Predicting Flat-Fading Channels via Meta-Learned Closed-Form Linear Filters and Equilibrium Propagation

Abstract

Predicting fading channels is a classical problem with a vast array of applications, including as an enabler of artificial intelligence (AI)-based proactive resource allocation for cellular networks. Under the assumption that the fading channel follows a stationary complex Gaussian process, as for Rayleigh and Rician fading models, the optimal predictor is linear, and it can be directly computed from the Doppler spectrum via standard linear minimum mean squared error (LMMSE) estimation. However, in practice, the Doppler spectrum is unknown, and the predictor has only access to a limited time series of estimated channels. This paper proposes to leverage meta-learning in order to mitigate the requirements in terms of training data for channel fading prediction. Specifically, it first develops an offline low-complexity solution based on linear filtering via a meta-trained quadratic regularization.Then, an online method is proposed based on gradient descent and equilibrium propagation (EP). Numerical results demonstrate the advantages of the proposed approach, showing its capacity to approach the genie-aided LMMSE solution with a small number of training data points.

Speeding up Training of Linear Predictors for Multi-Antenna Frequency-Selective Channels via Meta-Learning

“…In this section, we present experimental results for the prediction of multi-antenna and/or frequency-selective channels. Numerical examples for single-antenna frequency-flat channels for both offline and online learning scenarios can be found in the conference version of this paper [ 45 ]. For all the experiments, we compute the normalized mean squared error (NMSE) , which is averaged over 100 samples for 200 new frames.…”

“…In the following, we study the impact of (i) the number of antennas , (ii) the number of channel taps W , (iii) the number of training samples , and (iv) the number of previous frames F , for various prediction schemes: (a) conventional learning, (b) transfer learning, and (c) meta-learning, where each scheme is implemented by using either the naïve or the LSTD parametrization. We set , , and for conventional learning [ 9 , 45 ], whereas , , and for transfer and meta-learning.…”

“…Part of this paper was presented in [ 45 ], which only covered meta-learning for the case of single-antenna frequency-flat channels. As compared to [ 45 ], this journal version includes both transfer and meta-learning, and it addresses the general scenario of multi-antenna frequency-selective channels by introducing and developing the LSTD model class of linear predictors.…”

Learning to Broadcast for Ultra-Reliable Communication with Differential Quality of Service via the Conditional Value at Risk

“…To demonstrate the importance of optimizing the -CVaR rate for applications that focus on the performance of a small fraction of the clients with the worst channel gains, in Fig. 5, we plot the expected -CVaR rate as a function of the fraction with power = 20dB, Rician fading distribution ℎ ∼ CN(2, 1), = 6 layers, and datasets of size = 10 4 , and for rateand power-allocation vectors and optimized based on different metrics: (i) the surrogate empirical -CVaR rate ˜ G ( , ) defined in (36), (ii) the surrogate average rate ˜ G 1 ( , ) defined in (37), and (iii) the surrogate empirical outage rate ˜ G ( , ) = ( , , [⌊ ⌉] ). It is observed that, for most values of ∈ (0, 1], the average achievable rate for the -fraction of clients with the worst channel gains increases significantly if the rate-and power-allocation vectors are optimized to maximize the surrogate empirical -CVaR rate.…”

“…A review of meta-learning with emphasis on applications to communication systems is available in [28]. Representative examples include meta-learning for learning to demodulate [29], [30] or decode [31]; for end-to-end learning of encoder and decoder [32]; for beamforming adaptation [33], [34]; for proactive resource allocation [35], [36]; and for channel estimation [37].…”