F

Gifford-McMann

15

20

4

20

0.4*F

 

Total Front-End Cost, FE$

 

FE$ = Cooler$ + 3(Bands)*2(Polarizations)* LNA$

LNA$ = $0.8K*(Fmax/10)^.3

i.e. FE$ = $11.9K  for Pulse Cooling with Fmax = 20 GHz 

 

Total Electronics Cost, EL$, per Antenna

 

EL$ = FE$+ 3*Feed$+LO$+IF$+Fixed$

Feed$ = $1K,   LO$ = $5K,    IF$ = 2*(0.5 + 2*BW),     Fixed$ = $1K

i.e. EL$ = 11.9 + 3*1 + 5 + 2*4.5 +1 = $29.9K

 

Total System Noise, Tsys

 

Tsys = Tlna + [10 + 4* (F/10)]
Signal Processing Cost Model

 

·        EACH ANTENNA

1.    Digitization

                   Cd  =  [kd (B/Nch)e + cd] Nch     (exponent  e  is approximately 2)

                   Cost per channel increases faster than bandwidth  => more channels

·        Presently expensive -- total for array is more than the correlator!

2.    Tracking         

·        Primarily delay and phase tracking of sources

·        Per antenna per beam -- multi beaming is probably needed to mitigate small FOV of station beam.

·        All-digital implementation assumed

·        EACH STATION

1.    Summation to form phased-array, per beam

·        Multi-beaming probably needed due to small station beam

2.    Transmission to central processing facility

·        available bandwidth shared among beams.

·        CENTRAL PROCESSING (CORRELATION)

1.    Per antenna section

·        filter bank for  L  spectral channels

·        cost grows as  B log(L)  if minimum-memory FFTs are used

2.    Interconnection section

·        can dominate cost for large  N

·        natural architecture grows as  B N 3

·        clever architecture grows as  B N  log(N)

3.    Cross correlation section

·        grows as  B L N 2  (note  L  dependence, even for FX architecture)