论文标题
具有多个无线计算的SISO系统的强大干扰管理
Robust Interference Management for SISO Systems with Multiple Over-the-Air Computations
论文作者
论文摘要
在本文中，我们考虑了总和的空中计算。具体来说，我们希望计算$ m \ geq 2 $ sums $ s_m = \ sum_ {k \ in \ mathcal {d} m} m} x_k $在共享的复杂值Mac上一次带有最小的透明式错误（$ \ mthsf {mse} $）。在计算其他总和$ s_m $，$ m \ neq n $中，找到适当的TX-RX缩放因子在计算$ s_n $中的低误差与其在计算中引起的干扰之间的平衡。在本文中，我们有兴趣设计一种最佳的TX-RX缩放策略，该策略将于点的均值错误$ \ max_ {m \ in [1：M]} \ Mathsf {MSE} _M $受到最大功率$ P $的TX功率约束。我们表明，TX-RX缩放策略$ \ left的最佳设计（\ bar {\ mathbf {a}}，\ bar {\ mathbf {b}}} \ right）涉及优化（a）阶段和（b）它们的绝对价值（a），以分配$ m $ $ $ $ $ sums $ sums $ sums $ sums $ $ m。 （$ m = m_r+m_i $）对RX信号的真实和虚构部分的计算以及（ii）单独地将每个部分的计算最小化。本文的主要重点是（b）。我们得出了有关优化问题的可行性的条件（i），以及（ii）对$ m_w = 2 $计算的本地最小值的TX-RX缩放策略（$ w = r $）或虚构（$ w = i $）部分。 $ m_w = 2 $对单个RX链上的大量模拟表明，$ΔD= | \ Mathcal {d} _2 | - | - | \ Mathcal {d} _1 | $在干扰水平上起着重要的作用在ergodic worst-case $ \ mathsf {mse {mse} $中起重要作用。在非常高的$ \ Mathsf {snr} $上，通常只有具有最弱的通道传输的传感器，而所有剩余的传感器都以较小的方式传输以限制干扰。有趣的是，我们观察到，由于残留的干扰，Ergodic最差案例$ \ Mathsf {Mse} $并没有消失。相反，它收敛到$ \ frac {| \ Mathcal {d} _1 || \ Mathcal {d} _2 |} {k} {k} $ as $ \ MATHSF {snr} \ rightArlow \ rightarrow \ infty $。
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 $ΔD=|\mathcal{D}_2|-|\mathcal{D}_1|$ 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 $\mathsf{SNR}\rightarrow\infty$.
