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

$$\sum_{n=1}^N(\alpha \exp(j2\pi n/N)) \text{ where } \alpha = +1\text{ or }-1 \text{ and } j^2=-1.$$


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.

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