Table
1 shows the transmission procedure. Two APs use the same frequency channel and time slot and simultaneously carry out DL MU-MIMO transmission. Thus, each AP uses the ZF transmit beamforming to prevent ICI from affecting the STAs in the neighboring cell. The CSI matrices between each AP and the STAs in the BSS,
\(\mathbf{H}_{D,0,i}\) and
\(\mathbf{H}_{D,1,j}\), are estimated. The CSI matrices between each AP and the STAs associated with the AP in the OBSS and whose ICI power is larger than threshold
\(P_{th}\),
\(\mathbf{H}_{I,1,i}\) and
\(\mathbf{H}_{I,0,j}\), are also estimated. 802.11 standard specifies both implicit and explicit feedback for CSI acquisition [
18]. In high density environments, implicit feedback achieves high efficiency by reducing the amount of feedback for CSI acquisition. The simple extension of implicit feedback in 801.11n for cooperative ICI mitigation system is described in [
19,
20]. Here, it is assumed with loss of generality that the power levels of ICI affecting
\(\hbox {STA}_{0,i^{\prime }}\,(i^{\prime } =0,{\ldots },~U_{0}-1,~U_{0}\le M) \,P_{ICI,i^{\prime }}\) and
\(\hbox {STA}_{1,j^{\prime }}\,(j^{\prime }=0,{\ldots },~U_{1}-1\),
\(U_{1}\le M) \,P_{ICI,j^{\prime }}\) are larger than
\(P_{th}\). The ZF transmit beamforming weights are calculated using
\(\tilde{\mathbf{H}}_{D,0,i}\),
\(\tilde{\mathbf{H}}_{D,1,j}\),
\(\tilde{\mathbf{H}}_{I,1,j}\), and
\(\tilde{\mathbf{H}}_{I,0,i}\) which are the estimates of
\(\mathbf{H}_{D,0,i}\),
\(\mathbf{H}_{D,1,j}\),
\(\mathbf{H}_{I,1,i}\) and
\(\mathbf{H}_{I,0,j}\).
Table 1
Transmission procedure of the proposed scheme
(1): Initialization: \(P_{th}\)
|
(2): Select the STAs associated with the AP in the OBSS |
(2a): if \(P_{ICIj} \ge P_{th}\)
|
Select it as the ICI affecting \(\hbox {STA}_{1,j^{{\prime }}}\)
|
end |
(3): Estimate the CSI matrices |
(3a): Estimate the CSI between the AP and the STAs in the BSS \(\tilde{\mathbf{H}}_{D,0,i}\)
|
(3b): Estimate the CSI between the AP and the ICI-affected STAs \(\tilde{\mathbf{H}}_{I,1,j}\)
|
(4): Calculated the transmit beamforming weight matrix obtained by Eqs. ( 4)–( 6) \(\mathbf{W}_{0,k}\)
|
(5): Transmit the data sequence |
In
\(\hbox {AP}_{0}\), the transmit beamforming weight for
\(\hbox {STA}_{0,k}\) is determined so as to prevent the intra-cell interference from affecting
\(\hbox {STA}_{0,i}\,(i=0,{\ldots },M-1,~i\ne k)\) associated with
\(\hbox {AP}_{0}\) and the ICI affecting
\(\hbox {STA}_{1,j^{\prime }}\,(j^{\prime }=0,{\ldots },~U_{1}-1)\) associated with
\(\hbox {AP}_{1}\). By using singular value decomposition (SVD), the interference CSI matrix for
\(\hbox {STA}_{0,k}\) is expressed as
$$\begin{aligned} \tilde{\mathbf{H}}^{{\varvec{\prime }}}_{I,0,k}&= \left[ {\tilde{\mathbf{H}}_{D,0,0}^T \;\ldots \;\tilde{\mathbf{H}}_{D,0,k-1}^{T}\;\tilde{\mathbf{H}}_{D,0,k+1}^T \;\ldots \;\tilde{\mathbf{H}}_{D,0,M-1}^{T}\;\tilde{\mathbf{H}}_{I,1,0}^T \;\ldots \;\tilde{\mathbf{H}}_{I,1,U_{1}-1}^{T}}\right] ^{T} \nonumber \\&= \mathbf{U}_{I,0,k} \left[ {{ \begin{array}{cc} {{\varvec{\Sigma }}_{I,0,k}}&{} \mathbf{0} \\ \end{array}}}\right] \left[ {{\begin{array}{cc} {\mathbf{V}_{I,0,k}^{(s)}}&{\mathbf{V}_{I,0,k}^{(n)}} \end{array}}}\right] ^{H}, \end{aligned}$$
(4)
where
\(\mathbf{U}_{I,0,k}\in {\mathbb {C}}^{L(M+U_{1}-1)\times L(M+U_{1} -1)}\) denotes the left singular vectors and the diagonal elements of
\({\varvec{\Sigma }}_{I,0,k}\) are the square roots of
\(\lambda _{0,0}\),
\(\lambda _{0,1},{\ldots }\),
\(\lambda _{0,K-1}\), which are null space eigenvalues.
\(\mathbf{V}_{I,0,k}^{(s)} \in {\mathbb {C}}^{K\times L(M+U_{1}-1)}\) and
\(\mathbf{V}_{I,0,k}^{(n)} \in {\mathbb {C}}^{K\times (K-L(M+U_{1}-1))}\) respectively represent the right singular vectors for the signal space and the null space. Here,
\(\mathbf{V}_{I,0,k}^{(n)}\) is a set of vectors that do not interfere with the other STAs in the BSS and OBSS. If the channel estimates of
\(\tilde{\mathbf{H}}^{{\varvec{\prime }}}_{I,0,k}\) are perfect, the utilization of
\(\mathbf{V}_{I,0,k}^{(n)}\) makes it possible to prevent the interference from affecting
\(\hbox {STA}_{0,k}\,(i=0,{\ldots },M-1,~i\ne k)\) and
\(\hbox {STA}_{1,j^{\prime }}\,(j^{\prime }=0,{\ldots },~U_{1}-1)\). To obtain a transmit beamforming weight that does not interfere with the other STAs in the BSS and OBSS, the null space channel matrix,
\(\tilde{\mathbf{H}}^{{\varvec{\prime }}}_{D,0,k} \mathbf{V}_{I,0,k}^{(n)}\), is decomposed by SVD to yield
$$\begin{aligned} \tilde{\mathbf{H}}^{{\varvec{\prime }}}_{D,0,k} \mathbf{V}_{I,0,k}^{(n)} =\mathbf{U}_{D,0,k} \left[ {{ \begin{array}{cc} {{\varvec{\Sigma }}_{D,0,k}}&{} \mathbf{0} \\ \end{array}}}\right] \left[ {{ \begin{array}{cc} {\mathbf{V}_{D,0,k}^{(s)}}&{} {\mathbf{V}_{D,0,k}^{(n)}} \\ \end{array}}}\right] ^{H}, \end{aligned}$$
(5)
where
\(\mathbf{U}_{D,0,k}\in {\mathbb {C}}^{L\times L}\) denotes the left singular vectors of
\(\tilde{\mathbf{H}}^{{\varvec{\prime }}}_{D,0,k} \mathbf{V}_{I,0,k}^{(n)}\) and the diagonal elements of
\({\varvec{\Sigma }}_{D,0,k}\) are the square roots of
\(\lambda ^{\prime }_{0,0}\),
\(\lambda ^{\prime }_{0,1},{\ldots }, \lambda ^{\prime }_{0,L-1}\), which are the eigenvalues.
\(\mathbf{V}_{D,0,k}^{(s)} \in {\mathbb {C}}^{(K-L(M+U_{1}-1))\times L}\) and
\(\mathbf{V}_{D,0,k}^{(n)} \in {\mathbb {C}}^{(K-L(M+U_{1}-1))\times (K-L(M+U_{1}))}\) represent the right singular vectors of
\(\tilde{\mathbf{H}}^{{\varvec{\prime }}}_{D,0,k} \mathbf{V}_{I,0,k}^{(n)}\) for the signal space and the null space, respectively. Here,
\(\mathbf{V}_{D,0,k}^{(s)}\) is the transmit weight that does not interfere with and maximizes the channel capacity for
\(\hbox {STA}_{0,k}\). Therefore, the transmit beamforming weight
\(\mathbf{W}_{0,k}\) is obtained as
$$\begin{aligned} \mathbf{W}_{0,k} =\mathbf{V}_{I,0,k}^{(n)}~\mathbf{V}_{D,0,k}^{(s)}. \end{aligned}$$
(6)
The transmit beamforming weight which does not interfere with the other STAs in the BSS and OBSS and maximizes to the channel capacity for
\(\hbox {STA}_{1,k}\) associated with
\(\hbox {AP}_{1}\),
\(\mathbf{W}_{1,k}\), is obtained as
$$\begin{aligned} \mathbf{W}_{1,k} =\mathbf{V}_{I,1,k}^{(n)}~\mathbf{V}_{D,1,k}^{(s)}, \end{aligned}$$
(7)
where
\(\mathbf{V}_{I,0,k}^{(n)} \in {\mathbb {C}}^{K\times (K-L(M+U_{1}-1))}\) represents the right singular vectors of
\(\tilde{\mathbf{H}}_{I,1,i}\) for the null space, and
\(\mathbf{V}_{D,0,k}^{(s)} \in {\mathbb {C}}^{(K-L(M+U_{1}-1))\times L}\) represents the right singular vectors of
\(\tilde{\mathbf{H}}^{{\varvec{\prime }}}_{D,0,k} \mathbf{V}_{I,0,k}^{(n)}\) for the signal space.
The proposed scheme prevents not only interference between multiple STAs in the BSS but also ICI whose power is larger than the threshold \(P_{th}\) for the STAs in the neighboring cells by using ZF beamforming. Moreover, it does not perform null beamforming (or ICI mitigation) for the STAs when the ICI power is less than \(P_{th}\) since its effect is small at those STAs and does not need to be suppressed. Therefore, the spatial resource of the transmit antennas can be used not to suppress ICI but to obtain a diversity gain for the STAs in the BSS; this leads to a higher channel capacity. In this scheme, each AP uses ICI power as a basis for adaptively detecting whether null beamforming is to be carried out for the STAs in the OBSS. Here, ICI can be estimated by using the receive signal strength indicator (RSSI) in a wireless LAN system. This simply enables the spatial resource to be used effectively for improving system throughput. Furthermore, the proposed scheme does not estimate the CSI between the AP and the STAs associated with the neighboring AP when the ICI power is less than \(P_{th}\), whereas the conventional schemes need to estimate all of the CSI of the neighboring cell’s STAs. Therefore the proposed scheme can reduce the overhead for the CSI estimation.