Precoding Design with Joint Dynamic Channel Assignment and Band Selection Techniques for Downlink CoMP OFDMA Systems

Abstract

Multi cell transmission can prevent the multi-cell interference by localizing the signals at different sub-band for the downlink (DL) localized orthogonal frequency division multiple access (OFDMA) systems. However, the synchronized errors, such as carrier frequency offset (CFO), will induce the challenging problems of interference due to the non-orthogonality between the subcarriers and cells. In this paper, we propose the novel precoding design with joint dynamic channel assignment and band selection techniques for DL coordinated multipoint (CoMP) OFDMA systems with CFO effect. Further, a two-stage pre-processing technique is proposed to eliminate the above interference problems and reduce the computational complexity of the cell-edge users for DL CoMP OFDMA systems. Moreover, the central unit can assign the resource dynamically to enhance the link quality. Therefore, the dynamic channel on/off assignment techniques and the dynamic band selection techniques are proposed to enhance the bit error rate (BER) performance. Simulation results confirm that the proposed precoding transceiver provides excellent BER and lower computational complexity of the cell-edge communication than the conventional block diagonalization technique.

Appendix: Derivation of New LQ Decomposition in (8)

In (8), the new rearranged channel matrix is ${\mathbf{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{H} }}_{k}$. The new ${\mathbf{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{H} }}_{k}$ is used to derive the new LQ decomposition as follows.

For example, in a 2 × n channel matrix ${\mathbf{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{H} }}_{k}$, ${\mathbf{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{H} }}_{k}$ can be described by

$${\mathbf{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{H} }}_{k} = \left[ {\begin{array}{*{20}c} {{\bar{\mathbf{h}}}_{1} } \\ {{\bar{\mathbf{h}}}_{2} } \\ \end{array} } \right]$$

(19)

where ${\bar{\mathbf{h}}}_{1}$ and ${\bar{\mathbf{h}}}_{2}$ are 1 × n matrices. The LQ decomposition of ${\mathbf{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{H} }}_{k}$ can be written as

$$\left[ {\begin{array}{*{20}c} {{\bar{\mathbf{h}}}_{1} } \\ {{\bar{\mathbf{h}}}_{2} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {l_{11} } & 0 \\ {l_{21} } & {l_{22} } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {{\bar{\mathbf{q}}}_{1} } \\ {{\bar{\mathbf{q}}}_{2} } \\ \end{array} } \right]$$

(20)

where l ₁₁, l ₂₁, and l ₂₂ are scalars. The ${\bar{\mathbf{q}}}_{1}$ and ${\bar{\mathbf{q}}}_{2}$ are the orthonormal vectors, i.e., ${\bar{\mathbf{q}}}_{x}^{\text{H}} {\bar{\mathbf{q}}}_{y} = 1$ and ${\bar{\mathbf{q}}}_{x}^{\text{H}} {\bar{\mathbf{q}}}_{y} = 0$ ${\mathbf{(}}x \ne y{\mathbf{)}}$,respectively. Based on the first row in (20), and, since ${\bar{\mathbf{q}}}_{1}$ is an orthonormal property, we can derive the l ₁₁ and ${\bar{\mathbf{q}}}_{1}$, i.e.,

$${\bar{\mathbf{h}}}_{1} = l_{11} {\bar{\mathbf{q}}}_{1}$$

(21)

where ${\bar{\mathbf{q}}}_{1} = {{{\bar{\mathbf{h}}}_{1} } \mathord{\left/ {\vphantom {{{\bar{\mathbf{h}}}_{1} } {\left\| {{\bar{\mathbf{h}}}_{1} } \right\|}}} \right. \kern-0pt} {\left\| {{\bar{\mathbf{h}}}_{1} } \right\|}}$ and $l_{11} = \left\| {{\bar{\mathbf{h}}}_{1} } \right\|$. Next, by applying the known ${\bar{\mathbf{q}}}_{1}$ and ${\bar{\mathbf{q}}}_{1}^{\text{H}} {\bar{\mathbf{q}}}_{2} { = 0}$ property, the l ₁₂ can be derived by the second row in (20):

$${\bar{\mathbf{h}}}_{2} = l_{21} {\bar{\mathbf{q}}}_{1} + l_{22} {\bar{\mathbf{q}}}_{2}$$

(22)

where $l_{12} = {\bar{\mathbf{q}}}_{1}^{\text{H}} {\bar{\mathbf{h}}}_{2}$. Finally, substituting the known l ₁₂ and ${\bar{\mathbf{q}}}_{1}$ into (22), gets the new ${\mathbf{\bar{\bar{h}}}}_{2}$, i.e.,

$$\begin{aligned} {\mathbf{\bar{\bar{h}}}}_{2} & = {\bar{\mathbf{h}}}_{2} - l_{12} {\bar{\mathbf{q}}}_{1} \\ & = l_{22} {\bar{\mathbf{q}}}_{2} \\ \end{aligned}$$

(23)

Next, since ${\bar{\mathbf{q}}}_{2}$ has the same orthonormal property described in (21), the l ₂₂ and ${\bar{\mathbf{q}}}_{2}$ can be derived by (23), i.e.,

$${\bar{\mathbf{q}}}_{2} = {{{\mathbf{\bar{\bar{h}}}}_{2} } \mathord{\left/ {\vphantom {{{\mathbf{\bar{\bar{h}}}}_{2} } {\left\| {{\mathbf{\bar{\bar{h}}}}_{2} } \right\|}}} \right. \kern-0pt} {\left\| {{\mathbf{\bar{\bar{h}}}}_{2} } \right\|}}$$

(24)

$$l_{22} = \left\| {{\mathbf{\bar{\bar{h}}}}_{2} } \right\|$$

(25)

The procedures described in (19)–(25) get the new LQ decomposition of the rearranged channel matrix ${\mathbf{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{H} }}_{k}$. Notably, ${\mathbf{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{H} }}_{k}$ for a n × n channel matrix can be derived by referring to the procedures listed in (19)–(25).