  We use the double affine Hecke algebra of type GL_N to construct an explicit
consistent system of q-difference equations, which we call the bispectral
quantum Knizhnik-Zamolodchikov (BqKZ) equations. BqKZ includes, besides
Cherednik's quantum affine KZ equations associated to principal series
representations of the underlying affine Hecke algebra, a compatible system of
q-difference equations acting on the central character of the principal series
representations. We construct a meromorphic self-dual solution \Phi of BqKZ
which, upon suitable specializations of the central character, reduces to
symmetric self-dual Laurent polynomial solutions of quantum KZ equations. We
give an explicit correspondence between solutions of BqKZ and solutions of a
particular bispectral problem for the Ruijsenaars' commuting trigonometric
q-difference operators. Under this correspondence \Phi becomes a self-dual
Harish-Chandra series solution \Phi^+ of the bispectral problem. Specializing
the central character as above, we recover from \Phi^+ the symmetric self-dual
Macdonald polynomials.
