Super-Resolution for Achieving Frequency Division Duplex (FDD) Channel Reciprocity

Channel state information at transmitter (CSIT) allows wireless communication systems to fully utilize the degree of freedom of the channel. Time division duplex (TDD) systems can take the advantage of channel reciprocity to obtain forward link CSIT from reverse link training. We tackle the seemingly impossible task of doing the same for frequency division duplex (FDD) systems, where the conventional method is to obtain CSIT from feedback from the receiver. Channel state feedback causes delay and consumes prohibitive amount of system resource, especially when the number of transmit antennas is large, such as in massive MIMO systems. However, if the channel parameters, such as the complex path gain, path delay, and angle of arrival/departure of each individual path, are accurately estimated from pilot signals in one frequency band, the channel state in another frequency band can be calculated from these parameters. Accuracy is the key because small estimation error will be magnified by the multiplication of the frequency difference between the bands. The required accuracy is not achievable for narrow band and single antenna systems. But current and future wireless systems have and will have increasingly large bandwidth and number of antennas, making the FDD channel reciprocity possible. To achieve the FDD channel reciprocity, we propose to employ super-resolution theory. Another possible compressed sensing approach is to put the channel parameters on a multi-dimensional grid and for each point of the grid, estimate the corresponding complex gain. We adapt both approaches for our problem and show that the compressed sensing approach is not well suited for this purpose and the super-resolution approach can achieve our goal.