I want to make sure that my units are all correct. I've been using the formula
$$ \frac{P_S}{P_N} = \frac{E_S}{N_0} \frac{R_S}{B} $$
The dimensions that I'm confident of are
- $P_S$, $P_N$ : Watts (Joules/sec)
- $N_0$ : Joules/(sec*Hz)
- $B$ : Hz
The last two are then (I think)
- $R_S$ : symbols/sec
- $E_S$ : Joules/symbol
If those are all correct, and given that
$$ \frac{E_S}{N_0} = \frac{P_S}{P_N} \frac{B}{R_S} $$
it seems like the units of $\frac{E_S}{N_0}$ are
$$ \frac{\text{Hz}}{\text{symbols/sec}} = \frac{1}{\text{symbol}} $$
I was under the impression that it should be dimensionless. Is this correct?