Larry D’Addario, Sander Weinreb, - SKA · PDF fileSander Weinreb, Caltech/JPL,...

CostEQ2.doc Created on 7/21/2001 9:35 AM of 18

Cost Equation for the SKA

Sander Weinreb, Caltech/JPL, [email protected]

Larry D’Addario, NRAO and SETI Institute, [email protected]

July 21, 2001

1. General form of spreadsheet

2. Performance and cost parameters

3. Results: Cost vs antenna diameter and other parameters

4. Front-end model (Modified July 21, 2001)

5. Signal processing model Appendix A - Notes on Signal Processing Costs for SKA (Added July 21,2001) Appendix B - Cost Dependence When Field of View is Maintained (Added July 21, 2001

(Full Excel Spreadsheet is available as a file on SKA web sites: SKAcostEq1.xls)

mailto:[email protected]

mailto:[email protected]

CostEQ2.doc

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$.

Created on 7/21/2001 9:35 AM of 18


Param Array Performance ParametersDefault Value Param Array Cost Parameters Default Value

Ns Number of stations in array 100 Cso Fixed cost per station, land, civil, 300M Specified Figure of Merit, M = A/Tsys 20,000 Ka Antenna cost coefficient, 0.10B Processed total continuum bandwidth 4.0 X Antenna cost exponent 3.0Nl Number of spectral line channels 16,000 Ccl Cooling cost per antenna 20.0D Physical diameter of element (meters) 10.0 Cfd Average dual-polariz feed cost 2.0Ef Aperature efficiency 0.70 Cln Average LNA + mixer cost 0.8Tant Antenna noise temperature, Tant = 10 14 Clo LO cost 3.0Kln Lna noise coefficient dependant upon 0.40 Cifo Fixed IF cost per polarization 1.0Tphy Physical temperature of LNA 15 Kif Dual IF cost per GHz of bandwidt 0.2F Frequency for system temperature spe 10 a1 _Digitization coefficient 2.00Nbn Number of frequency bands 3 e _Digitization exponent 2.00Kch _Number of separately digitized chann 4 a2 _Digitization constant 0.50Le _Average distance, element to station 0.50 d _Tracking coefficient (per GHz) 0.72Nbeam_Beams per station 4 f _Tracking constant 0.10

Kproc _Processing cost coefficient (per 0.48Kmem _Memory cost (per word) 2.10E-04kct _Corner turner cost coefficient (p 1.00E-03Kcor _Correlator cost coef (per baselin 0.024Kchip Price per large FPGA chip 0.14

Color code:Purple: correction of error since previous version.Blue: change to value or formula since previous version.Red: variable whose value changes across this sheetGreen: variable whose value is different from previous sheetBold type: input parameter; normal type means value is calculated.

SKA Cost Equation Input ParametersUnits: K$US(2001), meters, GHz


SKA Cost vs Antenna Diameter for 3 Cooling TemperaturesAeff/Tsys = 20,000, Aeff=360,000, Tsys=18K, BW=4GHz,

Antenna Cost = 0.1D^3 K$, 2001 Electronics Cost = $54K per Element

$0

$500,000

$1,000,000

$1,500,000

$2,000,000

$2,500,000

5.0 10.0 15.0 20.0 25.0 30.0

Element Diameter, Meters

Cos

t, $K

(US2

001)

0

5,000

10,000

15,000

20,000

25,000

Num

ber o

f Ant

enna

s

15K Cryogenics 60K Cryogenics 180K Cryogenics# Antennas, 15K # Antennas, 60K # Antennas, 180K


SKA Cost Breakdown by Subsystem vs Antenna DiameterAeff/Tsys = 20,000, Aeff=360,000, Tsys=18K, BW=4GHz, 15K CryogenicsAntenna Cost = 0.1D^3 K$, 2001 Electronics Cost = $54K per Element

Fixed CostsCivil Station

Signal Transmission Central Processing

Electronics

Antenna

0

500,000

1,000,000

1,500,000

2,000,000

5 8 10 12 15 20 30Antenna Diameter, Meters

Tota

l Cos

t, $K

Fixed Costs Civil Station


Electronics Antenna


SKA Cost Breakdown by Subsystem vs Antenna DiameterAeff/Tsys = 20,000, Aeff=360,000, Tsys=18K, BW=4GHz, 15K CryogenicsAntenna Cost = 0.1D^3 K$, 2010Electronics Cost = $15K per Element



Electronics

Antenna

0

500,000

1,000,000

1,500,000

2,000,000


Tota

l Cos

t, $K



Electronics Antenna


SKA Cost vs Antenna Diameter Compares Current and Projected (2010) Electronics CostsAll for 15K cryogenics, 4 GHz BW, 100 Stations, A/T = 20,000

Antenna Cost = 0.1D^3 $K

$0

$500,000

$1,000,000

$1,500,000

$2,000,000

5.0 10.0 15.0 20.0 25.0 30.0


Tota

l C

ost,

$K

(US2

001)

$10

$100

$1,000

$10,000

$100,000

Ante

nna

Uni

t Cos

t, $K

$54K Electronics $15K Electronics Antenna Cost


SKA Cost vs Processed Bandwidth for Two Antenna Diameters

All for 15K Cryogenics

$0

$500,000

$1,000,000

$1,500,000

$2,000,000

0.0 2.0 4.0 6.0 8.0Processed Bandwidth, GHz

Cos

t, $K

(US2

001)

6551 x 10m Antenna 2912 x 15m Antenna


SKA Cost vs Number of Stations for Two Processed Bandwidths

All for 15K Cryogenics, 10m antennas. A/T = 20,000

$0

$500,000

$1,000,000

$1,500,000

$2,000,000

$2,500,000

0 100 200 300 400

Number of Stations

Cos

t, $K

(US2

001)

0

20

40

60

80

Ant

enna

s pe

r Sta

tion

1 GHz Bandwidth 4 GHz Bandwidth Antennas per Station


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+16 Peltier 180 3 24 120 2.4*F+10

Pulse or Klemenko 60 6 10 50 1.0*F+4 Gifford-McMann 15 20 4 20 0.4*F+1

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)] F>1 GHz, Not Including Antenna Losses


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

12

Appendix A - Notes on Signal Processing Costs for SKA L. D’Addario 2001-Jul-04; revised Jul-07, Jul-12

ANTENNA-ELEMENT SIGNAL PROCESSING COSTS 1. Digitization In present technology, this is an expensive element of the overall signal processing. We estimate about 10k$ per element for 4 GHz bandwidth, which becomes 45M$ for 4500 elements (100 stations of 45 elements each). This is about equal to the cost of the central signal processing (correlator) and 3% of the total cost of the array, based on our current estimates for one reasonable case. The cost of digitization rises faster than the bandwidth of each separately-digitized channel, and appears to go approximately as the square over the range 10 to 1000 MHz for presently available commercial devices. Therefore, it is advantageous to break up the total bandwidth prior to digitization into as many channels as practical, provided that performance does not suffer. In our cost estimates, we have usually used at least 4 channels (to allow for 2 polarizations at 2 independent sky frequencies) and kept the channel bandwidth at 1 GHz or less. 2. Tracking For each signal channel of each antenna element, it is necessary to provide for time-varying adjustment of the delay and phase so as to track a desired direction on the sky. In our cost estimates, we assume that this is accomplished digitally. The cost of computation and control for this purpose appears to be negligible (<1% of the total in all cases studied). The elements are clustered into Ns stations and the signals are combined so that each station is a phased array. This minimizes the cost of the central processing, which varies as approximately Ns

2 log Ns. However, it also reduces the field of view on the sky from the size of the element beam

to that of the phase array (station) beam. To mitigate this effect, the phase and delay tracking can be duplicated at each element so as to produce several simultaneous station beams. If the bandwidth per beam is fixed, then the total bandwidth increases along with the cost of signal transmission and central processing. Whether the increased sky coverage is worth the extra cost depends on the scientific goals. 3. Signal Transmission. The bandwidth B needs to be transmitted several times: Element to element's center; element center to control center; correlator F section to "corner turner"; and corner turner to correlator X section. In all cases we use the same coefficients for transmitter/receiver cost and installed fiber cost. Average fiber length is taken to be 0.5 km from elements within a station, 100 km from each station to the center, and zero (<<1 km) within the correlator. Sharing of parts of the transmission routes among stations could reduce this, but the number of stations has to exceed 350 before the transmission cost exceeds 5% of the total; at 100 stations it is around 1.5%

13

CORRELATOR COST DEPENDENCIES We assume that it's important to cross-correlate the signals from all stations, over the full bandwidth of each. The cost of this is proportional to the total bandwidth, regardless of whether that bandwidth represents a single channel on the sky or several independent channels (beams). There is a weak dependence on the number of channels, but this is insignificant if that number is small compared with the final number of subchannels into which the total bandwidth will be analyzed. The central processing separates naturally into a per-station part and a per-baseline part whose costs are proportional to B N and BN 2, respectively. Each cost term has additional factors that depend on the architecture and on the spectral resolution, as well as a coefficient that depends on the implementation technology. For the large-N case, the baseline term dominates the station term. For sufficiently large N, the baseline electronics will not fit into a single chip, nor a single circuit board or small set of boards, and therefore it must be partitioned into some number K of separate pacakages, each of which accomplishes 1/K of the processing. There are several ways to do the partitioning [1], and this determines the top-level architecture of the system. We concentrate here on the so-called ``FX'' architecture, where the bandwidth B from each antenna is partitioned by frequency into segments of bandwidth B/K and each element of the baseline part processes one such segment for all antennas. The available technology determines how much processing can be fit into one package, and thus how many packages K are required and how small each bandwidth segment B/K must be. We set K = t B N 2/2, where t is a technology-dependent coefficient that gets smaller as circuitry becomes denser and/or faster. The segmentation is done in the station part, which we assume to consist of one package per antenna. Therefore, C=N K interconnections are needed between different packages in order to get the signals from the station part to the baseline part. Substituting, we see that C = t B N 3/2. Because of this N 3 dependence, for sufficiently large N the cost can easily be dominated by the interconnections, even if t is small. This situation can be substantially improved by imposing an additional device between the station part and the baseline part whose purpose is to re-order the data; it is called a “corner turner'' [2]. Then the number of interconnections is reduced from N K to N+K, where N are needed from the station part to the corner turner, and K from the corner turner to the baseline part. Unfortunately, the corner turner itself is potentially a very large machine whose obvious implementation involves N K internal interconnections and data storage proportional to NK, hence its size grows as N 3. But a much more efficient implementation exists [2][3] that reduces it to a size proportional to N 2 log N, in a manner similar to the FFT's reduction of the number of operations in a discrete Fourier transform of size L from L 2 to L log L. In addition, a new architecture for the baseline part [4] allows it to be organized so that not all K segments need to be connected directly to the corner turner. This allows the corner turner size to be grow only as N log N.

14

It may be desired to analyze the bandwidth into many more than K subchannels, say L>>K, for spectroscopy. Then each of the K segments processes L/K subchannels. It is often suggested that the FX architecture allows L to be increased arbitrarily at negligible additional cost. In the station part, filter banks based on the FFT can be used so that the cost increases only as log(L); then, unless L is extreme, the cost of the station part remains small compared to the interconnections and baseline part. The interconnection cost is independent of L for a given B and N. In the baseline part, the computation rate (for cross multiplication and accumulation) is also independent of L, since the data rate of each subchannel goes as 1/L. However, L separate accumulators are needed per baseline, so storage requirements increase as L. Depending on the cost of storage compared with computation, this may be important. Usually it is not possible to take advantage of the low cost per bit of large RAM because efficient use of the computational hardware requires many multiply-add operations to be done in parallel at high speed, leading to many short memories rather than few large ones, and requiring them to be integrated on the same chip with the computational elements. This can cause the accumulator storage to be the dominant cost, so that the overall cost is nearly proportional to L. The dependence is then nearly the same as in the XF architecture, where the costs of both computation and storage are proportional to L. Indeed, this would make the absolute cost of the XF architecture smaller because the individual multipliers and accumulators are considerably less complex. All of this is summarized in the chart on the last page of this document. REFERENCES [1] L. D'Addario, ``Correlators: General design considerations.'' ATA Memo No. 24, 2001-Mar-13. [2] L. Urry, ``A corner turner architecture.'' ATA Memo No. 14, 2000-Nov-17. [3] L. D'Addario, ``Generalization of the memoryless corner turner to the non-square case.'' ATA Memo No. 22, 2001-Mar-16. (All of the above are temporarily available via http://astron.berkeley.edu/ral/ATAImagerDocs.html .) [4] L. Urry, this conference. JUSTIFICATIONS OF COST COEFFICIENTS a1,e digitizer cost parameters, fit to prices of commercial ADC chips a2 digitizer cost constant: guess at costs of downconversion, anti-alias filtering, circuit board,

$500. This can't be too far off.

15

d,e tracking coef, const: One XV300E should do 2 channels at 100 MHz, costs $144; based on preliminary design for ATA. So 722$/GHz. Constant term, $100, is just a guess to cover packaging and power.

Kproc Xilinx XV300E, 3072slices/1929perFFT1024inPlace -> 1.5 radix4 butterflys=3 radix2, $144/3= $48 ea., @100 MHz -> 480 $/butterfly/GHz Kmem Xilinx XV300E: 144$/(2mem)*(32b/word)/(131072b block RAM)/100MHz = 0.0001758 k$/word/GHz where half of chip cost is allocated to memory Kcorr Xilinx XV300E: 3072slices/51perMAC = 60 MACs, 100 MHz each, $144/chip 144$/(2comp)/60MAC/100MHz = .0120 k$/MAC/GHz where half of chip cost is allocated to computation Kinfr Total chip cost/$144 -> chip count. 16 chips/board, $160 for board, rack, power. Check: Total central processing for B=0.2, Ns=350, Nl=2048 is 5.6M$ -- ATA case B=16, Ns= 64, Nl=8192 is 58.7M$ -- ALMA case The ATA result is about 4x higher than the independent cost estimate (hardware only) made for the proposal. That proposal used future FPGA prices that are indeed about 4x lower per unit performance than the present prices used here; with this correction, the agreement is excellent. The ALMA result is also about 4x higher than its presently projected actual cost, but its architecture is quite different than assumed here.

16

Correlator Cost Model: FX Architecture

Filtering Interconnection Correlation Computation αααα B N log L ββββ B N log N ααααB N 2 / 2 Storage χχχχ B N L (control only) δδδδ B L N 2 / 2 Where: B is the total processed bandwidth N is the number of stations L is the number of spectral channels Greek symbols are cost coefficients, dependent on technology. Correlation does not include cross-polarized products.

17

Appendix B - Cost Dependence When Field of View is Maintained

LRD, 2001-Jul-12 The analyses presented at the conference considered the cost dependence on various parameters, including antenna size, front end cooling temperature, and electronics costs, while keeping the number of stations constant. This required varying the number of antennas per station in order to have enough collecting area to meet the Ae/Tsys requirement. Formally, the number of phased array beams was kept constant at 4. But the cost would be nearly unaffected if the number of beams were larger, provided that the processed bandwidth B is shared among all the beams. Here we consider relaxing that restriction. If the antennas are clustered into stations at Ns each, and if they are close-packed within a station, then each station beam is about 1/ Ns the size of the primary antenna (element) beam in solid angle. So if we still want to image the whole primary beam, we will need Ns phased-array beams. I put this into the spreadsheet to look at the dependence on Ns. Rather than sharing B among the beams, I fixed the bandwidth/beam b, making the total bandwidth B = 2 b Ns (2 for polarization). Naturally this can lead to very large B and high cost for transmission and central processing, so I considered values of b only from 0.1 to 0.5 GHz. The result is given in the accompanying figure. It can be seen that a shallow minimum in the total cost occurs at Ns = 200. Above this, the slow increase in total cost is caused by rapid increase in central processing (correlation) cost, which reaches 33% of the total at 400 antennas per station and 500 MHz bandwidth. Below the minimum, the correlator cost continues to decrease (in spite of the larger number of beams required), but the total cost is strongly affected by the processing required at each station to form many beams, including both digitization (assumed separate for each beam) and tracking.

18

SKA Cost vs Number of Stations forBeam-filled case, 0.1 and 0.5 GHz/beam

All for 15K Cryogenics, 12m antennas, 4550 total, A/T = 20,000

$0

$500,000

$1,000,000

$1,500,000

$2,000,000

$2,500,000

$3,000,000

$3,500,000

0 100 200 300 400

Number of Stations

Cos

t, $K

(US2

001)

0

20

40

60

80

100

Ant

s/st

n ==

bea

ms

0.1 GHz/beam 0.5 GHz/beam Antennas per Station

SKA Cost Estimates July 21, 2001Units K$US(2001), meters, GHz

Antenna Diameter, Meters 10,0Parameter Array Parmeters ValueC Total array cost, fixed costs, elements, processing 1.270.322Cat Total antenna cost, Ne*Ns*Ca 691.538Celt Total electronics cost, Ne*Ns*Ce 412.710Cpt Total processing cost includiing station sum 65.275Ctr Signal transmission costs 20.800Csot Total civil costs at stations, Ns*Cso 30.000Co Fixed cost per array - design + central civil 50.000Cs Total station cost, elements + combining electronics 11.345Cm Total element cost, antenna + receivers + processing 160Cp Central Signal processing costs 65.002Ns Number of stations in array 100Ne Number of elements per station 69Deq Equivalent single-antenna diameter of station 83N Total number of elements, N = Ns*Ne 6.915A Effective area of array, A=N*Ae 380.000M Specified Figure of Merit, M = A/Tsys 20.000M Computed Figure of Merit, M = A/Tsys 20.000Tsys System noise temperature at frequency, F 19B Processed total continuum bandwidth 4,0Nl Number of spectral line channels 16.000R Antenna/Electronics ratio, Ca/Ce 1,68Ropt Minimum cost ratio, Ropt = 1 / (X / 2 -1) 2,0

Antenna ParametersD Physical diameter of element (meters) 10,0Ap Physical area of element, Ap = 0.785*D^2 79Ef Aperature efficiency 0,70Ae Effective area of element, Ae=Ap*Ef 55Tant Antenna noise temperature, Tant = 10 +4*(F/10) 14Cs Cost per station, Cs =Cso + Ne*(Ca+Ce) 11.342Cso Fixed cost per station, land, civil, bunker, cables 300Ca Cost per antenna, Ca = Ka*D^X 100Ka Antenna cost coefficient, 0,10X Antenna cost exponent 3,0Csm Antenna cost per square meter physical area,K$/m^2 1,274

Receiver ParametersTsys Tsys = Tln +Tant 19Tln Tln = Kln*F+K1 5Kln Lna noise coefficient dependant upon cooler 0,40Tphy Physical temperature of LNA 15F Frequency for system temperature specification 10Ce Electronics cost per antenna, Goal 59,7Ce Ce = Ccl +Nbn*(Cfd +2* Cln) +Clo+Cif +Cpe 59,7Ccl Cooling cost per antenna 20,0Nbn Number of frequency bands 3Cfd Average dual-polariz feed cost 2,0Cln Average LNA + mixer cost 0,8Clo LO cost 3,0Cif Dual IF cost, Cif =2* (Cifo+Kif*B/2) 3,6Cifo Fixed IF cost per polarization 1,0Kif Dual IF cost per GHz of bandwidth 0,2

Signal Transmission ParametersCtr Cost of transmission, Ctr =Ns*(Clk + Ls*Cfb) 20.800Clk Fiber transceiver cost, Clk = Klk*B 8,00Klk Tranceiver cost per GHz 2,00Ls Average station to control center distance, km 100Cfb Fiber installed cost, per fiber per km 2

Signal Processing Parameters(FX architecture assumed for correlator)(Bandwidth shared among beams)

Cdig Digitization Cdig = (a1*(B/Kch)^e+a2) * Kch 10,00a1 _Digitization coefficient 2,00e _Digitization exponent 2,00a2 _Digitization constant 0,50Kch _Number of separately digitized channels 4Ctre Transmission, el to stn ctr (Klk*B + Le*Cfb) 9,00Le _Average distance, element to station center 0,50Ctrack Tracking, elements Ctrack = (d*B + f*Nbeams) 3,28d _Tracking coefficient (per GHz) 0,72f _Tracking constant 0,10Nbeams _Beams per station 4Cpe Element processing cost = Cdig+Ctre+Ctrack 22,28Csum Beam summation cost, c*B*(Ne-1) 2,726c _Summation coefficient 0,010Cps Station processing cost = Cpe*Ne + Csum 1.543Cfilt Filtering cost Cfilt = (Kproc+Kmem)*log2(Nl)*B*Ns 2.682,4Kproc _Processing cost coefficient (per GHz) 0,48Kmem _Memory cost (per word) 1,76E-04Cci Correlator interconnections Cci=Cct + 2*Klk*Ns*B 1.603Cct Cost of corner turner Cct = kct*B*Ns *log2(Ns) 2,7kct _Corner turner cost coefficient (per connection) 1,00E-03Ccor Cross correlation cost = (Kcor+Kmem*Nl) *B*Ns*Ns/2 56.496Kcor _Correlator cost coef (per baseline-GHz) 0,012Kchip Price per large FPGA chip 0,144Nchip Large chip count = (Cfilt+Cci+Ccor)/Kchip 422.091Cinfr Correlator infrastructure, $10/large chip 4.221Cpc Central processing cost = Cfilt+Cci+Ccor +Cinfr 65.002Cp Total signal processing cost = Cps*Ns+Cpc 219.349

File: skacosteq1.xls

Param Array Performance ParametersDefault Value Param Array Cost Parameters Default Value

Ns Number of stations in array 100 Cso Fixed cost per station, land, civil 300M Specified Figure of Merit, M = A/Tsys 20.000 Ka Antenna cost coefficient, 0,10B Processed total continuum bandwidth 4,0 X Antenna cost exponent 3,0Nl Number of spectral line channels 16.000 Ccl Cooling cost per antenna 20,0D Physical diameter of element (meters 10,0 Cfd Average dual-polariz feed cost 2,0Ef Aperature efficiency 0,70 Cln Average LNA + mixer cost 0,8Tant Antenna noise temperature, Tant = 10 14 Clo LO cost 3,0Kln Lna noise coefficient dependant upon 0,40 Cifo Fixed IF cost per polarization 1,0Tphy Physical temperature of LNA 15 Kif Dual IF cost per GHz of bandwidt 0,2F Frequency for system temperature sp 10 a1 _Digitization coefficient 2,00Nbn Number of frequency bands 3 e _Digitization exponent 2,00Kch _Number of separately digitized chan 4 a2 _Digitization constant 0,50Le _Average distance, element to station 0,50 d _Tracking coefficient (per GHz) 0,72Nbeam_Beams per station 4 f _Tracking constant 0,10

Kproc _Processing cost coefficient (pe 0,48Kmem _Memory cost (per word) 2,10E-04kct _Corner turner cost coefficient (p 1,00E-03Kcor _Correlator cost coef (per baseli 0,024Kchip Price per large FPGA chip 0,14

Color code: Klk Fiber Tranceiver per GHz 2Purple: correction of error since previous version.Blue: change to value or formula since previous version.Red: variable whose value changes across this sheetGreen: variable whose value is different from previous sheetBold type: input parameter; normal type means value is calculated.

SKA Cost Equation Input ParametersUnits: K$US(2001), meters, GHz


Antenna Diameter, Meters 5,0 8,0 10,0 12,0 15,0 20,0 30,0Parameter Array Parmeters Value Value Value Value Value Value ValueC Total array cost, fixed costs, elements, processing 2.163.512 1.364.319 1.270.322 1.282.439 1.386.654 1.652.120 2.286.299Cat Total antenna cost, Ne*Ns*Ca 345.769 553.230 691.538 829.845 1.037.307 1.383.076 2.074.613Celt Total electronics cost, Ne*Ns*Ce 1.650.839 644.859 412.710 286.604 183.427 103.177 45.857Cpt Total processing cost includiing station sum 66.104 65.430 65.275 65.190 65.121 65.067 65.029Ctr Signal transmission costs 20.800 20.800 20.800 20.800 20.800 20.800 20.800Csot Total civil costs at stations, Ns*Cso 30.000 30.000 30.000 30.000 30.000 30.000 30.000Co Fixed cost per array - design + central civil 50.000 50.000 50.000 50.000 50.000 50.000 50.000Cs Total station cost, elements + combining electronics 20.277 12.285 11.345 11.466 12.509 15.163 21.505Cm Total element cost, antenna + receivers + processing 72 111 160 232 397 860 2760Cp Central Signal processing costs 65.002 65.002 65.002 65.002 65.002 65.002 65.002Ns Number of stations in array 100 100 100 100 100 100 100Ne Number of elements per station 277 108 69 48 31 17 8Deq Equivalent single-antenna diameter of station 83 83 83 83 83 83 83N Total number of elements, N = Ns*Ne 27.662 10.805 6.915 4.802 3.074 1.729 768A Effective area of array, A=N*Ae 380.000 380.000 380.000 380.000 380.000 380.000 380.000M Specified Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000M Computed Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000Tsys System noise temperature at frequency, F 19 19 19 19 19 19 19B Processed total continuum bandwidth 4,0 4,0 4,0 4,0 4,0 4,0 4,0Nl Number of spectral line channels 16.000 16.000 16.000 16.000 16.000 16.000 16.000R Antenna/Electronics ratio, Ca/Ce 0,21 0,86 1,68 2,90 5,66 13,40 45,24Ropt Minimum cost ratio, Ropt = 1 / (X / 2 -1) 2,0 2,0 2,0 2,0 2,0 2,0 2,0

Antenna ParametersD Physical diameter of element (meters) 5,0 8,0 10,0 12,0 15,0 20,0 30,0Ap Physical area of element, Ap = 0.785*D^2 20 50 79 113 177 314 707Ef Aperature efficiency 0,70 0,70 0,70 0,70 0,70 0,70 0,70Ae Effective area of element, Ae=Ap*Ef 14 35 55 79 124 220 495Tant Antenna noise temperature, Tant = 10 +4*(F/10) 14 14 14 14 14 14 14Cs Cost per station, Cs =Cso + Ne*(Ca+Ce) 20.266 12.281 11.342 11.464 12.507 15.163 21.505Cso Fixed cost per station, land, civil, bunker, cables 300 300 300 300 300 300 300Ca Cost per antenna, Ca = Ka*D^X 13 51 100 173 338 800 2.700Ka Antenna cost coefficient, 0,10 0,10 0,10 0,10 0,10 0,10 0,10X Antenna cost exponent 3,0 3,0 3,0 3,0 3,0 3,0 3,0Csm Antenna cost per square meter physical area,K$/m^2 0,637 1,019 1,274 1,529 1,911 2,548 3,822

Receiver ParametersTsys Tsys = Tln +Tant 19 19 19 19 19 19 19Tln Tln = Kln*F+1 5 5 5 5 5 5 5Kln Lna noise coefficient dependant upon cooler 0,40 0,40 0,40 0,40 0,40 0,40 0,40Tphy Physical temperature of LNA 15 15 15 15 15 15 15F Frequency for system temperature specification 10 10 10 10 10 10 10Ce Electronics cost per antenna, Goal 59,7 59,7 59,7 59,7 59,7 59,7 59,7Ce Ce = Ccl +Nbn*(Cfd +2* Cln) +Clo+Cif +Cpe 59,7 59,7 59,7 59,7 59,7 59,7 59,7Ccl Cooling cost per antenna 20,0 20,0 20,0 20,0 20,0 20,0 20,0Nbn Number of frequency bands 3 3 3 3 3 3 3Cfd Average dual-polariz feed cost 2,0 2,0 2,0 2,0 2,0 2,0 2,0Cln Average LNA + mixer cost 0,8 0,8 0,8 0,8 0,8 0,8 0,8Clo LO cost 3,0 3,0 3,0 3,0 3,0 3,0 3,0Cif Dual IF cost, Cif =2* (Cifo+Kif*B/2) 3,6 3,6 3,6 3,6 3,6 3,6 3,6Cifo Fixed IF cost per polarization 1,0 1,0 1,0 1,0 1,0 1,0 1,0Kif Dual IF cost per GHz of bandwidth 0,2 0,2 0,2 0,2 0,2 0,2 0,2

Signal Transmission ParametersCtr Cost of transmission, Ctr =2*Ns*(Ne*Clk + Ls*Cfb) 20.800 20.800 20.800 20.800 20.800 20.800 20.800Clk Fiber transceiver cost, Clk = Klk*B 8,00 8,00 8,00 8,00 8,00 8,00 8,00Klk Tranceiver cost per GHz 2,00 2,00 2,00 2,00 2,00 2,00 2,00Ls Average station to control center distance, km 100 100 100 100 100 100 100Cfb Fiber installed cost, per fiber per km 2 2 2 2 2 2 2


Cdig Digitization Cdig = (a1*(B/Kch)^e+a2) * Kch 10,00 10,00 10,00 10,00 10,00 10,00 10,00a1 _Digitization coefficient 2,00 2,00 2,00 2,00 2,00 2,00 2,00e _Digitization exponent 2,00 2,00 2,00 2,00 2,00 2,00 2,00a2 _Digitization constant 0,50 0,50 0,50 0,50 0,50 0,50 0,50Kch _Number of separately digitized channels 4 4 4 4 4 4 4Ctre Transmission, el to stn ctr (Klk*B + Le*Cfb) 9,00 9,00 9,00 9,00 9,00 9,00 9,00Le _Average distance, element to station center 0,50 0,50 0,50 0,50 0,50 0,50 0,50Ctrack Tracking, elements Ctrack = (d*B + f*Nbeams) 3,28 3,28 3,28 3,28 3,28 3,28 3,28d _Tracking coefficient (per GHz) 0,72 0,72 0,72 0,72 0,72 0,72 0,72f _Tracking constant 0,10 0,10 0,10 0,10 0,10 0,10 0,10Nbeams _Beams per station 4 4 4 4 4 4 4Cpe Element processing cost = Cdig+Ctre+Ctrack 22,28 22,28 22,28 22,28 22,28 22,28 22,28Csum Beam summation cost, c*B*(Ne-1) 11,025 4,282 2,726 1,881 1,189 0,652 0,267c _Summation coefficient 0,010 0,010 0,010 0,010 0,010 0,010 0,010Cps Station processing cost = Cpe*Ne + Csum 6.174 2.412 1.543 1.072 686 386 171Cfilt Filtering cost Cfilt = (Kproc+Kmem)*log2(Nl)*B*Ns 2.682,4 2.682,4 2.682,4 2.682,4 2.682,4 2.682,4 2.682,4Kproc _Processing cost coefficient (per GHz) 0,48 0,48 0,48 0,48 0,48 0,48 0,48Kmem _Memory cost (per word) 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04Cci Correlator interconnections Cci=Cct + 2*Klk*Ns*B 1.603 1.603 1.603 1.603 1.603 1.603 1.603Cct Cost of corner turner Cct = kct*B*Ns ^2*log2(Ns) 2,7 2,7 2,7 2,7 2,7 2,7 2,7kct _Corner turner cost coefficient (per connection) 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03Ccor Cross correlation cost = (Kcor+Kmem*Nl) *B*Ns*Ns/2 56.496 56.496 56.496 56.496 56.496 56.496 56.496Kcor _Correlator cost coef (per baseline-GHz) 0,012 0,012 0,012 0,012 0,012 0,012 0,012Kchip Price per large FPGA chip 0,144 0,144 0,144 0,144 0,144 0,144 0,144Nchip Large chip count = (Cfilt+Cci+Ccor)/Kchip 422.091 422.091 422.091 422.091 422.091 422.091 422.091Cinfr Correlator infrastructure, $10/large chip 4.221 4.221 4.221 4.221 4.221 4.221 4.221Cpc Central processing cost = Cfilt+Cci+Ccor +Cinfr 65.002 65.002 65.002 65.002 65.002 65.002 65.002Cp Total signal processing cost = Cps*Ns+Cpc 682.403 306.172 219.349 172.186 133.599 103.586 82.148


SKA Cost Breakdown by Subsystem vs Antenna DiameterAeff/Tsys = 20,000, Aeff=360,000, Tsys=18K, BW=4GHz, 15K CryogenicsAntenna Cost = 0.1D^3 K$, 2001 Electronics Cost = $54K per Element



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Fixed Costs Civil StationSignal Transmission Central ProcessingElectronics Antenna


Antenna Diameter, Meters 5,0 8,0 10,0 12,0 15,0 20,0 30,0Parameter Array Parmeters Value Value Value Value Value Value ValueC Total array cost, fixed costs, elements, processing 2.539.097 1.709.110 1.650.843 1.712.295 1.901.543 2.320.499 3.274.894Cat Total antenna cost, Ne*Ns*Ca 509.554 815.287 1.019.108 1.222.930 1.528.662 2.038.217 3.057.325Celt Total electronics cost, Ne*Ns*Ce 1.862.115 727.389 465.529 323.284 206.902 116.382 51.725Cpt Total processing cost includiing station sum 66.629 65.635 65.406 65.281 65.179 65.100 65.043Ctr Signal transmission costs 20.800 20.800 20.800 20.800 20.800 20.800 20.800Csot Total civil costs at stations, Ns*Cso 30.000 30.000 30.000 30.000 30.000 30.000 30.000Co Fixed cost per array - design + central civil 50.000 50.000 50.000 50.000 50.000 50.000 50.000Cs Total station cost, elements + combining electronics 24.033 15.733 15.150 15.765 17.657 21.847 31.391Cm Total element cost, antenna + receivers + processing 58 97 146 218 383 846 2746Cp Central Signal processing costs 65.002 65.002 65.002 65.002 65.002 65.002 65.002Ns Number of stations in array 100 100 100 100 100 100 100Ne Number of elements per station 408 159 102 71 45 25 11Deq Equivalent single-antenna diameter of station 101 101 101 101 101 101 101N Total number of elements, N = Ns*Ne 40.764 15.924 10.191 7.077 4.529 2.548 1.132A Effective area of array, A=N*Ae 560.000 560.000 560.000 560.000 560.000 560.000 560.000M Specified Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000M Computed Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000Tsys System noise temperature at frequency, F 28 28 28 28 28 28 28B Processed total continuum bandwidth 4,0 4,0 4,0 4,0 4,0 4,0 4,0Nl Number of spectral line channels 16.000 16.000 16.000 16.000 16.000 16.000 16.000R Antenna/Electronics ratio, Ca/Ce 0,27 1,12 2,19 3,78 7,39 17,51 59,11Ropt Minimum cost ratio, Ropt = 1 / (X / 2 -1) 2,0 2,0 2,0 2,0 2,0 2,0 2,0


Receiver ParametersTsys Tsys = Tln +Tant 28 28 28 28 28 28 28Tln Tln = Kln*F+4 14 14 14 14 14 14 14Kln Lna noise coefficient dependant upon cooler 1,00 1,00 1,00 1,00 1,00 1,00 1,00Tphy Physical temperature of LNA 60 60 60 60 60 60 60F Frequency for system temperature specification 10 10 10 10 10 10 10Ce Electronics cost per antenna 45,7 45,7 45,7 45,7 45,7 45,7 45,7Ce Ce = Ccl +Nbn*(Cfd +2* Cln) +Clo+Cif +Cpe 45,7 45,7 45,7 45,7 45,7 45,7 45,7Ccl Cooling cost per antenna 6,0 6,0 6,0 6,0 6,0 6,0 6,0Nbn Number of frequency bands 3 3 3 3 3 3 3Cfd Average dual-polariz feed cost 2,0 2,0 2,0 2,0 2,0 2,0 2,0Cln Average LNA + mixer cost 0,8 0,8 0,8 0,8 0,8 0,8 0,8Clo LO cost 3,0 3,0 3,0 3,0 3,0 3,0 3,0Cif Dual IF cost, Cif =2* (Cifo+Kif*B/2) 3,6 3,6 3,6 3,6 3,6 3,6 3,6Cifo Fixed IF cost per polarization 1,0 1,0 1,0 1,0 1,0 1,0 1,0Kif Dual IF cost per GHz of bandwidth 0,2 0,2 0,2 0,2 0,2 0,2 0,2



Cdig Digitization Cdig = (a1*(B/Kch)^e+a2) * Kch 10,00 10,00 10,00 10,00 10,00 10,00 10,00a1 _Digitization coefficient 2,00 2,00 2,00 2,00 2,00 2,00 2,00e _Digitization exponent 2,00 2,00 2,00 2,00 2,00 2,00 2,00a2 _Digitization constant 0,50 0,50 0,50 0,50 0,50 0,50 0,50Kch _Number of separately digitized channels 4 4 4 4 4 4 4Ctre Transmission, el to stn ctr (Klk*B + Le*Cfb) 9,00 9,00 9,00 9,00 9,00 9,00 9,00Le _Average distance, element to station center 0,50 0,50 0,50 0,50 0,50 0,50 0,50Ctrack Tracking, elements Ctrack = (d*B + f*Nbeams) 3,28 3,28 3,28 3,28 3,28 3,28 3,28d _Tracking coefficient (per GHz) 0,72 0,72 0,72 0,72 0,72 0,72 0,72f _Tracking constant 0,10 0,10 0,10 0,10 0,10 0,10 0,10Nbeams _Beams per station 4 4 4 4 4 4 4Cpe Element processing cost = Cdig+Ctre+Ctrack 22,28 22,28 22,28 22,28 22,28 22,28 22,28Csum Beam summation cost, c*B*(Ne-1) 16,266 6,329 4,036 2,791 1,772 0,979 0,413c _Summation coefficient 0,010 0,010 0,010 0,010 0,010 0,010 0,010Cps Station processing cost = Cpe*Ne + Csum 9.099 3.554 2.275 1.580 1.011 569 253Cfilt Filtering cost Cfilt = (Kproc+Kmem)*log2(Nl)*B*Ns 2.682,4 2.682,4 2.682,4 2.682,4 2.682,4 2.682,4 2.682,4Kproc _Processing cost coefficient (per GHz) 0,48 0,48 0,48 0,48 0,48 0,48 0,48Kmem _Memory cost (per word) 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04Cci Correlator interconnections Cci=Cct + 2*Klk*Ns*B 1.603 1.603 1.603 1.603 1.603 1.603 1.603Cct Cost of corner turner Cct = kct*B*Ns ^2*log2(Ns) 2,7 2,7 2,7 2,7 2,7 2,7 2,7kct _Corner turner cost coefficient (per connection) 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03Ccor Cross correlation cost = (Kcor+Kmem*Nl) *B*Ns*Ns/2 56.496 56.496 56.496 56.496 56.496 56.496 56.496Kcor _Correlator cost coef (per baseline-GHz) 0,012 0,012 0,012 0,012 0,012 0,012 0,012Kchip Price per large FPGA chip 0,144 0,144 0,144 0,144 0,144 0,144 0,144Nchip Large chip count = (Cfilt+Cci+Ccor)/Kchip 422.091 422.091 422.091 422.091 422.091 422.091 422.091Cinfr Correlator infrastructure, $10/large chip 4.221 4.221 4.221 4.221 4.221 4.221 4.221Cpc Central processing cost = Cfilt+Cci+Ccor +Cinfr 65.002 65.002 65.002 65.002 65.002 65.002 65.002Cp Total signal processing cost = Cps*Ns+Cpc 974.858 420.412 292.463 222.960 166.094 121.864 90.272



Antenna Diameter, Meters 5,0 8,0 10,0 12,0 15,0 20,0 30,0Parameter Array Parmeters Value Value Value Value Value Value ValueC Total array cost, fixed costs, elements, processing 4.024.666 2.729.583 2.659.177 2.780.539 3.118.067 3.846.468 5.489.853Cat Total antenna cost, Ne*Ns*Ca 873.521 1.397.634 1.747.043 2.096.451 2.620.564 3.494.086 5.241.128Celt Total electronics cost, Ne*Ns*Ce 2.982.551 1.165.059 745.638 517.804 331.395 186.409 82.849Cpt Total processing cost includiing station sum 67.793 66.090 65.697 65.483 65.309 65.173 65.076Ctr Signal transmission costs 20.800 20.800 20.800 20.800 20.800 20.800 20.800Csot Total civil costs at stations, Ns*Cso 30.000 30.000 30.000 30.000 30.000 30.000 30.000Co Fixed cost per array - design + central civil 50.000 50.000 50.000 50.000 50.000 50.000 50.000Cs Total station cost, elements + combining electronics 38.889 25.938 25.234 26.447 29.823 37.107 53.541Cm Total element cost, antenna + receivers + processing 55 94 143 215 380 843 2743Cp Central Signal processing costs 65.002 65.002 65.002 65.002 65.002 65.002 65.002Ns Number of stations in array 100 100 100 100 100 100 100Ne Number of elements per station 699 273 175 121 78 44 19Deq Equivalent single-antenna diameter of station 132 132 132 132 132 132 132N Total number of elements, N = Ns*Ne 69.882 27.298 17.470 12.132 7.765 4.368 1.941A Effective area of array, A=N*Ae 960.000 960.000 960.000 960.000 960.000 960.000 960.000M Specified Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000M Computed Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000Tsys System noise temperature at frequency, F 48 48 48 48 48 48 48B Processed total continuum bandwidth 4,0 4,0 4,0 4,0 4,0 4,0 4,0Nl Number of spectral line channels 16.000 16.000 16.000 16.000 16.000 16.000 16.000R Antenna/Electronics ratio, Ca/Ce 0,29 1,20 2,34 4,05 7,91 18,74 63,26Ropt Minimum cost ratio, Ropt = 1 / (X / 2 -1) 2,0 2,0 2,0 2,0 2,0 2,0 2,0





Cdig Digitization Cdig = (a1*(B/Kch)^e+a2) * Kch 10,00 10,00 10,00 10,00 10,00 10,00 10,00a1 _Digitization coefficient 2,00 2,00 2,00 2,00 2,00 2,00 2,00e _Digitization exponent 2,00 2,00 2,00 2,00 2,00 2,00 2,00a2 _Digitization constant 0,50 0,50 0,50 0,50 0,50 0,50 0,50Kch _Number of separately digitized channels 4 4 4 4 4 4 4Ctre Transmission, el to stn ctr (Klk*B + Le*Cfb) 9,00 9,00 9,00 9,00 9,00 9,00 9,00Le _Average distance, element to station center 0,50 0,50 0,50 0,50 0,50 0,50 0,50Ctrack Tracking, elements Ctrack = (d*B + f*Nbeams) 3,28 3,28 3,28 3,28 3,28 3,28 3,28d _Tracking coefficient (per GHz) 0,72 0,72 0,72 0,72 0,72 0,72 0,72f _Tracking constant 0,10 0,10 0,10 0,10 0,10 0,10 0,10Nbeams _Beams per station 4 4 4 4 4 4 4Cpe Element processing cost = Cdig+Ctre+Ctrack 22,28 22,28 22,28 22,28 22,28 22,28 22,28Csum Beam summation cost, c*B*(Ne-1) 27,913 10,879 6,948 4,813 3,066 1,707 0,736c _Summation coefficient 0,010 0,010 0,010 0,010 0,010 0,010 0,010Cps Station processing cost = Cpe*Ne + Csum 15.598 6.093 3.899 2.708 1.733 975 433Cfilt Filtering cost Cfilt = (Kproc+Kmem)*log2(Nl)*B*Ns 2.682,4 2.682,4 2.682,4 2.682,4 2.682,4 2.682,4 2.682,4Kproc _Processing cost coefficient (per GHz) 0,48 0,48 0,48 0,48 0,48 0,48 0,48Kmem _Memory cost (per word) 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04Cci Correlator interconnections Cci=Cct + 2*Klk*Ns*B 1.603 1.603 1.603 1.603 1.603 1.603 1.603Cct Cost of corner turner Cct = kct*B*Ns ^2*log2(Ns) 2,7 2,7 2,7 2,7 2,7 2,7 2,7kct _Corner turner cost coefficient (per connection) 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03Ccor Cross correlation cost = (Kcor+Kmem*Nl) *B*Ns*Ns/2 56.496 56.496 56.496 56.496 56.496 56.496 56.496Kcor _Correlator cost coef (per baseline-GHz) 0,012 0,012 0,012 0,012 0,012 0,012 0,012Kchip Price per large FPGA chip 0,144 0,144 0,144 0,144 0,144 0,144 0,144Nchip Large chip count = (Cfilt+Cci+Ccor)/Kchip 422.091 422.091 422.091 422.091 422.091 422.091 422.091Cinfr Correlator infrastructure, $10/large chip 4.221 4.221 4.221 4.221 4.221 4.221 4.221Cpc Central processing cost = Cfilt+Cci+Ccor +Cinfr 65.002 65.002 65.002 65.002 65.002 65.002 65.002Cp Total signal processing cost = Cps*Ns+Cpc 1.624.758 674.279 454.938 335.790 238.305 162.483 108.325


SKA Cost vs Antenna Diameter for 3 Cooling TemperaturesAeff/Tsys = 20,000, Aeff=360,000, Tsys=18K, BW=4GHz,

Antenna Cost = 0.1D^3 K$, 2001 Electronics Cost = $54K per Element

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Antenna Diameter, Meters 10,0 10,0 10,0 10,0 15,0 15,0 15,0 15,0Parameter Array Parmeters Value Value Value Value Value Value Value ValueC Total array cost, fixed costs, elements, processing 1.104.173 1.152.641 1.270.322 1.588.670 1.285.394 1.316.074 1.386.654 1.564.696Cat Total antenna cost, Ne*Ns*Ca 691.538 691.538 691.538 691.538 1.037.307 1.037.307 1.037.307 1.037.307Celt Total electronics cost, Ne*Ns*Ce 296.116 328.066 412.710 664.983 131.607 145.807 183.427 295.548Cpt Total processing cost includiing station sum 16.319 32.637 65.275 130.549 16.280 32.560 65.121 130.242Ctr Signal transmission costs 20.200 20.400 20.800 21.600 20.200 20.400 20.800 21.600Csot Total civil costs at stations, Ns*Cso 30.000 30.000 30.000 30.000 30.000 30.000 30.000 30.000Co Fixed cost per array - design + central civil 50.000 50.000 50.000 50.000 50.000 50.000 50.000 50.000Cs Total station cost, elements + combining electronics 10.177 10.497 11.345 13.871 11.989 12.132 12.509 13.631Cm Total element cost, antenna + receivers + processing 143 147 160 196 380 385 397 434Cp Central Signal processing costs 16.250 32.501 65.002 130.004 16.250 32.501 65.002 130.004Ns Number of stations in array 100 100 100 100 100 100 100 100Ne Number of elements per station 69 69 69 69 31 31 31 31Deq Equivalent single-antenna diameter of station 83 83 83 83 83 83 83 83N Total number of elements, N = Ns*Ne 6.915 6.915 6.915 6.915 3.074 3.074 3.074 3.074A Effective area of array, A=N*Ae 380.000 380.000 380.000 380.000 380.000 380.000 380.000 380.000M Specified Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000M Computed Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000Tsys System noise temperature at frequency, F 19 19 19 19 19 19 19 19B Processed total continuum bandwidth 1,0 2,0 4,0 8,0 1,0 2,0 4,0 8,0Nl Number of spectral line channels 16.000 16.000 16.000 16.000 16.000 16.000 16.000 16.000R Antenna/Electronics ratio, Ca/Ce 2,34 2,11 1,68 1,04 7,88 7,11 5,66 3,51Ropt Minimum cost ratio, Ropt = 1 / (X / 2 -1) 2,0 2,0 2,0 2,0 2,0 2,0 2,0 2,0

Antenna ParametersD Physical diameter of element (meters) 10,0 10,0 10,0 10,0 15,0 15,0 15,0 15,0Ap Physical area of element, Ap = 0.785*D^2 79 79 79 79 177 177 177 177Ef Aperature efficiency 0,70 0,70 0,70 0,70 0,70 0,70 0,70 0,70Ae Effective area of element, Ae=Ap*Ef 55 55 55 55 124 124 124 124Tant Antenna noise temperature, Tant = 10 +4*(F/10) 14 14 14 14 14 14 14 14Cs Cost per station, Cs =Cso + Ne*(Ca+Ce) 10.177 10.496 11.342 13.865 11.989 12.131 12.507 13.629Cso Fixed cost per station, land, civil, bunker, cables 300 300 300 300 300 300 300 300Ca Cost per antenna, Ca = Ka*D^X 100 100 100 100 338 338 338 338Ka Antenna cost coefficient, 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10X Antenna cost exponent 3,0 3,0 3,0 3,0 3,0 3,0 3,0 3,0Csm Antenna cost per square meter physical area,K$/m^2 1,274 1,274 1,274 1,274 1,911 1,911 1,911 1,911

Receiver ParametersTsys Tsys = Tln +Tant 19 19 19 19 19 19 19 19Tln Tln = Kln*F+1 5 5 5 5 5 5 5 5Kln Lna noise coefficient dependant upon cooler 0,40 0,40 0,40 0,40 0,40 0,40 0,40 0,40Tphy Physical temperature of LNA 15 15 15 15 15 15 15 15F Frequency for system temperature specification 10 10 10 10 10 10 10 10Ce Electronics cost per antenna, Goal 42,8 47,4 59,7 96,2 42,8 47,4 59,7 96,2Ce Ce = Ccl +Nbn*(Cfd +2* Cln) +Clo+Cif +Cpe 42,8 47,4 59,7 96,2 42,8 47,4 59,7 96,2Ccl Cooling cost per antenna 20,0 20,0 20,0 20,0 20,0 20,0 20,0 20,0Nbn Number of frequency bands 3 3 3 3 3 3 3 3Cfd Average dual-polariz feed cost 2,0 2,0 2,0 2,0 2,0 2,0 2,0 2,0Cln Average LNA + mixer cost 0,8 0,8 0,8 0,8 0,8 0,8 0,8 0,8Clo LO cost 3,0 3,0 3,0 3,0 3,0 3,0 3,0 3,0Cif Dual IF cost, Cif =2* (Cifo+Kif*B/2) 2,4 2,8 3,6 5,2 2,4 2,8 3,6 5,2Cifo Fixed IF cost per polarization 1,0 1,0 1,0 1,0 1,0 1,0 1,0 1,0Kif Dual IF cost per GHz of bandwidth 0,2 0,2 0,2 0,2 0,2 0,2 0,2 0,2

Signal Transmission ParametersCtr Cost of transmission, Ctr =2*Ns*(Ne*Clk + Ls*Cfb) 20.200 20.400 20.800 21.600 20.200 20.400 20.800 21.600Clk Fiber transceiver cost, Clk = Klk*B 2,00 4,00 8,00 16,00 2,00 4,00 8,00 16,00Klk Tranceiver cost per GHz 2,00 2,00 2,00 2,00 2,00 2,00 2,00 2,00Ls Average station to control center distance, km 100 100 100 100 100 100 100 100Cfb Fiber installed cost, per fiber per km 2 2 2 2 2 2 2 2


Cdig Digitization Cdig = (a1*(B/Kch)^e+a2) * Kch 2,50 4,00 10,00 34,00 2,50 4,00 10,00 34,00a1 _Digitization coefficient 2,00 2,00 2,00 2,00 2,00 2,00 2,00 2,00e _Digitization exponent 2,00 2,00 2,00 2,00 2,00 2,00 2,00 2,00a2 _Digitization constant 0,50 0,50 0,50 0,50 0,50 0,50 0,50 0,50Kch _Number of separately digitized channels 4 4 4 4 4 4 4 4Ctre Transmission, el to stn ctr (Klk*B + Le*Cfb) 3,00 5,00 9,00 17,00 3,00 5,00 9,00 17,00Le _Average distance, element to station center 0,50 0,50 0,50 0,50 0,50 0,50 0,50 0,50Ctrack Tracking, elements Ctrack = (d*B + f*Nbeams) 1,12 1,84 3,28 6,16 1,12 1,84 3,28 6,16d _Tracking coefficient (per GHz) 0,72 0,72 0,72 0,72 0,72 0,72 0,72 0,72f _Tracking constant 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10Nbeams _Beams per station 4 4 4 4 4 4 4 4Cpe Element processing cost = Cdig+Ctre+Ctrack 6,62 10,84 22,28 57,16 6,62 10,84 22,28 57,16Csum Beam summation cost, c*B*(Ne-1) 0,682 1,363 2,726 5,452 0,297 0,595 1,189 2,379c _Summation coefficient 0,010 0,010 0,010 0,010 0,010 0,010 0,010 0,010Cps Station processing cost = Cpe*Ne + Csum 458 751 1.543 3.958 204 334 686 1.759Cfilt Filtering cost Cfilt = (Kproc+Kmem)*log2(Nl)*B*Ns 670,6 1.341,2 2.682,4 5.364,8 670,6 1.341,2 2.682,4 5.364,8Kproc _Processing cost coefficient (per GHz) 0,48 0,48 0,48 0,48 0,48 0,48 0,48 0,48Kmem _Memory cost (per word) 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04Cci Correlator interconnections Cci=Cct + 2*Klk*Ns*B 401 801 1.603 3.205 401 801 1.603 3.205Cct Cost of corner turner Cct = kct*B*Ns ^2*log2(Ns) 0,7 1,3 2,7 5,3 0,7 1,3 2,7 5,3kct _Corner turner cost coefficient (per connection) 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03Ccor Cross correlation cost = (Kcor+Kmem*Nl) *B*Ns*Ns/2 14.124 28.248 56.496 112.992 14.124 28.248 56.496 112.992Kcor _Correlator cost coef (per baseline-GHz) 0,012 0,012 0,012 0,012 0,012 0,012 0,012 0,012Kchip Price per large FPGA chip 0,144 0,144 0,144 0,144 0,144 0,144 0,144 0,144Nchip Large chip count = (Cfilt+Cci+Ccor)/Kchip 105.523 211.045 422.091 844.182 105.523 211.045 422.091 844.182Cinfr Correlator infrastructure, $10/large chip 1.055 2.110 4.221 8.442 1.055 2.110 4.221 8.442Cpc Central processing cost = Cfilt+Cci+Ccor +Cinfr 16.250 32.501 65.002 130.004 16.250 32.501 65.002 130.004Cp Total signal processing cost = Cps*Ns+Cpc 62.098 107.600 219.349 525.832 36.627 65.877 133.599 305.923


SKA Cost vs Processed Bandwidth for Two Antenna Diameters

All for 15K Cryogenics

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6551 x 10m Antenna 2912 x 15m Antenna


Antenna Diameter, Meters 10,0 10,0 10,0 10,0 10,0 10,0 10,0 10,0Parameter Array Parmeters Value Value Value Value Value Value Value ValueC Total array cost, fixed costs, elements, processing 1.067.172 1.104.173 1.200.832 1.484.780 1.197.318 1.270.322 1.506.960 2.342.751Cat Total antenna cost, Ne*Ns*Ca 691.538 691.538 691.538 691.538 691.538 691.538 691.538 691.538Celt Total electronics cost, Ne*Ns*Ce 296.116 296.116 296.116 296.116 412.710 412.710 412.710 412.710Cpt Total processing cost includiing station sum 4.418 16.319 62.778 246.326 17.671 65.275 251.112 985.304Ctr Signal transmission costs 10.100 20.200 40.400 80.800 10.400 20.800 41.600 83.200Csot Total civil costs at stations, Ns*Cso 15.000 30.000 60.000 120.000 15.000 30.000 60.000 120.000Co Fixed cost per array - design + central civil 50.000 50.000 50.000 50.000 50.000 50.000 50.000 50.000Cs Total station cost, elements + combining electronics 20.054 10.177 5.239 2.769 22.390 11.345 5.823 3.061Cm Total element cost, antenna + receivers + processing 143 143 143 143 160 160 160 160Cp Central Signal processing costs 4.349 16.250 62.711 246.261 17.396 65.002 250.843 985.043Ns Number of stations in array 50 100 200 400 50 100 200 400Ne Number of elements per station 138 69 35 17 138 69 35 17Deq Equivalent single-antenna diameter of station 118 83 59 42 118 83 59 42N Total number of elements, N = Ns*Ne 6.915 6.915 6.915 6.915 6.915 6.915 6.915 6.915A Effective area of array, A=N*Ae 380.000 380.000 380.000 380.000 380.000 380.000 380.000 380.000M Specified Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000M Computed Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000Tsys System noise temperature at frequency, F 19 19 19 19 19 19 19 19B Processed total continuum bandwidth 1,0 1,0 1,0 1,0 4,0 4,0 4,0 4,0Nl Number of spectral line channels 16.000 16.000 16.000 16.000 16.000 16.000 16.000 16.000R Antenna/Electronics ratio, Ca/Ce 2,34 2,34 2,34 2,34 1,68 1,68 1,68 1,68Ropt Minimum cost ratio, Ropt = 1 / (X / 2 -1) 2,0 2,0 2,0 2,0 2,0 2,0 2,0 2,0





Cdig Digitization Cdig = (a1*(B/Kch)^e+a2) * Kch 2,50 2,50 2,50 2,50 10,00 10,00 10,00 10,00a1 _Digitization coefficient 2,00 2,00 2,00 2,00 2,00 2,00 2,00 2,00e _Digitization exponent 2,00 2,00 2,00 2,00 2,00 2,00 2,00 2,00a2 _Digitization constant 0,50 0,50 0,50 0,50 0,50 0,50 0,50 0,50Kch _Number of separately digitized channels 4 4 4 4 4 4 4 4Ctre Transmission, el to stn ctr (Klk*B + Le*Cfb) 3,00 3,00 3,00 3,00 9,00 9,00 9,00 9,00Le _Average distance, element to station center 0,50 0,50 0,50 0,50 0,50 0,50 0,50 0,50Ctrack Tracking, elements Ctrack = (d*B + f*Nbeams) 1,12 1,12 1,12 1,12 3,28 3,28 3,28 3,28d _Tracking coefficient (per GHz) 0,72 0,72 0,72 0,72 0,72 0,72 0,72 0,72f _Tracking constant 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10Nbeams _Beams per station 4 4 4 4 4 4 4 4Cpe Element processing cost = Cdig+Ctre+Ctrack 6,62 6,62 6,62 6,62 22,28 22,28 22,28 22,28Csum Beam summation cost, c*B*(Ne-1) 1,373 0,682 0,336 0,163 5,492 2,726 1,343 0,652c _Summation coefficient 0,010 0,010 0,010 0,010 0,010 0,010 0,010 0,010Cps Station processing cost = Cpe*Ne + Csum 917 458 229 115 3.087 1.543 772 386Cfilt Filtering cost Cfilt = (Kproc+Kmem)*log2(Nl)*B*Ns 335,3 670,6 1.341,2 2.682,4 1.341,2 2.682,4 5.364,8 10.729,7Kproc _Processing cost coefficient (per GHz) 0,48 0,48 0,48 0,48 0,48 0,48 0,48 0,48Kmem _Memory cost (per word) 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04Cci Correlator interconnections Cci=Cct + 2*Klk*Ns*B 200 401 802 1.603 801 1.603 3.206 6.414Cct Cost of corner turner Cct = kct*B*Ns ^2*log2(Ns) 0,3 0,7 1,5 3,5 1,1 2,7 6,1 13,8kct _Corner turner cost coefficient (per connection) 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03Ccor Cross correlation cost = (Kcor+Kmem*Nl) *B*Ns*Ns/2 3.531 14.124 56.496 225.984 14.124 56.496 225.984 903.936Kcor _Correlator cost coef (per baseline-GHz) 0,012 0,012 0,012 0,012 0,012 0,012 0,012 0,012Kchip Price per large FPGA chip 0,144 0,144 0,144 0,144 0,144 0,144 0,144 0,144Nchip Large chip count = (Cfilt+Cci+Ccor)/Kchip 28.240 105.523 407.213 1.599.096 112.961 422.091 1.628.854 6.396.385Cinfr Correlator infrastructure, $10/large chip 282 1.055 4.072 15.991 1.130 4.221 16.289 63.964Cpc Central processing cost = Cfilt+Cci+Ccor +Cinfr 4.349 16.250 62.711 246.261 17.396 65.002 250.843 985.043Cp Total signal processing cost = Cps*Ns+Cpc 50.197 62.098 108.558 292.106 171.745 219.349 405.187 1.139.379


SKA Cost vs Number of Stations for Two Processed BandwidthsAll for 15K Cryogenics, 10m antennas. A/T = 20,000

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Antenna Diameter, Meters 5,0 8,0 10,0 12,0 15,0 20,0 30,0Parameter Array Parmeters Value Value Value Value Value Value ValueC Total array cost, fixed costs, elements, processing 882.635 836.916 916.797 1.023.367 1.204.861 1.530.433 2.207.545Cat Total antenna cost, Ne*Ns*Ca 345.769 553.230 691.538 829.845 1.037.307 1.383.076 2.074.613Celt Total electronics cost, Ne*Ns*Ce 414.923 162.079 103.731 72.035 46.103 25.933 11.526Cpt Total processing cost includiing station sum 21.844 21.506 21.429 21.386 21.352 21.325 21.306Ctr Signal transmission costs 20.100 20.100 20.100 20.100 20.100 20.100 20.100Csot Total civil costs at stations, Ns*Cso 30.000 30.000 30.000 30.000 30.000 30.000 30.000Co Fixed cost per array - design + central civil 50.000 50.000 50.000 50.000 50.000 50.000 50.000Cs Total station cost, elements + combining electronics 7.863 7.436 8.242 9.311 11.129 14.387 21.160Cm Total element cost, antenna + receivers + processing 27 66 115 188 352 815 2715Cp Central Signal processing costs 21.292 21.292 21.292 21.292 21.292 21.292 21.292Ns Number of stations in array 100 100 100 100 100 100 100Ne Number of elements per station 277 108 69 48 31 17 8Deq Equivalent single-antenna diameter of station 83 83 83 83 83 83 83N Total number of elements, N = Ns*Ne 27.662 10.805 6.915 4.802 3.074 1.729 768A Effective area of array, A=N*Ae 380.000 380.000 380.000 380.000 380.000 380.000 380.000M Specified Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000M Computed Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000Tsys System noise temperature at frequency, F 19 19 19 19 19 19 19B Processed total continuum bandwidth 4,0 4,0 4,0 4,0 4,0 4,0 4,0Nl Number of spectral line channels 16.000 16.000 16.000 16.000 16.000 16.000 16.000R Antenna/Electronics ratio, Ca/Ce 0,84 3,45 6,75 11,66 22,77 53,98 182,19Ropt Minimum cost ratio, Ropt = 1 / (X / 2 -1) 2,0 2,0 2,0 2,0 2,0 2,0 2,0





Cdig Digitization Cdig = (a1*(B/Kch)^e+a2) * Kch 2,00 2,00 2,00 2,00 2,00 2,00 2,00a1 _Digitization coefficient 0,40 0,40 0,40 0,40 0,40 0,40 0,40e _Digitization exponent 2,00 2,00 2,00 2,00 2,00 2,00 2,00a2 _Digitization constant 0,10 0,10 0,10 0,10 0,10 0,10 0,10Kch _Number of separately digitized channels 4 4 4 4 4 4 4Ctre Transmission, el to stn ctr (Klk*B + Le*Cfb) 2,00 2,00 2,00 2,00 2,00 2,00 2,00Le _Average distance, element to station center 0,50 0,50 0,50 0,50 0,50 0,50 0,50Ctrack Tracking, elements Ctrack = (d*B + f*Nbeams) 0,92 0,92 0,92 0,92 0,92 0,92 0,92d _Tracking coefficient (per GHz) 0,18 0,18 0,18 0,18 0,18 0,18 0,18f _Tracking constant 0,05 0,05 0,05 0,05 0,05 0,05 0,05Nbeams _Beams per station 4 4 4 4 4 4 4Cpe Element processing cost = Cdig+Ctre+Ctrack 4,92 4,92 4,92 4,92 4,92 4,92 4,92Csum Beam summation cost, c*B*(Ne-1) 5,512 2,141 1,363 0,940 0,595 0,326 0,134c _Summation coefficient 0,005 0,005 0,005 0,005 0,005 0,005 0,005Cps Station processing cost = Cpe*Ne + Csum 1.366 534 342 237 152 85 38Cfilt Filtering cost Cfilt = (Kproc+Kmem)*log2(Nl)*B*Ns 1.341,0 1.341,0 1.341,0 1.341,0 1.341,0 1.341,0 1.341,0Kproc _Processing cost coefficient (per GHz) 0,24 0,24 0,24 0,24 0,24 0,24 0,24Kmem _Memory cost (per word) 5,00E-05 5,00E-05 5,00E-05 5,00E-05 5,00E-05 5,00E-05 5,00E-05Cci Correlator interconnections Cci=Cct + 2*Klk*Ns*B 203 203 203 203 203 203 203Cct Cost of corner turner Cct = kct*B*Ns ^2*log2(Ns) 2,7 2,7 2,7 2,7 2,7 2,7 2,7kct _Corner turner cost coefficient (per connection) 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03Ccor Cross correlation cost = (Kcor+Kmem*Nl) *B*Ns*Ns/2 16.200 16.200 16.200 16.200 16.200 16.200 16.200Kcor _Correlator cost coef (per baseline-GHz) 0,010 0,010 0,010 0,010 0,010 0,010 0,010Kchip Price per large FPGA chip 0,050 0,050 0,050 0,050 0,050 0,050 0,050Nchip Large chip count = (Cfilt+Cci+Ccor)/Kchip 354.873 354.873 354.873 354.873 354.873 354.873 354.873Cinfr Correlator infrastructure, $10/large chip 3.549 3.549 3.549 3.549 3.549 3.549 3.549Cpc Central processing cost = Cfilt+Cci+Ccor +Cinfr 21.292 21.292 21.292 21.292 21.292 21.292 21.292Cp Total signal processing cost = Cps*Ns+Cpc 157.938 74.668 55.452 45.014 36.473 29.831 25.086


SKA Cost vs Antenna Diameter Compares Current and Projected (2010) Electronics CostsAll for 15K cryogenics, 4 GHz BW, 100 Stations, A/T = 20,000

Antenna Cost = 0.1D^3 $K

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$54K Electronics $15K Electronics Antenna Cost

SKA Cost Breakdown by Subsystem vs Antenna DiameterAeff/Tsys = 20,000, Aeff=360,000, Tsys=18K, BW=4GHz, 15K CryogenicsAntenna Cost = 0.1D^3 K$, 2010Electronics Cost = $15K per Element



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Electronics Antenna


Antenna Diameter, Meters 12,0 12,0 12,0 12,0 12,0 12,0 12,0 12,0Parameter Array Parmeters Value Value Value Value Value Value Value ValueC Total array cost, fixed costs, elements, processing 1.925.363 1.562.279 1.447.036 1.522.012 3.638.425 2.551.656 2.187.368 2.363.413Cat Total antenna cost, Ne*Ns*Ca 829.845 829.845 829.845 829.845 829.845 829.845 829.845 829.845Celt Total electronics cost, Ne*Ns*Ce 990.372 583.549 380.138 278.432 2.584.454 1.380.590 778.658 477.692Cpt Total processing cost includiing station sum 29.745 48.084 85.453 160.535 148.726 240.421 427.264 802.676Ctr Signal transmission costs 10.400 20.800 41.600 83.200 10.400 20.800 41.600 83.200Csot Total civil costs at stations, Ns*Cso 15.000 30.000 60.000 120.000 15.000 30.000 60.000 120.000Co Fixed cost per array - design + central civil 50.000 50.000 50.000 50.000 50.000 50.000 50.000 50.000Cs Total station cost, elements + combining electronics 36.723 14.438 6.351 3.071 68.677 22.427 8.348 3.570Cm Total element cost, antenna + receivers + processing 379 294 252 231 711 460 335 272Cp Central Signal processing costs 28.832 47.632 85.232 160.429 144.161 238.162 426.159 802.147Ns Number of stations in array 50 100 200 400 50 100 200 400Ne Number of elements per station 96 48 24 12 96 48 24 12Deq Equivalent single-antenna diameter of station 118 83 59 42 118 83 59 42N Total number of elements, N = Ns*Ne 4.802 4.802 4.802 4.802 4.802 4.802 4.802 4.802A Effective area of array, A=N*Ae 380.000 380.000 380.000 380.000 380.000 380.000 380.000 380.000M Specified Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000M Computed Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000Tsys System noise temperature at frequency, F 19 19 19 19 19 19 19 19B Processed total continuum bandwidth 19,2 9,6 4,8 2,4 96,0 48,0 24,0 12,0Nl Number of spectral line channels 4.096 4.096 4.096 4.096 4.096 4.096 4.096 4.096R Antenna/Electronics ratio, Ca/Ce 0,84 1,42 2,18 2,98 0,32 0,60 1,07 1,74Ropt Minimum cost ratio, Ropt = 1 / (X / 2 -1) 2,0 2,0 2,0 2,0 2,0 2,0 2,0 2,0





Cdig Digitization Cdig = (a1*(B/Kch)^e+a2) * Kch 99,89 49,94 24,97 12,49 192,09 96,05 48,02 24,01a1 _Digitization coefficient 2,00 2,00 2,00 2,00 2,00 2,00 2,00 2,00e _Digitization exponent 2,00 2,00 2,00 2,00 2,00 2,00 2,00 2,00a2 _Digitization constant 0,50 0,50 0,50 0,50 0,50 0,50 0,50 0,50Kch _Number of separately digitized channels 192,093823 96,0469113 48,0234557 24,0117278 192,093823 96,0469113 48,0234557 24,0117278Ctre Transmission, el to stn ctr (Klk*B + Le*Cfb) 39,42 20,21 10,60 5,80 193,09 97,05 49,02 25,01Le _Average distance, element to station center 0,50 0,50 0,50 0,50 0,50 0,50 0,50 0,50Ctrack Tracking, elements Ctrack = (d*B + f*Nbeams) 23,44 11,72 5,86 2,93 78,76 39,38 19,69 9,84d _Tracking coefficient (per GHz) 0,72 0,72 0,72 0,72 0,72 0,72 0,72 0,72f _Tracking constant 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10Nbeams _Beams per station 96 48 24 12 96 48 24 12Cpe Element processing cost = Cdig+Ctre+Ctrack 162,74 81,87 41,44 21,22 463,95 232,47 116,74 58,87Csum Beam summation cost, c*B*(Ne-1) 18,258 4,516 1,105 0,264 91,290 22,582 5,526 1,321c _Summation coefficient 0,010 0,010 0,010 0,010 0,010 0,010 0,010 0,010Cps Station processing cost = Cpe*Ne + Csum 15.649 3.936 996 255 44.652 11.187 2.809 708Cfilt Filtering cost Cfilt = (Kproc+Kmem)*log2(Nl)*B*Ns 5.534,3 5.534,3 5.534,3 5.534,3 27.671,6 27.671,6 27.671,6 27.671,6Kproc _Processing cost coefficient (per GHz) 0,48 0,48 0,48 0,48 0,48 0,48 0,48 0,48Kmem _Memory cost (per word) 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04Cci Correlator interconnections Cci=Cct + 2*Klk*Ns*B 3.847 3.848 3.849 3.850 19.236 19.241 19.246 19.251Cct Cost of corner turner Cct = kct*B*Ns ^2*log2(Ns) 5,4 6,4 7,3 8,3 27,1 31,9 36,7 41,5kct _Corner turner cost coefficient (per connection) 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03Ccor Cross correlation cost = (Kcor+Kmem*Nl) *B*Ns*Ns/2 17.578 35.157 70.314 140.627 87.892 175.784 351.569 703.137Kcor _Correlator cost coef (per baseline-GHz) 0,012 0,012 0,012 0,012 0,012 0,012 0,012 0,012Kchip Price per large FPGA chip 0,144 0,144 0,144 0,144 0,144 0,144 0,144 0,144Nchip Large chip count = (Cfilt+Cci+Ccor)/Kchip 187.223 309.302 553.453 1.041.750 936.113 1.546.508 2.767.266 5.208.748Cinfr Correlator infrastructure, $10/large chip 1.872 3.093 5.535 10.417 9.361 15.465 27.673 52.087Cpc Central processing cost = Cfilt+Cci+Ccor +Cinfr 28.832 47.632 85.232 160.429 144.161 238.162 426.159 802.147Cp Total signal processing cost = Cps*Ns+Cpc 811.293 441.259 284.442 262.431 2.376.755 1.356.836 987.873 1.085.381


SKA Cost vs Number of Stations forBeam-filled case, 0.1 and 0.5 GHz/beam

All for 15K Cryogenics, 12m antennas, 4550 total, A/T = 20,000

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Larry D’Addario, Sander Weinreb, - SKA · PDF fileSander Weinreb, Caltech/JPL,...

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