I am wondering whether I can get the upper bound in closed form,

$\sum_n(\alpha \exp(j2\pi n/N))$ where $\alpha = +1\ or -1$

If alpha is just positive one, this would be just a single value,

but I'm trying to get the upper bound when alpha is +1 or -1, randomly,

while the total amount of +1 and -1 is different at most 1. (N/2 or N/2+1)

I have looked for exponential sums materials, but can't see things like this.

edit : $\alpha $ is generated by LFSR, so it holds pseudo randomness property.
or equivalently, it is a maximal length sequences.