Abstract
This paper proposes two nonlinear blind equalizers: the nonlinear constant modulus algorithm (NCMA) and the nonlinear modified constant modulus algorithm (NCMA) by applying a nonlinear transfer function (NTF) into constant modulus algorithm (CMA) and modified constant modulus algorithm (MCMA), respectively. The effect of the NTF on CMA and MCMA is theoretically analyzed, which implies that the NTF can make their decision regions much sharper so that the proposed two nonlinear blind equalizers are more robust against the convergency error compared to their linear counterparts. The embedded single layer in NCMA and NMCMA simultaneously guarantees a comparably speedy convergency. On 16-quadrature amplitude modulation (QAM) symbols, computer simulations show that NCMA achieves an 8dB lower convergency mean square error (MSE) than CMA, and NMCMA achieves a 15dB lower convergency MSE than MCMA.
Highlights
Constant modulus algorithm (CMA) [1,2,3,4,5,6] is widely used for blind equalization [2,5,6,7,8,9,10] for constant modulus transmissions in communication systems in order to overcome the propagation channel corruption, mitigate the inter-symbol interference (ISI) and recover the transmitted symbols, which usually has a satisfied performance in common situations
This paper proposes two nonlinear blind equalizers: the nonlinear constant modulus algorithm (NCMA) and the nonlinear modified constant modulus algorithm (NCMA) by applying a nonlinear transfer function (NTF) into constant modulus algorithm (CMA) and modified constant modulus algorithm (MCMA), respectively
The effect of the NTF on CMA and MCMA is theoretically analyzed, which implies that the NTF can make their decision regions much sharper so that the proposed two nonlinear blind equalizers are more robust against the convergency error compared to their linear counterparts
Summary
Constant modulus algorithm (CMA) [1,2,3,4,5,6] is widely used for blind equalization [2,5,6,7,8,9,10] for constant modulus transmissions in communication systems in order to overcome the propagation channel corruption, mitigate the inter-symbol interference (ISI) and recover the transmitted symbols, which usually has a satisfied performance in common situations. The following theoretical derivation provides that the NTF can make the decision region much sharper so that the proposed nonlinear blind equalizers are more robust against the convergency error. Based on this discovery, by applying the nonlinear transfer function (NTF) to CMA and MCMA, the nonlinear CMA (NCMA) and nonlinear modified CMA (NMCMA) are proposed, and their adaptive learning rules are theoretically derived in this paper.
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