Low-complexity calibration of mutually coupled non-reciprocal multi-antenna OFDM transceivers

Abstract

Abstract-In adaptive time division duplex (TDD) broadcast multi-antenna orthogonal frequency division multiplexing (OFDM) systems, non-reciprocal transceiver chains at the base station (BS) cause multi-user interference. This is due to the inappropriate spatial filter design at the BS based on the reverse link estimate. Hence, BS transceiver calibration is required. Provided that an estimate of the forward link channel is available at the BS, e.g., in a calibration phase, the transceiver parameters can be estimated by solving a total least squares (TLS) problem. In addition, if mutual coupling between the antennas exists the number of unknown front-end parameters to be estimated increases. Consequently, large matrices need to be decomposed via singular value decomposition (SVD) to attain a calibrated system. To deal with these large matrices a conjugate gradient (CG) method for solving the TLS problem iteratively is proposed in this paper. Simulation results show that the calibration based on the CG method achieves almost the same performance compared to the TLS solution but with significantly reduced complexity.

Calibration for single-carrier preFDE transceivers based on property mapping principles

“…It is modeled by a MMSE error model with constant estimation error variance σ 2 e [9]. Accordingly, this results in…”

“…To ensure a sufficient length of the solution vector, L c ≥ L f should be guaranteed, thus, for equal physical channel lengths, zero padding can be applied in (9) for the UL channel vectors. As a consequence, the length of the impulse responses must be chosen carefully to ensure a solution to (9). The existing block-diagonal structure of G C can be exploited by simply decomposing (9) into N M single-filter equations due to the joint linear correspondence.…”

“…As a consequence, the length of the impulse responses must be chosen carefully to ensure a solution to (9). The existing block-diagonal structure of G C can be exploited by simply decomposing (9) into N M single-filter equations due to the joint linear correspondence. It is worth to mention that a multiple application of the proposed algorithm can be parallelized, but may lead to different solutions of the individual filter vectors for different channel realizations as compared to the stacked formulation (9).…”

“…An even closer approximation to this solution can be achieved by overparameterization of (9). Therefore, simply multiple measurements of UL and DL channels can be used and the calibration time τ p is increased such that   …”

“…By establishing a calibration phase during regular transmission with the help of additional feedback, almost equivalent effective UL and DL channels can be recovered. The authors demonstrated the superior performance of the application of such a scheme in comparison with robust pre-equalizer strategies for multicarrier systems [8], [9], where the transceiver influences are assumed to be frequencyindependent. There, total least squares (TLS) problems must be solved to acquire estimates of the RF front-end parameters.…”