Precoder assisted channel estimation in complex projective space

A single input single output finite impulse response channel driven by a linear precoder can at best be identified up to an unknown complex-valued scaling factor. Although this scale ambiguity can be removed by setting the first channel coefficient to one, if its true value is very close to zero then the resulting channel estimate will be grossly inaccurate. This paper shows that an alternative is to treat the channel vector as a point in complex projective space. A novel optimisation algorithm is derived for estimating the channel vector by minimising the squared error on complex projective space.