Adaptive two-stage maximum likelihood estimation for cellular radio

The problem of optimal detection over nonselective fading channels for cellular radio is treated from the viewpoint of adaptive two-stage maximum likelihood estimation (MLE). Data for transmission are divided into blocks, each preceded by one or more reference symbols. For selective fading, the receiver consists of an adaptive filter (AF) and a two-stage maximum likelihood estimator (TSMLE). For nonselective fading, TSMLE is preceded by a fixed filter. For quadrature modulation, the complex output of the filter contains two sets of unknowns, the quadrature data symbols (QDS) and the quadrature gains (QG) between transmitter and filter output. Stage I generates MLE estimates of the QG during the reference period and Stage II generates QDS estimates during the data intervals. AF coefficients are adjusted using a QR-decomposition least squares (QRD-LS) algorithm. A likelihood ratio test is performed to produce noise-free data estimates which Stage I in turn can use, in a decision aided manner, to update its gain estimates for the next interval. The quadrature gain estimates can be used to further correct reference carrier phase errors. Nonrecursive and recursive estimation procedures are developed. Bit error rate (BER) expressions are presented for 4-PSK and π/4-DQPSK. Numerical results show that the scheme meets the North American Digital Cellular (NADC) system performance specifications (IS-54) with a margin. The BER floor is an order of magnitude lower than those of other schemes reported in the literature. For nonselective fading the BER floor is practically eliminated. This, and results reported elsewhere (Haeb and Meyr, 1989), lead us to conclude that schemes performing quadrature gain estimation can be used to lower error probabilities, attractively