Multimodulus algorithms for blind equalization
Creators: name: Yang, Jian
Publisher: name: University of British Columbia
Year: 2009

description: In bandwidth-efficient digital transmission, the training of a receiver requires a start-up procedure. This start-up includes the three steps of setting the automatic gain control, recovering timing, and converging the adaptive filters. For many applications, start-up is facilitated by using a known training sequence, which can be used as an ideal reference by the receiver. However, sometimes the use of a training sequence is not feasible or not desirable. In this case, start-up has to be done blindly. The most challenging aspect of blind start-up is the convergence of the adaptive equalizer. This function is called blind equalization. Without ideal reference, the receiver has to make decisions about what data have been transmitted. Normally we use a decision device to make the assumptions on the input signals. This decision device is also called a slicer. These decisions are highly unreliable because the received data are corrupted by intersymbol interference due to distortion introduced by the communication link. As a result, the equalizer does not converge with the conventional least mean square (LMS) algorithm because the probability of wrong decisions is too high. The requirement for reducing wrong decisions leads to the development of blind algorithms. Several algorithms were developed in the past for blind equalization. The two most common ones are the constant modulus algorithm (CMA) and the reduced constellation algorithm (RCA). Both algorithms have been successfully used in many practical applications in data communications. However, improved blind algorithms are still in demand in order to meet the requirements of high data rate communications, where the implementation of blind equalization is required to be simple and reliable. RCA is simple to implement but is not very reliable. CMA is very reliable but has a high complexity., In this thesis, an improved blind algorithm, called multimodulus algorithm (MMA), is proposed. This new algorithm is more reliable than RCA and less complex than CMA. Blind algorithms, such as RCA or CMA, do not take full advantage of the knowledge of the statistics of the data signal, because they only use one statistical quantity, called modulus, during blind convergence. In contrast, MMA makes better usage of the knowledge of the statistics of the data signal and employs multiple moduli to achieve initial convergence. The use of multiple moduli makes MMA very flexible and easily adaptable to applications using two-dimensional transmission schemes with nonsquare or very dense signal constellations. Both RCA and CMA are not very effective for these types of applications. Most blind equalization algorithms minimize a cost function. Our investigation has shown that the minimum (residual) value of this cost function has a great influence on the reliability and speed of convergence of the corresponding blind algorithm. For example, for CMA, RCA and MMA, this residual value increases when the bandwidth efficiency of the transmission system increases, and the blind algorithms suffer a corresponding decrease in performance. Two generalized versions of MMA are proposed to circumvent the above problem. One is called generalized MMA (GMMA). The basic version of MMA uses multiple moduli primarily for nonsquare constellations when nonuniform symbol distributions are utilized. Multiple moduli are also used with GMMA but the additional purpose there is to decrease the residual value of the cost function. A similar effect is achieved by using another blind algorithm, called windowed MMA (WMMA). With WMMA, only one modulus is used, but the tap coefficients of the filter are only updated with some of the data, which leads to a reduction of the residual value of the cost function. The new MMA algorithm has been extensively tested with computer simulations. Most simulation results presented here were obtained with the 155 Mb/s 64-CAP transceiver specified in the ATM LAN standard for category 3 unshielded-twisted-pair office wiring. However, our results are equally applicable to other applications, such as the 52 Mb/s 16-CAP transceiver defined in DAVIC's specification for fiber-to-the-curb networks. Some preliminary experimental results obtained in the laboratory with such a 16-CAP transceiver are presented in this thesis. The computer simulations and laboratory experiments have confirmed that the basic MMA and its generalized algorithms show improved blind convergence performance or complexity savings when compared to previously available algorithms. MMA will likely be incorporated in future broadband access systems from Lucent Technologies, and will replace RCA and CMA, which were previously used, or eliminate the need for a training sequence.