  We propose a valid scheme to measure the Hubble parameter $H(z)$ at high
redshifts by detecting the Sandage-Loeb signal (SL signal) which can be
realized by the next generation extremely large telescope. It will largely
extend the current observational Hubble parameter data (OHD) towards the
redshift region of $z \in [2.0,5.0]$, the so-called "redshift desert", where
other dark energy probes are hard to provide useful information of the cosmic
expansion. Quantifying the ability of this future measurement by simulating
observational data for a CODEX (COsmic Dynamics and EXo-earth experiment)-like
survey and constraining various cosmological models, we find that the SL signal
scheme brings the redshift upper-limit of OHD from $z_\mathrm{max}=2.3$ to
$z_\mathrm{max}\simeq 5.0$, provides more accurate constraints on different
dark energy models, and greatly changes the degeneracy direction of the
parameters. For the $\Lambda$CDM case, the accuracy of $\Omega_m$ is improved
by $58\%$ and the degeneracy between $\Omega_m$ and $\Omega_ {\Lambda}$ is
rotated to the vertical direction of $\Omega_k = 0$ line strongly; for the
$w$CDM case, the accuracy of $w$ is improved by $15\%$. The Fisher matrix
forecast on different time-dependent $w(z)$ is also performed.
