Multimodulus Blind Equalization Algorithm Using Oblong QAM Constellations for Fast Carrier Phase Recovery

Adaptive channel equalization without a training sequence is known as blind equalization [1]-[11]. Consider a complex baseband model with a channel impulse response of cn. The channel input, additive white Gaussian noise, and equalizer input are denoted by sn, wn and un, respectively, as shown in Fig. 1. The transmitted data symbols, sn, are assumed to consist of stationary independently and identically distributed (i.i.d.) complex non-Gaussian random variables. The channel is possibly a non-minimum phase linear time-invariant filter. The equalizer input, un = sn ∗ cn + wn is then sent to a tap-delay-line blind equalizer, fn, intended to equalize the distortion caused by inter-symbol interference (ISI) without a training signal, where ∗ denotes the convolution operation. The output of the blind equalizer, yn = f ⋆ n ∗ un = sn ∗ hn + f ⋆ n ∗ wn, can be used to recover the transmitted data symbols, sn, where ⋆ denotes complex conjugation and hn = f ⋆ n ∗ cn denotes the impulse response of the combined channel-equalizer system whose parameter vector can be written as the time-varying vector hn = [hn(1), hn(2), . . .]T with M arbitrarily located non-zero components at a particular instant, n, during the blind equalization process, where M = 1, 2, 3, . . .. For example, if M = 3 and IM = {1, 2, 5} is any M-element subset of the integers, then hn = [hn(1), hn(2), 0, 0, hn(5), 0 . . . 0]T is a representative value of hn.