For the BPSK alphabet

this paper presents a novel concept of an

ε

-equalization qualitatively different from the classical zero-forcing equalization

educes a necessary and sufficient condition for existence of the

ε

-equalizer.The paper takes the complementary projection operator of a received data matrix as the annihilator of a transmitted sequence vector to be detected

and then formulates the blind detection problem of BPSK signals into a quadratic programming with binary constraints.Finally

the paper extends and applies the above

ε

-equalization concept and blind detection algorithm successfully in the QPSK case with complex channels

by redefining a complex argument as a real one.Simulations demonstrate its superior performance to the subspace method and linear prediction method whether SIMO channels have common zero

s or not and the zeros lie within the unit circle or not.