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I am no expert in EDGE, but I think it is a form of PSK modulation but I will take a stab at it from an RF engineers perspective. Basically, when you transmit a signal, it gets corrupted in the air. The amplitude drops with range, the phase changes with distance, fading, reflections, momentary events like a truck driving by the receive antenna, etc. In the receiver, there can be other effects that screw up the the demodulation process. There can be DC phase errors in the demodulator, momentary artifacts from the IF filtering, troubles in re-synchronizing the signal, DC offsets in mixers, etc etc.
Many of these "DC offset" effects can look like the origin of the amplitude/phase decision plane has moved. For example, suppose the amplitude of the received IF signal is 55 mV, and the phase is 11 degrees. So you are trying to determine, is the transmitted phase really 0 or 22 degrees, so that you can guess which word was sent? If because of system errors, the real (error free) IF signal would have been 70mV and 15 degrees, but your system put in a temporary -4 degree and -15 mV origin error, you make a bad decision, and have a bit error.
By supressing the "origin offset", you somehow correct for the "DC" mistakes your system is making, and make better detection decisions. In the above, your system would rotate the phase decision plane +4 degrees.
If you view the phase detection plane as a polar plane, you can see that DC errors in gain can turn into phase detection errors as well.
OOS requirement for EDGE is the same as GSM which is 32dB.
OOS can be taken as( -<Q>)/(+<Q>) ratio.
Bad OOS can be due to LO feedthrough/selfmixing, mismatch of stages...
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