  We determine the unitary dual of the geometric graded Hecke algebras with
{unequal} parameters which appear in Lusztig's classification of unipotent
representations for {exceptional} $p$-adic groups. The largest such algebra is
of type $F_4.$ Via the Barbasch-Moy correspondence of unitarity applied to this
setting, this is equivalent to the identification of the corresponding unitary
unipotent representations with real central character of the $p$-adic groups.
In order for this correspondence to be applicable here, we show (following
Lusztig's geometric classification, and Barbasch and Moy's original argument)
that the set of tempered modules with real central character for a geometric
graded Hecke algebra is linearly independent when restricted to the Weyl group.
