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：考虑一个包含多个单天线中继器的无线网络，这些中继器放大并实时转发接收到的信号，以提升信道秩和系统覆盖范围。由于中继间干扰形成的正反馈，稳定性可能成为关键问题。我们研究确定中继器在不破坏系统稳定性的前提下可使用的最大放大增益问题。具体而言，通过应用盖尔圆盘定理，我们获得了一个边界，该边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，我们展示了所得边界的实用性，并阐述了中继器部署策略的相关见解。