TigerSHARC CLU Closer look at the XCORRS M. Smith, University of Calgary, Canada

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Presentation transcript:

TigerSHARC CLU Closer look at the XCORRS M. Smith, University of Calgary, Canada

The practice Suppose we have the vector – in-phase and out-of- phase data gathered over an antenna from a satellite for example. Gain issues make it x j, 16+16j, 16+16j, j 16+16j, 16+16j j, 16+16j, 16+16j, j 16+16j, 16+16j, j 16+16j, 16+16j, etc Question – if the original data from the satellite had this form -1-j,1+j,1+j, -1-j,1+j,1+j, -1-j,1+j,1+j, -1-j,1+j,1+j, -1-j,1+j,1+j, -1-j,1+j,1+j, How is the satellite data delayed? FOR THIS EXAMPLE …….. 0, 3, 6, 9, 12 etc

Tackle the issue with FIR First – modify correlation function to handle complex values Ignore that issue at the moment Imagine 1024 data points PRN Need to do 1024 FIR each of 1024 taps We know how to optimize to do 2 taps every cycle (one in X and one in Y) Cycle time is 1024 * 512 cycles = 1 ms at 500 MHz XCORS can do 8 * 16 taps each cycle in each compute block – 148 times faster

Where does the CLU fit in?

XCORRS definition

THEORY Mathematical definition Uses registers TR D C And something called CUT

Satellite data Quad fetch brings in 8 complex values 8 bits each Pattern here is j, 1 + 0j, 1 + 0j, j, 1 + 0j, 1 + 0j, ……….

PRN code – 2 bit complex number Seems strange to have two dummy bits But actually makes sense PRN j, 1 + j, 1 + j, j, 1 + j, 1 + j, ………. +1, -1 are associated with the PSK – more next lecture Problem BINARY means 1 and 0, so how represent 1 and -1

PRN

0x3 value go in as C15 and C C15 = -1 –j C16 = +1 + j

Loading the THR registers

Standard XCORRS instruction Lower 46 bits ofTHR1:0 R7:3 TR0, TR1, TR2 ……. TR15

TR15:0 = XCORRS(R7:4, THR3:0) TR0 += D7 * C22 + D6 * C21 +… 8 taps TR1 += D7 * C21 + D6 * C20 +… 8 taps ……….. TR15 += D7 * C7 + D6 * C6 + … 8 taps 64 taps each cycles – on both x and y compute blocks – if set up properly 128 taps each cycle – these are “complex taps” compared to 2 real taps / cycle after lab. 3

TR15:0 = XCORRS(R7:4, THR3:0) (CUT -7) TR0 += D7 * C22 + D6 * C21 + … 8 taps TR1 += D7 * C21 + D6 * C20 + … 8 taps ……….. TR14 += D7 * C8 + D6 * C7 2 taps TR15 += D7 * C7 1 taps

TR15:0 = XCORRS(R7:4, THR3:0) (CUT -15) TR0 += D7 * C22 + D6 * C21 … 8 taps TR1 += D7 * C21 + D6 * C20 … 7 taps ……….. TR7 += D7 * C15 … 1 taps TR0 += 0 … 0 taps ……….. TR15 += 0 … 0 taps

TR15:0 = XCORRS(R7:4, THR3:0) (CUT +15) TR0 += 0 … 0 taps TR1 += D0 *C14 1 taps ……….. TR7 += D6 * C14 + D5 * C13 + … 7 taps TR0 += D7 * C14 + D6 * C13 + … 8 taps ……….. TR15 += D7 * C7 + D6 * C7 + … 8 taps

TR15:0 = XCORRS(R7:4, THR3:0) (CUT -15) TR0 += D7 * C22 + D6 * C21 … 8 taps TR1 += D7 * C21 + D6 * C20 … 7 taps ……….. TR7 += D7 * C15 … 1 taps TR0 += 0 … 0 taps ……….. TR15 += 0 … 0 taps

TR15:0 = XCORRS(R7:4, THR3:0) (CUT -7) TR0 += D7 * C22 + D6 * C21 + … 8 taps TR1 += D7 * C21 + D6 * C20 + … 8 taps ……….. TR14 += D7 * C8 + D6 * C7 2 taps TR15 += D7 * C7 1 taps

TR15:0 = XCORRS(R7:4, THR3:0) TR0 += D7 * C22 + D6 * C21 +… 8 taps TR1 += D7 * C21 + D6 * C20 +… 8 taps ……….. TR15 += D7 * C7 + D6 * C6 + … 8 taps 64 taps each cycles – on both x and y compute blocks – if set up properly 128 taps each cycle – these are “complex taps” compared to 2 real taps / cycle after lab. 3

Problem at this point -- THR3:2 empty Need to bring in more PRN values

TR15:0 = XCORRS(R7:4, THR3:0) (CUT +15) TR0 += 0 … 0 taps TR1 += D0 *C14 1 taps ……….. TR7 += D6 * C14 + D5 * C13 + … 7 taps TR0 += D7 * C14 + D6 * C13 + … 8 taps ……….. TR15 += D7 * C7 + D6 * C7 + … 8 taps

Final Result Maximum correlation occurs every 3 shifts – which is what we expect Is it the correct results

Correlation – result expected In step -1 +0j, 1 + 0j, 1 + 0j, … 16 times with -1 - j, 1 + j, 1 + j, … 16 times -1 * * * = 0x30 -- Real component Out of step -1 +0j, 1 + 0j, 1 + 0j, … 16 times with 1 + j, 1 + j, -1 - j, … 16 times -1 * * * = -0x10 = 0xFFF0

Final Result 1) Now have correlation values for 16 shifts in TR registers – store to external memory Repeat for all other necessary shifts – find the maximum 2) Now make parallel in SISD mode 3) Now make parallel in SIMD

Take home Quiz 4 Old requirement Do Lab 4 with FFT and XCORRS Write tests and demonstrate XCORRS used for correlation a)Not parallel instruction format – but in a loop b) Now do in optimized SISD mode c) Now do in optimized SIMD mode