User waveforms, constellations, and
fi
lters
The constellation RAM is accessed with a 9-bit address that is the concatenation
of a (9 – N)-bit symbol set and an N-bit symbol. The address is computed from
the current symbol and set with the equation:
constellation address = ( set × 2N) mod 512
where N is the number of bits per symbol. As an example, suppose the symbol
reader is reading in 2-bit symbols and that the current symbol is 3 and that the
current symbol set is 5. The symbol will be mapped to the constellation point
stored at address 3 + 5 × 22 = 23. At startup the
fi
rst symbol set is initialized
to zero.
For simple constellations, symbol set RAM is cleared and the symbol maps
directly to a constellation point. For a constellation that rotates by
π
/4 after each
symbol, we will have 8 different constellations before the constellation has rotated
by exactly 2
π
. For N-bit symbols, the rotation is accomplished by
fi
lling symbol
set RAM with 2N 1s, followed by 2N 2s, followed by 2N 3s, etc until we reach 2N
7s, followed by 2N 0s. For differential encoding, the encoding of the next symbol
is determined by the previous symbol. In this case, each symbol gets mapped to a
different constellation, and so we have 2N different constellations.
For each user constellation, two parameters must be declared: bits/symbol and
whether the I and Q points in the constellation are to be staggered or not. Most
constellations do not operate in staggered mode; both I and Q points enter their
respective pulse shaping
fi
lters simultaneously. Staggered mode is required for
offset modulation in which the Q values shift into their
fi
lter half a symbol after
the I values have shifted.
User constellations are downloaded into SRAM with the following command:
WRTC i, j, <arb data>. Parameter i indicates the number of bits/symbol, N.
It will normally range from 1 to 9. A value of 16 or 32 is accepted to enable
staggered modulation when constellation mapping is bypassed. Parameter j
indicates whether staggered operation is desired. Set j = 1 for staggered operation,
otherwise set j = 0. <arb data> should be a de
fi
nite arbitrary block with 2560 bytes
of binary data. The <arb data> block is organized as 512 32-bit IQ pairs followed
by 512 bytes of symbol set data. Each 32-bit IQ pair consists of a 16-bit I value
followed by a 16-bit Q value in a big-endian format.
NOTE.
You can read more about big-endian byte order and downloading binary
data here. (See page 58.)
Constellation example
As an example, we will compute the constellation for QPSK with the symbol
mapping de
fi
ned in the following
fi
gure.
68
TSG4100A Series RF Signal Generators User Manual
