  Finding sets of binary sequences with low auto- and cross-correlation
properties is a hard combinatorial optimization problem with numerous
applications, including multiple-input-multiple-output (MIMO) radar and global
navigation satellite systems (GNSS). The sum of squared correlations, sometimes
referred to as the integrated sidelobe level (ISL), is a quartic function in
the variables and is a commonly-used metric of sequence set quality. In this
paper, we show that the ISL minimization problem may be formulated as a
mixed-integer quadratic program (MIQP). We then present a block coordinate
descent (BCD) algorithm that iteratively optimizes over subsets of variables.
The subset optimization subproblems are also MIQPs which may be handled more
efficiently using specialized solvers than using exhaustive search; this allows
us to perform BCD over larger variable subsets than previously possible. Our
approach was used to find sets of four binary sequences of lengths up to 1023
with better ISL performance than Gold codes and sequence sets found using
existing BCD methods.
