MIMO	Multiple-input multiple-output
LZF	Linear zero-forcing
LMMSE	Linear minimum mean-square-error
ML	Maximum likelihood
MP	Message passing
BP	Belief propagation
QR-BP	QR-decomposition-based BP
IC	Interference cancellation
QR-SBP	Scheduled QR-BP with IC and candidate constraints
AWGN	Additive white Gaussian noise
LLR	Log-likelihood ratio
BER	Bit-error ratio
FER	Frame-error ratio
SNR	Signal-to-noise ratio
MFB	Matched-filter bound
Mathematical Symbols
The following mathematical symbols are used in this manuscript:
K	Number of transmit antennas
M	Number of receive antennas
Q	Number of bits assigned for each transmit symbol
N	Number of bits included in each transmit signal vector
$\mathsf{X}$	$2^Q$-ary constellation set
$\mathbf{y}$	$M\times 1$ receive signal vector
$\mathbf{H}$	$M\times K$ MIMO channel matrix
${\mathbf{h}}_m$	mth row of $\mathbf{H}$
$\mathbf{x}$	$K\times 1$ transmit signal vector
$\mathbf{n}$	$M\times 1$ AWGN vector
$b_n$	nth bit among the bit sequence in each $\mathbf{x}$
${\alpha }_{mn}$	Message from the nth bit node to the mth observation node
${\beta }_{mn}$	Message from the mth observation node to the nth bit node
${\mathsf{X}}^{K,b}$	Set of $K\times 1$ vectors whose elements are the members of $\mathsf{X}$ with $b_n=0$ or 1
$l_n$	LLR of $b_n$
$\mathbf{Q}$	$M\times M$ unitary matrix with $\mathbf{H}=\mathbf{Q}[\mathbf{R};{\mathbf{0}}_{(M-K)\times K}]$
$\mathbf{R}$	$K\times K$ upper triangular matrix with $\mathbf{H}=\mathbf{Q}[\mathbf{R};{\mathbf{0}}_{(M-K)\times K}]$
${\mathbf{r}}_m$	mth row of $\mathbf{R}$
${\tilde{\mathbf{r}}}_m$	$1\times (K-m+1)$ vector containing the non-zero elements of ${\mathbf{r}}_m$
$\tilde{\mathbf{y}}$	$K\times 1$ receive signal vector for the QR-BP detector
$\tilde{\mathbf{n}}$	$K\times 1$ AWGN vector for the QR-BP detector
${\widehat{x}}_k$	A hard decision symbol of $x_k$
${\tilde{\mathbf{y}}}^{(k)}$	$K\times 1$ receive signal vector for the message updating of the bit sequence in $x_k$
${\mathbf{z}}^{(k)}$	$k\times 1$ effective receive signal vector for $x_k$ in the proposed QR-SBP detector
${\mathbf{x}}^{(k)}$	$k\times 1$ effective transmit signal vector for $x_k$ in the proposed QR-SBP detector
${\tilde{\mathbf{n}}}^{(k)}$	$k\times 1$ effective AWGN vector for $x_k$ in the proposed QR-SBP detector
${\mathbf{R}}^{(k)}$	$k\times k$ effective channel matrix for $x_k$ in the proposed QR-SBP detector
${\mathcal{B}}_{mn}^b$	Set to update ${\beta }_{mn}$ with $b=0$ and 1 in the proposed QR-SBP detector
${{\tilde{\mathbf{r}}}_m}^{(k)}$	$1\times w$ vector containing the non-zero elements of the mth row of ${\mathbf{R}}^{(k)}$
${\mathsf{X}}_{(k)}^{w,b}$	Set of $w\times 1$ vectors for $x_k$ whose elements are the members of $\mathsf{X}$ with $b_n=b$
${\delta }_{(k)}^w$	Number of surviving $w\times 1$ vectors in ${\mathsf{X}}_{(k)}^{w,b}$
${\mathsf{Y}}_{(k)}^{w,b}$	Set containing the ${\delta }_{(k)}^w$ surviving $w\times 1$ vectors in ${\mathsf{X}}_{(k)}^{w,b}$
${\delta }^{*}$	Maximum ${\delta }_w^{(k)}$ for all w and k
$t_{max}$	Number of maximum BP iterations