  We consider the problem of maximizing a non-negative submodular function
under the $b$-matching constraint, in the semi-streaming model. When the
function is linear, monotone, and non-monotone, we obtain the approximation
ratios of $2+\varepsilon$, $3 + 2 \sqrt{2} \approx 5.828$, and $4 + 2 \sqrt{3}
\approx 7.464$, respectively. We also consider a generalized problem, where a
$k$-uniform hypergraph is given, along with an extra matroid or a $k'$-matchoid
constraint imposed on the edges, with the same goal of finding a $b$-matching
that maximizes a submodular function. When the extra constraint is a matroid,
we obtain the approximation ratios of $k + 1 + \varepsilon$, $k + 2\sqrt{k+1} +
2$, and $k + 2\sqrt{k + 2} + 3$ for linear, monotone and non-monotone
submodular functions, respectively. When the extra constraint is a
$k'$-matchoid, we attain the approximation ratio $\frac{8}{3}k+ \frac{64}{9}k'
+ O(1)$ for general submodular functions.
