Performance Analysis of Multi-Level Error Corrected Hierarchical Modulation in Multiple Antenna Systems

In this paper, Hierarchical QAM has been analyzed for 2-layer and 3-layer cases across various system parameters. Hierarchical 16QAM has 2 priority levels - HP (High Priority) and LP (Low Priority). Hierarchical 64QAM similarly has 3 priority levels - HP, MP (Medium Priority) and LP. In the proposed system, $(7,4)$ Hamming codes are used as Error Correction Codes (ECC). A generalized equation has also been proposed for constellation mapping of Hierarchical QAM. Uniform $64QAM$ requires an $E_{b}/N_{0}$ of $18\mathrm{~dB}$ to achieve a bit error rate (BER) of $10^{-4}$. However, in the proposed system, only $13.5\mathrm{~dB}$ of $E_{b}/N_{0}$ is required to achieve the same $BER$ for the $HP$ bits. It is further brought down to $9.5\mathrm{~dB}$ after error correction
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. The above mentioned 3-layer system has been implemented for a $1\times 2~{MISO}$ system with simple transmit beamforming and for a $2\times 2~{MIMO}$ system with a Zero forcing (ZF) Detector. Their BER performances have been analyzed in detail.