Massive MIMO under multi-keyhole channels: Does the use-and-then-forget bounding technique work?

This paper considers the uplink of a massive MIMO system under the multi-keyhole channels. Two capacity bounding techniques, namely use-and-then-forget (UF) and full-side-information (FSI), are used to obtain the achievable rates. With UF scheme, the base station (BS) utilizes the mean value of the effective channel gain to detect the signal, while with the FSI scheme, the BS exploits the full channel knowledge for signal detection. By using the law of large numbers and the Jensen's inequality, we derive the tight approximations of the rates which can be represented in simple and insightful closed-form expressions. These closed-form expressions enable us to get important insights for future design of massive MIMO. Under keyhole effects, the FSI scheme yields a much higher rate than the UF scheme does, especially when the number of keyholes is small. Therefore, though the UF bounding technique is widely used in massive MIMO literature due to its simple closed-form expressions, the FSI bounding technique should be used if the channels are keyhole channels.