  We propose a relative trace formula approach and state the corresponding
fundamental lemma toward the global restriction problem involving Bessel or
Fourier-Jacobi periods of unitary groups $\mathrm{U}_n\times\mathrm{U}_m$,
extending the work of Jacquet-Rallis for $m=n-1$ (which is a Bessel period). In
particular, when $m=0$, we recover a relative trace formula proposed by Flicker
concerning Kloosterman/Fourier integrals on quasi-split unitary groups. As
evidence for our approach, we prove the fundamental lemma for
$\mathrm{U}_n\times\mathrm{U}_n$ in positive characteristics.
