Phase-shift keying is the scheme that scales to high bit rates — option 2 — and it does so for two independent reasons.

First, it is the most bandwidth-efficient of the three. FSK must reserve room for two separate carrier frequencies plus their sidebands, so by Carson's rule its bandwidth is

\(BW_{FSK}=2\left(\Delta f+R_{b}\right)\)

against \(2R_{b}\) for ASK and PSK. For a given channel width, PSK therefore carries more bits per second.

Second, and more importantly, it extends to M-ary signalling. Phase can be divided finely and evenly round a circle — 4-PSK, 8-PSK, 16-QAM and beyond — and each doubling of the constellation adds one bit per symbol:

\(R_{b}=R_{s}\log_{2}M\)

so QPSK sends two bits per symbol in the same bandwidth as BPSK. Amplitude cannot be subdivided so freely, because the levels crowd together in noise and the peak power must rise; frequency cannot, because each extra tone costs more spectrum. All high-rate systems — modems, Wi-Fi, LTE, satellite links — are built on phase and quadrature-amplitude constellations for exactly this reason.

The error performance points the same way. For coherent detection, BPSK needs 3 dB less energy per bit than FSK for the same error rate:

\(P_{e,PSK}=Q\left(\sqrt{\dfrac{2E_{b}}{N_{0}}}\right),\qquad P_{e,FSK}=Q\left(\sqrt{\dfrac{E_{b}}{N_{0}}}\right)\)

because antipodal symbols are as far apart as a given energy allows. ASK is worse still, since noise adds directly to the amplitude that carries the information.

Flagged because "high bit rate" is not a quantitative criterion; but on bandwidth efficiency, noise performance and extensibility alike, PSK is the answer.