That's what I did also, along the passenger side. Actually I ran the power, remote turn on, and signal all along that path. It was in an 89 Accord Lxi Hatchback. Usually this is not a good idea to run the power and signal parallel to each other like that, but my signal cable had special tripple shielding and had a center ground wire that all helped reduce interferance. I figured it was just going to my sub and crisp quality wasn't too much of an issue. I didn't hear any feedback from running the power and signal right next to each other.

Hardest part was getting the power cable (4gauge) through the firewall. We used an exsisting gromit that the A/C unit emptied through. We should have drilled, but I didn't feel like going to find the drill.

Another hard part was getting the power wire under one of the panels on the part where you knock your shoes, had 2 really big torqus(sp) screws that needed to come out. That only took 10mins.

That was on my old Accord, I plan on putting as much of it as I can back into my new(used) 96 Prelude.