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Lattice Semiconductor
Correlator IP Core
General Description
A correlation function determines how closely a data sequence matches a reference, or “coef?cient” sequence. A
high correlation value means that the data sequence closely matches the coef?cient sequence. A low correlation
value means that the data sequence is dissimilar to the coef?cient sequence. The basic correlator equation is given
by:
corr _ w in 1
r k =
d i + k c i
k = 0,1,…,n u m_lags-1
(1)
i = 0
The terms of the equation are:
? d i – Input data sequence. The Correlator IP core allows the input sequence to be from 1 to 8 bits wide, and either
signed (two’s complement) or unsigned data.
? c i – Coef?cient (or code) sequence. In the Correlator IP core, this sequence must be loaded into internal memory
prior to a correlation operation. This sequence is always binary {1,0}; however, the coef?cient sequence may rep-
resent either an unsigned sequence {1,0} or a signed sequence {+1,-1}. In the case of a signed coef?cient
sequence, a 1 in the sequence represents a value of +1 and a 0 in the sequence represents a value of -1. The d i
and c i inputs must both be of the same type, either signed or unsigned.
? r k – Correlation result output sequence (correlation between d i and c i inputs).
? corr_win – Correlation window. This is the number of elements in the input data sequence over which the corre-
lation function is calculated. This is also referred to as the number of “taps.” For the Correlator IP core this num-
ber is determined by the user when con?guring the core. Once selected, the number of data elements (and
coef?cient terms) is then ?xed at this number for all correlation operations. The number of terms in the coef?cient
sequence is always equal to the number of taps (corr_win) speci?ed.
? num_lags – Total number of lags for which the correlation is performed. This is also the length of the correlation
result sequence, r k.
From Equation 1, a correlation operation takes an input data sequence d i of length “corr_win” and multiplies each
term in the sequence against the terms of the reference coef?cient sequence c i , summing the results of all of the
multiplications to produce the result r k . The input data sequence is then shifted by one element and the operation is
repeated to produce the next term in the r k sequence. This is done “num_lags” times.
In the Correlator IP core, each time a new data term is input to the core, one correlation operation is performed
across “corr_win” data and coef?cient terms, producing one result, r. The “k” index in Equation 1 does not apply
since the Correlator always produces one new result when it receives one new data value. Old data beyond the
de?ned correlation window size is not held in memory.
In addition to the basic correlation function described above, the Correlator IP core can be con?gured to perform
complex correlations, de?ned by the equation:
corr _ w in 1
r k =
d i + k c i
k = 0,1,…,n u m_lags-1
(2)
i = 0
In this case, the data and coef?cient input sequences are both complex and each contains a real input sequence
and an imaginary input sequence. For the Correlator IP core, the input data sequence is a sequence of signed
(two’s complement) numbers from 1 to 8 bits wide, and the coef?cient sequence is a binary sequence where a
coef?cient value of 1 represents +1 and a coef?cient value of 0 represents a -1. Equation 2 represents the complex
conjugate of c i . The complex conjugate multiplication expressed in Equation 2 is given as:
dc = (d re c re + d im c im ) + j(d im c re - d re c im )
2
(3)
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