We consider a wireless network with multiple single-antenna repeaters that amplify and instantaneously re-transmit the signals they receive to improve the channel rank and system coverage. Due to the positive feedback formed by inter-repeater interference, stability could become a critical issue. We investigate the problem of determining the maximum amplification gain that the repeaters can use without breaking the system stability. Specifically, we obtain a bound by using the Gershgorin disc theorem, which reveals that the maximum amplification gain is restricted by the sum of channel amplitude gains. We show by case studies the usefulness of the so-obtained bound and provide insights on how the repeaters should be deployed.

翻译：本文研究一种配备多个单天线中继器的无线网络，这些中继器通过放大并瞬时重传接收信号来改善信道秩与系统覆盖范围。由于中继器间干扰形成的正反馈机制，系统稳定性可能成为关键问题。我们研究了在保证系统稳定性的前提下确定中继器可使用的最大放大增益的问题。具体而言，通过应用Gershgorin圆盘定理，我们推导出一个约束界，该界表明最大放大增益受限于信道幅度增益之和。通过案例研究，我们证明了所得约束界的实用性，并就中继器的部署策略提供了深入见解。