A local converse theorem for ${\text{U}}_{2r+1}$

Let $E\mathrm{/}F$ be a quadratic extension of $p$-adic fields and ${\text{U}}_{2r+1}$ be the unitary group associated with $E\mathrm{/}F$. We prove the following local converse theorem for ${\text{U}}_{2r+1}$: given two irreducible generic supercuspidal representations $\pi ,{\pi }_0$ of ${\text{U}}_{2r+1}$ with the same central character, if $\gamma(s,\pi\times \tau,\psi)=\gamma(s,\pi_0\times \tau,\psi)$forallirreduciblegenericrepresentation$\tau$of$$\text{GL}$_n(E)$andforall$n$with$1\le n\le r$,then$\pi\cong \pi_0$. The proof depends on analysis of the local integrals which define local gamma factors and uses certain properties of partial Bessel functions developed by Cogdell-Shahidi-Tsai recently.