# Performance Analysis of Channel Extrapolation in FDD Massive MIMO Systems

## TL;DR

This paper investigates the feasibility of extrapolating downlink channel responses from uplink estimates in FDD massive MIMO systems, proposing high-resolution estimation methods and analyzing their theoretical and practical performance.

## Contribution

It introduces a high-resolution channel estimation approach for FDD massive MIMO, deriving bounds and analyzing factors affecting extrapolation accuracy.

## Key findings

- MSE inversely proportional to number of receive antennas
- Extrapolation penalty scales with frequency offset squared
- Channel extrapolation viable with accurate calibration and favorable conditions

## Abstract

Channel estimation for the downlink of frequency division duplex (FDD) massive MIMO systems is well known to generate a large overhead as the amount of training generally scales with the number of transmit antennas in a MIMO system. In this paper, we consider the solution of extrapolating the channel frequency response from uplink pilot estimates to the downlink frequency band, which completely removes the training overhead. We first show that conventional estimators fail to achieve reasonable accuracy. We propose instead to use high-resolution channel estimation. We derive theoretical lower bounds (LB) for the mean squared error (MSE) of the extrapolated channel. Assuming that the paths are well separated, the LB is simplified in an expression that gives considerable physical insight. It is then shown that the MSE is inversely proportional to the number of receive antennas while the extrapolation performance penalty scales with the square of the ratio of the frequency offset and the training bandwidth. The channel extrapolation performance is validated through numeric simulations and experimental measurements taken in an anechoic chamber. Our main conclusion is that channel extrapolation is a viable solution for FDD massive MIMO systems if accurate system calibration is performed and favorable propagation conditions are present.