Hybrid beamforming systems are a cost and energy efficient architectural approach for large-scale antenna arrays operating at millimetre-wave frequencies. The separation of the beamforming process into an analogue beamforming network and a digital precoding part enables the reduction of digital channels, while preserving a precise beam steering capability. Especially subarray-based hybrid beamforming systems distinguish them due to a low complex analogue beamforming network. However, to determine the ideal analogue and digital precoding matrices the channel state information has to be estimated. This estimation process is hampered by the electrical interconnection of different antenna elements within the analogue beamforming network. Hence, a separation of the antenna elements of the subarrays in the digital domain is not possible. Furthermore, actual channel estimation methods for hybrid beamforming systems are based on beam training techniques, which suffer from long estimation times. To overcome these problems we developed a two-stage channel estimation method for subarraybased hybrid beamforming systems using sparse array estimations. In the first stage, only one antenna element of each subarray at the transmitter is active during the channel estimation, resulting in a sparse array estimation. To distinguish the transmitters at the receiver side the transmitters are separated in the frequency domain using different orthogonal frequency division multiplexing subcarriers. For recovering the full-dimensional channel matrix we present two algorithms. The first algorithm is based on a two-dimensional interpolation of the channel matrix, while the second algorithm uses multiple subsequent channel measurements. The presented estimation method enables thereby a direct determination of the channel matrix with only one or a few measurements.
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