Two Novel Blind Equalization Algorithms for Rectangular Quadrature Amplitude Modulation Constellations

Two novel blind equalization techniques for odd bit rectangular quadrature amplitude modulation (RQAM) signaling are proposed in this paper, namely, rectangular contour algorithm (<inline-formula> <tex-math notation="LaTeX">$\text{R}_{\mathrm { {RECT}}}$ </tex-math></inline-formula> CA) and improved rectangular contour algorithm (IRCA). The proposed <inline-formula> <tex-math notation="LaTeX">$\text{R}_{\mathrm { {RECT}}}$ </tex-math></inline-formula> CA algorithm minimizes the dispersion of constant with respect to a rectangular-shaped zero error contour. The algorithm exploits the geometry of the RQAM to correct phase error within 180°, thus enhancing the convergence rate while minimizing the equalizer mis-adjustments. On the other hand, the proposed IRCA algorithm employs the estimated output from the decision device into the cost function, thus guiding the equalizer output to reside on multiple zero error rectangular shaped moduli. This method of feeding back the slicer output further reduces the mis-adjustment between the transmitted constellation and the new cost function in an efficient manner, which leads to faster convergence and better intersymbol interference suppression. The proposed algorithms can also work for the square QAM by mere change of only two constellation dependent constants, thus facilitating the implementation in hardware to enable transmission of both even and odd number of bits per symbol based constellations. Steady-state error analysis, MSE, and residual ISI comparison through the simulation results confirm the good performance of the proposed algorithms. Furthermore, the convergence characteristics of the proposed IRCA scheme establish the supremacy of IRCA over <inline-formula> <tex-math notation="LaTeX">$\text{R}_{\mathrm { {RECT}}}$ </tex-math></inline-formula>CA, which is its parent algorithm.