An Interference Cancellation Technique for Distributed MIMO Systems

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.

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,

$$\begin{aligned} {\mathbf {w}}_{k,m}^{u}={\mathbf {w}}_{k,m,\text{q}}^{u}-{\mathbf {w}}_{k,m,\text{n} }^{u}, \end{aligned}$$

(30)

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

$$\begin{aligned} {\mathbf {w}}_{k,m,\text{n}}^{u}={\mathbf {B}}_{k,m}^{u}{\mathbf {w}}_{k,m,\text{a} }. \end{aligned}$$

(31)

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

$$\begin{aligned} {\mathbf {w}}_{k,m,\text{a}}=\underset{{\mathbf {w}}_{\text{a}}}{\min }\left( {\mathbf {w}}_{k,m,\text{q}}^{u}-{\mathbf {B}}_{k,m}^{u}{\mathbf {w}}_{\text{a} }\right) ^{H}{\mathbf {R}}_{m}\left( {\mathbf {w}}_{k,m,\text{q}}^{u} -{\mathbf {B}}_{k,m}^{u}{\mathbf {w}}_{\text{a}}\right) . \end{aligned}$$

(32)

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

$$\begin{aligned} {\mathbf {w}}_{k,m,\text{a}}=\left[ \left( {\mathbf {B}}_{k,m}^{u}\right) ^{H}{\mathbf {R}}_{m}{\mathbf {B}}_{k,m}^{u}\right] ^{-1}\left( {\mathbf {B}} _{k,m}^{u}\right) ^{H}{\mathbf {R}}_{m}{\mathbf {w}}_{k,m,\text{q}}^{u}. \end{aligned}$$

(33)

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

$$\begin{aligned} {\mathbf {w}}_{k,m,\text{a}}\left[ n+1\right] ={\mathbf {w}}_{k,m,\text{a}}\left[ n\right] +\mu {\mathbf {u}}_{k,m}^{u}\left[ n\right] y_{k,m}^{u^{*}}\left[ n\right] , \end{aligned}$$

(34)

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]

$$\begin{aligned} \mu \le \frac{2}{\left\| {\mathbf {u}}_{k,m}^{u}\left[ n\right] \right\| }, \end{aligned}$$

(35)

where $\left\| {\mathbf {u}}_{k,m}^{u}\left[ n\right] \right\|$ denotes the vector 2-norm of ${\mathbf {u}}_{k,m}^{u}\left[ n\right]$.

Fig. 5

The GSC structure