  A major drawback of orthogonal frequency division multiplexing (OFDM) systems
is their high peak-to-mean envelope power ratio (PMEPR). The PMEPR problem can
be solved by adopting large codebooks consisting of complementary sequences
with low PMEPR. In this paper, we present a new construction of polyphase
complementary sets (CSs) using generalized Boolean functions (GBFs), which
generalizes Schmidt's construction in 2007, Paterson's construction in 2000 and
Golay complementary pairs (GCPs) given by Davis and Jedwab in 1999. Compared
with Schmidt's approach, our proposed CSs lead to lower PMEPR with higher
code-rate for sequences constructed from higher-order ($\geq 3$) GBFs. We
obtain polyphase complementary sequences with maximum PMEPR of $2^{k+1}$ and
$2^{k+2}-2M$ where $k,M$ are non-negative integers that can be easily derived
from the GBF associated with the CS.
