I understand that cell phones transmit speech signals in digital form through 2G/3G or other standards. But I could not find anything about the signal processing method lying in between the analog signals captured by the microphone and the final digital signal (which I think is not the complete speech signal but a reduced form) that is modulated over the respective modulation scheme. Is there any compression algorithm or some enhancement algorithm before the modulation stage?
Yes, the cellular phones use various forms of compression to convert the captured analog audio (speech) into the digital bitstream for transmission through 2G/3G/.../.
The specific method used depends on the GSM version which might dictate its own bandwidth constraint and backward or forward compatibility issues into the audio encoding stage.
Most typically a 2G/3G system utilizes a variant of voice code based on a linear predictive coding (LPC) scheme which converts the analog sound captured by the microphone into a set of coefficients (parameters) according to the vocal tract model of the speaker. Unlike PCM, mp3, ogg, ra, etc., this is not a waveform coder but a parametric voice coder therefore.
The speech is reproduced at the recevier side by using a similar code excited LPC (CELP) which uses various excitation signals for the vocal tract model to reproduce the input signal as natural as possible.
You can find more details in the literature by the keywords vocoder, LPC, CELP, GSM speech coding etc...