## 1 Introduction
### Context and Prior Art  
A classical approach to tackle this problem is to optimize finite impulse response (FIR) filters [9], or recursive linear filters via autoregressive (AR) models [3, 4, 5] such as Kalman filtering (KF) [6, 7, 8], by estimating channel statistics from the available pilot data. Although recursive linear filters generally outperform FIR filters when an accurate model of the state-transition dynamics is available [10, 11], FIR filters are typically advantageous in the presence of limited amounts of pilot data [12]. More recently, deep learning-based nonlinear predictors have also been proposed to adapt to channel statistics through the training of neural networks, namely recurrent neural networks [13; 14; 15; 16], convolutional neural networks [17; 18], and multi-layer perceptrons [19].  
As reported in [14; 15; 16; 19], deep learning-based predictors tend to require larger training (pilot) data, and fail to outperform well-designed linear filters in the low-data regime. Some solutions addressing this issues include [20], which applies reinforcement learning to determine whether to predict channels or not at the current time, and the use of hypernetworks to adapt parameters of a KF accordingly to current channel dynamics [12].  
Most prior work, with the notable exception of [12], focuses on the optimization of channel predictors under the assumption of a stationary spatio-temporal correlation function across the time interval of interest. This conventional approach fails to leverage common structure that may exist across multiple frames, with each frame being characterized by distinct spatio-temporal correlations (see Figure 1). Reference [12] allowed for varying Doppler spectra across frames, through a deep learning-based hypernetwork that is used to adapt the parameters of a generative model [12].  
This paper takes a different approach that allows us to move beyond the single-antenna setting studied in [12]. As described in the next subsection, key ingredients of the proposed methods are transfer learning and meta-learning. Transfer learning [21] and meta-learning [22] aim at using knowledge from distinct tasks in order to reduce the data requirements on a new task of interest. Given a large enough resemblance between different tasks, both transfer learning and meta-learning have shown remarkable performance to reduce the sample complexity in general machine learning problems [23]. Transfer learning applies to a specific target task, whereas meta-learning caters to adaptation to any new task (see e.g., [24]).  
Previous applications of transfer learning to communication systems include beamforming for multi-user, multiple-input, single-output (MISO) downlink [25] and for intelligent reflecting surfaces (IRS)-assisted MISO downlink [26], and downlink channel prediction [27; 28] (see also [25; 27]). Meta-learning has been applied to communication systems, including demodulation [29; 30; 31; 32], decoding [33], end-to-end design of encoding and decoding with and without a channel model [34; 35]: MIMO detection [36], beamforming for multiuser MISO downlink systems via [37], layered division multiplexing for ultra-reliable communications [38], UAV trajectory design [39], and resource allocation [40].