What is the input dimension for LMS update algorithm
The output of an FIR filter is
$$
y(n) = \sum_{i=0}^{N-1}w_i(n)x(n-i)
$$
Say the weight vector $\mathbf{w}(n)$ has a length of $N$, i.e.,
$$\mathbf{w}(n) = [w_0(n), w_1(n), \ldots, w_{N-1}(n)]^T$$
and the input vector $\mathbf{x}(n)$ should have the same length as $\mathbf{w}(n)$:
$$\mathbf{x}(n) = [x(n), x(n-1), \ldots, x(n-N+1)]^T$$
Therefore the output $y(n)=\mathbf{w}^T(n)\mathbf{x}(n)$ is a scalar, and the error signal $e(n)$ and disired signal $d(n)$ are also scalar. They represent the signals at discrete time $n$. You should update the filter weights sample by sample.