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A novel formulation of Tomlinson-Harashima pre- coding (THP) for multiple-input-single-output (MISO) frequency- selective broadcast channels is proposed. The formulation natu- rally takes into account the spatial, temporal, frequency and user dimensions simultaneously, so that parameters for the four dimen- sions can be jointly optimized. Relationships among the four di- mensions are explored, and methods for choosing two of the pa- rameters are discussed. Of particular interests are the role of the frequency dimension in the system, and ways to exploit it to con- currently support a large number of users, especially when the number of channel taps is large. Performance of the system is evaluated in terms of its sum rate, rate region and symbol error rate (SER). I. INTRODUCTION Tomlinson-Harashima precoding (THP) was first proposed more than thirty years ago as a transmit equalization strategy to counter intersymbol interference (ISI) in single-input-single- output (SISO) frequency-selective channels (1), (2). By pre- subtracting post-cursor ISI at the transmitter, THP circumvents two infamous problems in classical decision feedback equal- ization: the error propagation problem, and the decision de- lay problem associated with the use of forward-error-correction codes. However, THP has its own drawbacks, all of which are caused by its signature modulo operators (8). First, the mod- ulo operator at the transmitter forbids the probability distribu- tion of the transmit signal to shape like the capacity-achieving Gaussian distribution. At high signal-to-noise ratios (SNRs), a penalty of 1.53 dB results for pulse amplitude modulation (PAM) or square quadrature amplitude modulation (QAM) with a large number of alphabets. This degradation is called the |
