  We give an explicit construction of linearly independent families of knots
arbitrarily deep in the (n)-solvable filtration of the knot concordance group
using the \rho^1-invariant. A difference between previous constructions of
infinite rank subgroups in the concordance group and ours is that the deepest
infecting knots in the construction we present are allowed to have vanishing
Tristram-Levine signatures.
