I am working on a paper that has the following formula that is written as $$ \sum^{-1}_{j=-\mu} <r_{j+\mu},s_j> $$
Here, I am interpreting $r$ and $s$ as vectors. $\mu$ is a scalar number. What is the meaning of the vector indices? Also, I do not think that vector $r_0$ and $r_1$ are distinct vectors. Could they be a shifted version of each other?
This is from the following paper: Mehlan, Ralf, and Heinrich Meyr. "Optimum frame synchronization for asynchronous packet transmission." Proceedings of ICC'93-IEEE International Conference on Communications. Vol. 2. IEEE, 1993.
It doesn't make sense, so I went to the paper and couldn't find the formula as you have written. What I did find was $$\sum_{j=-\mu}^{-1}<r_{j+\mu},p_{P+j}>$$ All other parts in the paper where it contains $<r_{j+\mu},s_{j}>$ the summation starts at $0$ which is good because then $s$ does not have a negative index. $r_0$ and $r_1$ are distinct as they are defined in equation (1) and it is further evident in Figure (1).
For the summation above we have positive indices since when $j=-\mu$ you have $<r_{-\mu+\mu},p_{P-\mu}>=<r_{0},p_{P-\mu}>$ and all the following terms for $j=-\mu+1,-\mu+2,\ldots,-1$ both $r$ and $p$ have positive indices. Specifically $r_{1},r_{2},\ldots,r_{\mu-1}$ and $p_{P-\mu+1},p_{P-\mu+2},\ldots,p_{P-1}$.
If I indeed did miss the formula indicate what page.