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Channel estimation: Note, the above procedure relies on accurate knowledge of the wireless channel, H, at the base station. Any error in estimating H leads to interference for the clients and reduces their data rate. First, let us focus on TDD systems, where the uplink and downlink happen on the same frequency. Recall, from Eq. 1, the wireless channel depends on the frequency and distance. Wireless signals travel the same paths on uplink and downlink. Therefore, for a base station-client pair using TDD, the channel for the uplink and the downlink are equal modulo some hardware factors that can be calibrated for. This principle is called reciprocity. The client transmits some pilot symbols known to the base station so that the base station can estimate the uplink channel, and use reciprocity to infer the downlink channel (which is just a constant multiplication to the uplink channel). In terms of overhead, this process requires just 𝐾 uplink pilots, one for each transmitting client, and is independent of the number of antennas on the base station as base station antennas can simultaneously sense the signal. For FDD, the uplink and downlink transmission happen on different frequencies. Therefore, the downlink channel is not equal to the uplink channel anymore. For FDD base stations to leverage MIMO, the base station sends 𝑀 pilot symbols one on each antenna. Each client measures the downlink wireless channel from each antenna to itself and sends the 𝑀 channel values as feedback to the base station. In total, 𝐾 clients send 𝑀 × 𝐾 channel values as feedback. This feedback incurs overhead that scales with the number of antennas and number of clients (𝑀 × 𝐾). Past work [20, 39] has shown that in TDD, massive MIMO can enable theoretically infinite scaling with increasing number of antennas and clients. However, this feedback overhead caps the scaling for FDD systems, since it scales up with 𝑀 and 𝐾 as well, and the spectrum becomes the bottleneck. We refer the reader to [40] for a detailed discussion on massive MIMO.
我的理解是这样的，在TDD系统中，Uplink and Downlink是reciprocity的，所以只需要从Uplink去估计整个信道的特征就好了，而Uplink的前导信号复杂性只取决于“该link的tx”，也就是client个数；
但是对于FDD系统，Uplink和Downlink信道特征不相同，需要探针信号：基站->用户->基站。根据刚刚的【前导信号复杂性只取决于“该link的tx”】的理论，那第一次的复杂性为基站MIMO个数，第二次的复杂性为用户MIMO个数，总复杂性为二者的乘积。
