How to express linear convolution using positive frequencies from channel and symbol DFT vectors?
I think already your fist equation is potentially wrong. The output of the channel is given by LINEAR convolution signal and channel impulse response, not by circular convolution. Circular convolution can be used but only if signal and impulse response of the channel are sufficiently small and enough zero padding is applied to avoid wrap-around errors. 

Dumping the imaginary part of the spectrum is also problematic. This basically an "analytic" signal (at least if the negative frequencies are set to 0). This typically is a non-causal operation and it becomes very difficult to determine when you will be getting wrap around errors and when you don't. You will almost certainly end up with a non-causal impulse response of the channel.

What exactly are you trying to achieve and why?