An “Aha!” Moment for History!

Sometimes thoughts on history can give us an “Aha!” moment.. not just new things! At-least for me, reminiscing on a forgotten memory and getting back the thought in all its glory gave me the same high!

Yesterday, during my self-learning hour, I was perplexed by a problem…

We all remember that EDGE is 3-times faster than GPRS because it uses 8PSK instead of GMSK as a modulation scheme.

I remembered that GMSK is like QPSK having 4 discrete states while 8PSK has 8 discrete states.

I assumed that the discrete states are being used as the symbols and by Nyquist Limit, for the same bandwidth, 8PSK should only be 1.5 times faster than GPRS i.e. log2(8) versus log2(4). Kept returning back to this point for half a day!

Then – finally, when I got some personal time, I searched on the Internet and read somewhere that GMSK is not exactly QPSK but like OQPSK (Offset QPSK).

That set off my memory… AHA!

GMSK does not use the discrete states but the direction of the offset from the discrete states i.e. +Δφ or -Δφ (in a Phase diagram – clockwise or anti-clockwise). So, it has only 2 symbols! So, per Nyquist Limit for capacity of noiseless channels, EDGE is 3-times faster than GPRS (as they both use GSM bandwidth) and log2(8) is 3 times log2(2).

As I soon recalled: PSK uses φ, n-PSK uses n discrete states of φ, Offset n-PSK uses Δφ from the discrete states and GMSK uses +/- direction of the Δφ from the discrete states as the symbol set!

QED!
GMSK was a very inefficient but totally reliable modulation scheme! And, a memory of first principles gives you a high always!

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