Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Robust Interference Management for SISO Systems with Multiple
  Over-the-Air Computations   In this paper, we consider the over-the-air computation of sums.
Specifically, we wish to compute $M\geq 2$ sums
$s_m=\sum_{k\in\mathcal{D}m}x_k$ over a shared complex-valued MAC at once with
minimal mean-squared error ($\mathsf{MSE}$). Finding appropriate Tx-Rx scaling
factors balance between a low error in the computation of $s_n$ and the
interference induced by it in the computation of other sums $s_m$, $m\neq n$.
In this paper, we are interested in designing an optimal Tx-Rx scaling policy
that minimizes the mean-squared error $\max_{m\in[1:M]}\mathsf{MSE}_m$ subject
to a Tx power constraint with maximum power $P$. We show that an optimal design
of the Tx-Rx scaling policy $\left(\bar{\mathbf{a}},\bar{\mathbf{b}}\right)$
involves optimizing (a) their phases and (b) their absolute values in order to
(i) decompose the computation of $M$ sums into, respectively, $M_R$ and $M_I$
($M=M_R+M_I$) calculations over real and imaginary part of the Rx signal and
(ii) to minimize the computation over each part -- real and imaginary --
individually. The primary focus of this paper is on (b). We derive conditions
(i) on the feasibility of the optimization problem and (ii) on the Tx-Rx
scaling policy of a local minimum for $M_w=2$ computations over the real
($w=R$) or the imaginary ($w=I$) part. Extensive simulations over a single Rx
chain for $M_w=2$ show that the level of interference in terms of $\Delta
D=|\mathcal{D}_2|-|\mathcal{D}_1|$ plays an important role on the ergodic
worst-case $\mathsf{MSE}$. At very high $\mathsf{SNR}$, typically only the
sensor with the weakest channel transmits with full power while all remaining
sensors transmit with less to limit the interference. Interestingly, we observe
that due to residual interference, the ergodic worst-case $\mathsf{MSE}$ is not
vanishing; rather, it converges to $\frac{|\mathcal{D}_1||\mathcal{D}_2|}{K}$
as $\mathsf{SNR}\rightarrow\infty$.

26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys