Finite-Length MMSE Tomlinson–Harashima Precoding for Frequency Selective Vector Channels

Iterative MMSE Transmit and Receive Filter Design for Frequency Selective MU-MISO Systems

“…For THP, modulo operators M(•) are deployed at the receivers to increase the degrees of freedom for the transmitter, since they map any element of a coset of the corresponding lattice to its representative in the fundamental Voronoi region (see e.g., [12], [20]). The transmitter chooses the element of the coset by means of the modulo feedback loop comprising the spatial feedback filter F (lower triangular with zero main diagonal to avoid a delay-free loop) and the temporal feedback filter T [n] (strictly causal to ensure realizability) of order N T…”

“…, F, are diagonal, since the receivers cannot cooperate. Since any vector a ∈ τ Z B + j τ Z B can be added to the modulo input without changing its output, i.e., M(x + a ) = M(x), the transmitter can choose a desired value for this shift of the received signal (e.g., [12]). This shift of the received signal is removed by the modulo operators at the receivers and its desired value is created by the modulo operator in the feedback loop at the transmitter.…”

“…Compared to matched filter [2] and zero-forcing (ZF) schemes [3]- [7], minimum MSE (MMSE) based linear precoders show an excellent performance [8]- [11]. For THP, the receivers are equipped with modulo operators giving the transmitter the additional degrees of freedom to add a perturbation signal by means of a modulo feedback loop to reduce transmit power (e.g., [12]). As for linear precoding, MMSE-THP [11]- [14] clearly outperforms ZF-THP [14]- [17].…”

“…Nevertheless, FIR precoders were proposed in [8], [12] and infinite impulse response (IIR) THP was considered in [14]. FIR precoders are preferable compared to block processing for frequency selective channels due to the substantially reduced complexity.…”

Minimum SER Block Precoding and Equalization for Frequency-Selective Fading Channels

“…This can further enhance performance and capacity, when perfect CSI is made available at the transmitter side [2]. Hence, designing transmitters based on exact CSI is well motivated, which is of particular great interest in downlink transmission [1]- [13]. Transmitter design based on a capacity criterion has been studied in [3] [4] which specifies the achievable rate of reliable communication.…”