I need the exact Cramer Rao Bound expression for frequency estimation of two-dimensional multi-component complex sinusoidal signal whose components are closely spaced. For widely spaced situation, I use the below CRB expression but for closely spaced situation the CRB expression is different.

\begin{equation} \label{CRB} CRB_{\widehat{f}_{k,l}}=\frac{6 F_{s_1} F_{s_2}}{4 \pi^{2} N_{1} N_{2}(N_{k}^{2}-1) ho_l} , \; \forall k \in\{1,2\}, \end{equation} where $ ho_{l}= A_{l}^2 / \sigma^2$ represents the SNR.

I used the below formula for 2-D multiple signal (given in latex format):

A 2-D multiple sinusoid observed in the presence of additive white Gaussian noise (AWGN) can be represented by \begin{equation} \label{2-D signal} s_L({n_{1},n_{2}})=\sum\limits_{l=1}^{L}A_l e^{j 2\pi\left(\frac{ f_{1,l} n_{1}} {F_{s_{1}}} + \frac{f_{2,l} n_{2}} {F_{s_2} } ight)} + w({n_{1},n_{2}}), \end{equation} where $0 \leq n_{1} \leq N_1-1$ and $0 \leq n_{2} \leq N_2-1$. Here, $N_k$ are the signal lengths, where $k \in \{1,2\}$, $f_{k,l}$ are the frequencies of the $l$\textsuperscript{th} individual sinusoidal component at the $k$\textsuperscript{th} dimension, in which $l=1,2,\cdots,L$, and $F_{s_k}$ are the sampling frequencies at the $k$\textsuperscript{th} dimension. $A_l$ is the constant complex amplitude of the $l$\textsuperscript{th} individual sinusoidal component and phases of complex amplitudes are uniformly distributed over $(0,2 \pi]$. $w(n_{1}, n_{2})$ is assumed to be circularly symmetric AWGN with zero mean and a variance of $\sigma^2$.

Please explain the solution in detail and step-by-step. And finally derive the exact CRLB expression. I dont need a general solution. I can find them in the books.