Table 1 Equivalent tensorial formulation for different systems

STS-CDMA [25, 29]

(1,M _t ,R,M _r )

${\mathbf{1}}_R^T$

Full

$\mathcal{Y}\in {ℂ}^{M_r\times N\times P}$

$(\bar{\mathbf{H}}\mathit{\Omega },\mathbf{S},\mathbf{C})$

SM-CDMA [2]/KRST [13]

(1,M _t ,M _t ,M _r )

${\mathbf{1}}_R^T$

${\mathbf{I}}_{M_t}$

$\mathcal{Y}\in {ℂ}^{M_r\times N\times P}$

$(\bar{\mathbf{H}},\mathbf{S},\mathbf{C})$

MCBS-CDMA [9]

(F,1,R,1)

Full

${\mathbf{1}}_R^T$

$\mathcal{Y}\in {ℂ}^{F\times N\times P}$

$(\bar{\mathbf{H}}\mathit{\Theta },\mathbf{S},\mathbf{C})$ ^a

MCDS-CDMA [7]

(F,1,R,1)

I _R

${\mathbf{1}}_R^T$

$\mathcal{Y}\in {ℂ}^{F\times N\times P}$

$(\bar{\mathbf{H}},\mathbf{S},\mathbf{C})$ ^a

MC-CDMA^b[5]

(F,1,R,1)

Full

${\mathbf{1}}_R^T$

${\bar{\mathbf{Y}}}_1\in {ℂ}^{F\times N}$

$(\bar{\mathbf{H}}\mathit{\Theta },\mathbf{S},{\mathbf{1}}_R^T)$ ^a

Spatial multiplexing^b[31]

(1,M _t ,M _t ,M _r )

${\mathbf{1}}_R^T$

${\mathbf{I}}_{M_t}$

${\bar{\mathbf{Y}}}_1\in {ℂ}^{M_r}\times N$

$(\bar{\mathbf{H}},\mathbf{S},{\mathbf{1}}_R^T)$