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

Overview Recap GPS correlation Look at XCORRS instruction in detail This was part of Take home quiz for 5005 Additional information on the web Xcorrs.asm – assembly code discussed in class Xmain.cpp – demonstrates the use of the xcorrs.asm code XcorrsTest.cpp – demonstrates testing of all the functions being used Additional correlation presentations (not XCORRS) from Analog Devices developers In 2005, we pointed out many errors in TigerSHARC XCORRS explanation – if my figures are not the same as in the manual, then they fixed the manual errors

GPS Positioning Concepts (1) For now make 2 assumptions: We know the distance to each satellite We know where each satellite is With this information from 2 satellites – you know you are on a “plane of intersection. Require 3 satellites for a 3-D position in this “ideal” scenario Requires 4 satellites to account for local receiver clock drift.

Determining Time Use the PRN code to determine time Use time to determine distance to the satellite distance = speed of light * time (1) Signal send by satellite Signal received by you You know the signal sent Perform correlations till you get a match

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 much 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 – 1 add + 1 multiplication + 2 memory fetches to 3 adds + 4 multiplications plus 4 memory fetches 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 -- accumulate D -- 8 data? C -- 1 coefficient? And something called CUT – essentially a window operation f cut = 0 -- don’t use

2005 Lab. 4 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 another lecture Problem BINARY means 1 and 0, so how represent 1 and are stored as 1’s, +1 stored as 0’s (DAMY)

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) Doing 8 complex taps of 16 correlation at each cycle 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) Because of offsets, sometimes we must only use “some of the taps” 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 +7?) 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 result?

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

Overview Recap GPS correlation Look at XCORRS instruction in detail This was part of Take home quiz for 5005 Additional information on the web Xcorrs.asm – assembly code discussed in class Xmain.cpp – demonstrates the use of the xcorrs.asm code XcorrsTest.cpp – demonstrates testing of all the functions being used Additional correlation presentations (not XCORRS) from Analog Devices developers In 2005, we pointed out many errors in TigerSHARC XCORRS explanation – if my figures are not the same as in the manual, then they fixed the manual errors