Abstract
This study proposes an uncooperative-multi-cell-multiple-input–multiple-output system to increase the throughput of an ill-conditioned wireless MIMO downlink system. The proposed algorithm suppresses the inter-cell interference at each mobile station using a set of adaptive receive beamformers, but handles the intra-cell interference at each base station using a Tomlinson Harashima precoder. Using the singular vectors of channel matrices, the receive beamformers can be designed based on a linear-constrained-minimum-variance criterion. On the other hand, to obtain high enough degree of freedoms for cancelling the intra-cell interference at each base station, the precoder is applied to the re-assembled downlink virtual channel formed by the simplified channel state information. Using the proposed interference suppression techniques, a multi-cell downlink system with multiple uncooperative base stations can be decomposed into a set of parallel subchannels. The resulting system has better performance in channel capacity than conventional MIMO systems. Computer simulations support the validity of the proposed approach.
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This research was supported by Ministry of Science and Technology, ROC, under contract MOST106-2221-E-182-011.
Appendix: Adaptive Implementation of the Receive Beamformer
Appendix: Adaptive Implementation of the Receive Beamformer
Based on (7), the proposed receive beamformer can be implemented using a generalized-sidelobe-canceller (GSC) structure that executes the beamforming process in an adaptive manner. Based on the constraint \(\left( {\mathbf {C}}_{k,m}^{u}\right) ^{H}{\mathbf {w}} =\mathbf {f}_{m}\) in (7), the weight vector \({\mathbf {w}}_{k,m}^{u}\) can be decomposed as the difference of two parts,
where \({\mathbf {w}}_{k,m,\text{q}}^{u}={\mathbf {C}}_{k,m}^{u}\left[ \left( {\mathbf {C}}_{k,m}^{u}\right) ^{H}{\mathbf {C}}_{k,m}^{u}\right] ^{-1} \mathbf {f}_{m}\) is called the quiescent weight vector, which lies in the column space of \({\mathbf {C}}_{k,m}^{u}\), and \({\mathbf {w}}_{k,m,\text{n}}^{u}\) is called the null weight vector, which lies in the null space of \(\left( {\mathbf {C}}_{k,m}^{u}\right) ^{H}\), denoted as \(N\left( \left( {\mathbf {C}}_{k,m}^{u}\right) ^{H}\right)\). After defining the blocking matrix \({\mathbf {B}}_{k,m}^{u}\), which is constructed by the basis vectors of \(N\left( \left( {\mathbf {C}}_{k,m}^{u}\right) ^{H}\right)\), the null weight vector can thus be expressed as
where \({\mathbf {w}}_{k,m,\text{a}}\) denotes the associate coordinate vector. Substituting (31) and (30) into (7) shows, that the constrained optimization problem in (7) can be transformed into an unconstrained optimization problem
where \({\mathbf {R}}_{m}=E\left\{ {\mathbf {y}}_{m}\left[ n\right] {\mathbf {y}} _{m}^{H}\left[ n\right] \right\}\) denotes the autocorrelation matrix of \({\mathbf {y}}_{m}\left[ n\right]\). Some direct manipulations lead to
To avoid estimating the correlation matrix \({\mathbf {R}}_{m}\) in (33), \({\mathbf {w}}_{k,m,\text{a}}\) can also be adaptively obtained by using the least mean square error \(\left( \text{LMS}\right)\) algorithm [17]. Figure 5 shows the GSC structure for the receive beamformer. Letting \(d_{k,m}^{u}\left[ n\right] \overset{\Delta }{=}\left( {\mathbf {w}}_{k,m,\text{q}}^{u}\right) ^{H}{\mathbf {y}}_{m}\left[ n\right]\) and \({\mathbf {u}}_{k,m}^{u}\left[ n\right] =\left( {\mathbf {B}}_{k,m} ^{u}\right) ^{H}{\mathbf {y}}_{m}\left[ n\right]\), the coordinate weight can be adaptively determined by
where \(\mu\) denotes the associated step size and \({\bar{y}}_{k,m}^{u}\left[ n\right] =d_{k,m}^{u}\left[ n\right] -{\mathbf {w}}_{k,m,\text{a}}^{H}\left[ n\right] {\mathbf {u}}_{k,m}^{u}\left[ n\right]\) is the output signal of the receiver beamformer intending for the uth data stream from AP k to MS m. The LMS algorithm converges under the condition [17]
where \(\left\| {\mathbf {u}}_{k,m}^{u}\left[ n\right] \right\|\) denotes the vector 2-norm of \({\mathbf {u}}_{k,m}^{u}\left[ n\right]\).
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Wang, YY., Chen, WW. & Yang, SJ. An Interference Cancellation Technique for Distributed MIMO Systems. Wireless Pers Commun 98, 293–309 (2018). https://doi.org/10.1007/s11277-017-4870-3
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DOI: https://doi.org/10.1007/s11277-017-4870-3