An Efficient Practical MIMO–OFDM Scheme with Coded Modulation Diversity for Future Wireless Communications

Abstract

An efficient coded modulation diversity scheme is proposed to improve the performance of multiple-input-multiple-output orthogonal-frequency-division-multiplexing (MIMO–OFDM) systems in frequency-selective time-varying fading channels. By introducing the rotated modulation and space-time-frequency component interleavers, the proposed scheme globally optimizes powerful forward error correction codes, rotated quadrature amplitude modulation, linear precoding MIMO, and OFDM, thus can achieve modulation diversity and space-time-frequency diversities as much as possible. A simple efficient optimal precoder selection criterion is put forward for this scheme. Based on the analysis of average mutual information, optimal rotation angles are given for different modulation and coding schemes, and the superiority of the proposed scheme is proved. Both software simulation and hardware prototype test results also verify that this new scheme can significantly outperform the conventional bit-interleaved coded modulation scheme under the non-ideal channel estimation, which is up to 4.5 dB signal-to-noise-ratio gain. In a word, the proposed scheme is a simple, efficient and robust transmission technique for the future MIMO–OFDM wireless systems.

Appendix: Proof of Equation (16)

Proof

For the MIMO detection, after the phase-compensation operation in the Eq. (12), the reference complex signal of $\left( b_t^I,b_t^Q\right)$ is shown as the following:

$$\begin{aligned} REF_t^i = \frac{{g_t^i \cdot a_{ii}^*}}{{{{\left| {{a_{ii}}} \right| }^2}}} \end{aligned}$$

(16)

where, according to the Eq. (6), $g_t^i = {a_{ii}} \cdot x_t^i$, and $x_t^i$ is the transmit rotated modulation symbol.

Thus, $REF_t^i = \frac{{{a_{ii}} \cdot a_{ii}^*}}{{{{\left| {{a_{ii}}} \right| }^2}}}x_t^i = x_t^i$, that is to say, the received reference signal is the same as the transmit rotated signal.

According to the Eq. (12), the variance of the interference and noise $VAR(b_t^i - {x_j})$ is calculated as the following:

$$\begin{aligned} \begin{aligned} VAR\left( {b_t^i - {x_j}} \right)&= {\left| {\frac{{a_{ii}^*}}{{{{\left| {{a_{ii}}} \right| }^2}}}} \right| ^2} \cdot VAR\left( {g_t^i - {a_{ii}} \cdot {x_j}} \right) \\&= \frac{{VAR\left( {g_t^i - {a_{ii}} \cdot {x_j}} \right) }}{{{{\left| {{a_{ii}}} \right| }^2}}}\\ \end{aligned} \end{aligned}$$

(17)

According to the Eq. (8),

$$\begin{aligned} VAR\left( {g_t^i - {a_{ii}} \cdot {x_j}} \right) = \sum \limits _{k = 1,k \ne i}^N {{{\left| {{a_{ij}}} \right| }^2}} + \sum \limits _{k = 1}^N {{{\left| {{b_{ij}}} \right| }^2}} \cdot 2{\sigma ^2} \end{aligned}$$

(18)

Thus, the variance of the interference and noise is shown as the following:

$$\begin{aligned} VAR\left( {b_t^i - {x_j}} \right) = \frac{{\sum \nolimits _{k = 1,k \ne i}^N {{{\left| {{a_{ij}}} \right| }^2}} + \sum \nolimits _{k = 1}^N {{{\left| {{b_{ij}}} \right| }^2}} \cdot 2{\sigma ^2}}}{{{{\left| {{a_{ii}}} \right| }^2}}} \end{aligned}$$

(19)

According to the Eq. (9), it is easy to know

$$\begin{aligned} VAR\left( {b_t^i - {x_j}} \right) = \frac{1}{{SIN{R_i}}} \end{aligned}$$

(20)

That is to say, the variance is the reciprocal of SINR. Thus, the metric $E_{i,j}$ is computed as the following:

$$\begin{aligned} \begin{aligned} {E_{i,j}}&= - \left( {\frac{{{{\left| {b_i^I - x_j^I} \right| }^2}}}{{VAR\left( {b_i^I - x_j^I} \right) }} + \frac{{{{\left| {b_i^Q - x_j^Q} \right| }^2}}}{{VAR\left( {b_i^Q - x_j^Q} \right) }}} \right) \\&= - \left( {{{\left| {b_i^I - x_j^I} \right| }^2} \cdot SIN{R_I} + {{\left| {b_i^Q - x_j^Q} \right| }^2} \cdot SIN{R_Q}} \right) \\ \end{aligned} \end{aligned}$$

(21)