Channel Interpolation of Fading Channels and the Pilot Density Required for Predictor Antennas

Predictor antennas (PAs) are a potential solution to severe channel aging that can occur at high vehicular velocities in non line-of-sight (NLOS) environments. Channel aging reduces the performance of many advanced communication schemes based on channel state information at the transmitter (CSIT). Although PAs have been shown to work in combination with dense pilots in time and space, prediction performance can be reduced when channel estimates are sparse. This paper answers how densely pilots must be placed for PAs to be feasible when performing basic interpolation between channel estimates. This is important, especially for establishing upper limits on the length of the downlink (DL) frames required in a time-division duplex (TDD) system with PAs. Nearest-neighbor, linear, and spline interpolation are analyzed when applied to stochastic radio channels. A theoretical expression is derived for the power of the expected interpolation error for any interpolation method that can be expressed as a linear function of a set of measured values. The interpolation methods are evaluated on three theoretical channels with Rayleigh, flat, and Rician fading, and on two sets of channel measurements. The results indicate that linear and spline interpolation can be used with down to five and three samples per wavelength, respectively, without affecting the PA-based prediction NMSE. At two samples per wavelength, the prediction NMSE is still at a level that can be useful for precoding design in massive multiple-input multiple-output (M-MIMO) systems.

I. Introduction

Serving high-mobility users in a small-scale fading environment is a difficult problem in a cellular system. Small-scale fading punishes any transmission technique that uses channel state information (CSI) if there is a significant delay between measuring and using it. This delay, here referred to as the CSI delay, can arise for multiple reasons. One common source is the delay between transmitting uplink (UL) pilots in time-division duplex (TDD) systems and using the reciprocal CSI at a later downlink (DL) frame. The minimum CSI delay of this kind is typically between 1–5 ms in the 4G system, as exemplified in [1, Figure 23.15]. The calculation of channel estimates and precoders in massive multiple-input multiple-output (M-MIMO) systems and the use of a central computation of co-operative distributed transmission, such as joint transmission (JT) coordinated multipoint (COMP), are other possible sources of CSI delay which can be greater than the time difference between pilots.