低复杂度最大似然检测用于基于类型的空中计算
Low-Complexity Maximum Likelihood Detection for Type-Based Over-the-Air Computation
AI总结：
本文针对基于类型的空中计算（TBMA）在AWGN信道下的最大似然检测问题，提出了一种基于连续干扰消除的贪心算法，降低了计算复杂度，并推导了均方误差的解析表达式，证明其随信噪比指数下降，数值结果验证了TBMA在非线性函数场景下优于传统模拟OAC。
AI中文摘要：
类型多址（TBMA）是一种数字空中计算（OAC）方案，利用无线多址信道上的符号碰撞在接收端构建传输数据的直方图。本文研究了在加性高斯白噪声（AWGN）信道下TBMA中传输直方图的最优检测问题。由于可能的接收直方图数量随发射机数量和数据字母表大小组合增长，最大似然（ML）检测在计算上变得不可行。我们证明了ML检测问题可以通过基于连续干扰消除（SIC）的贪心算法求解。我们推导了ML检测器的解析均方误差（MSE），并表明其随信噪比（SNR）呈指数下降。数值结果验证了理论分析，并表明TBMA相比传统模拟OAC实现了优越的性能，特别是在非线性函数场景下。
英文摘要：
Type-based multiple access (TBMA) is a digital over-the-air computation (OAC) scheme that exploits symbol collisions over the wireless multiple-access channel to construct a histogram of the transmitted data at the receiver. This paper addresses the optimal detection of the transmitted histogram in TBMA over an additive white Gaussian noise (AWGN) channel. Since the number of possible received histograms grows combinatorially with both the number of transmitters and the data alphabet size, maximum-likelihood (ML) detection renders computationally infeasible. We prove that the ML detection problem can be solved by a greedy algorithm based on successive interference cancellation (SIC). We derive the analytical mean squared error (MSE) of the ML detector and show that it decreases exponentially with the SNR. Numerical results validate the theoretical analysis and demonstrate that TBMA achieves superior performance compared with conventional analog OAC, particularly for nonlinear functions.
