In this paper, a non-linear precoding algorithm with low out-of-band (OOB) radiation is proposed for massive multiple-input multiple-output (MIMO) systems. Massive MIMO sets more than one hundred antennas at each base station to achieve higher spectral efficiency and throughput. Full digital massive MIMO may constrain the resolution of digital-to-analog converters (DACs) since each DAC consumes a large amount of power. In massive MIMO systems with low resolution DACs, designing methods of DAC output signals by nonlinear processing are being investigated. The conventional scheme focuses only on a sum rate or errors in the received signals and so triggers large OOB radiation. This paper proposes an optimization criterion that takes OOB radiation power into account. Gibbs sampling is used as an algorithm to find sub-optimal solutions given this criterion. Numerical results obtained through computer simulation show that the proposed criterion reduces mean OOB radiation power by a factor of 10 as compared with the conventional criterion. The proposed criterion also reduces OOB radiation while increasing the average sum rate by optimizing the weight factor for the OOB radiation. As a result, the proposed criterion achieves approximately 1.3 times higher average sum rates than an error-based criterion. On the other hand, as compared with a sum rate based criterion, the throughput on each subcarrier shows less variation which reduces the number of link adaptation options needed although the average sum rate of the proposed criterion is smaller.

This paper proposes relay selection techniques for XOR physical layer network coding with MMSE based non-linear precoding in MIMO bi-directional wireless relaying networks. The proposed selection techniques are derived on the different assumption about characteristics of the MMSE based non-linear precoding in the wireless network. We show that the signal to noise power ratio (SNR) is dependent on the product of all the eigenvalues in the channels from the terminals to relays. This paper shows that the best selection techniques in all the proposed techniques is to select a group of the relays that maximizes the product. Therefore, the selection technique is called “product of all eigenvalues (PAE)” in this paper. The performance of the proposed relay selection techniques is evaluated in a MIMO bi-directional wireless relaying network where two terminals with 2 antennas exchange their information via relays. When the PAE is applied to select a group of the 2 relays out of the 10 relays where an antenna is placed, the PAE attains a gain of more than 13dB at the BER of 10-3.

This paper proposes coded modulation for physical layer network coding in multiple input multiple output orthogonal frequency division multiplexing (MIMO-OFDM) bi-directional wireless relay systems where precoding is applied. The proposed coded modulation enables the relays to decode the received signals, which improves the transmission performance. Soft input decoding for the proposed coded modulation is proposed. Furthermore, we propose two precoder weight optimization techniques, called “per subcarrier weight optimization” and “total weight optimization”. This paper shows a precoder configuration based on the optimization with the lattice reduction or the sorted QR-decomposition. The performance of the proposed network coding is evaluated by computer simulation in a MIMO-OFDM two-hop wireless relay system with the 16 quadrature amplitude modulation (QAM) or the 256QAM. The proposed coded modulation attains a coding gain of about 2dB at the BER of 10-4. The total weight optimization achieves about 1dB better BER performance than the other at the BER of 10-4.

This paper proposes an XOR physical layer network coding (XOR-PLNC) with non-linear precoding for quadrature amplitude modulations (QAMs) in bi-directional MIMO relay systems. The proposed XOR-PLNC applies power loading in order to improve the transmission performance. The proposed XOR-PLNC introduces a modulus adapted to channel gains. Moreover, the modulus is further reduced in cooperation with modulo operation which the non-linear precoding employs for improvement of transmission power efficiency. The use of the reduced modulus improves the energy efficiency of the signal transmission, which improves the transmission performance in the proposed XOR-PLNC. The performance is evaluated by computer simulations in bi-directional MIMO relay channels with 16QAM to 1024QAM.

Non-linear precoding (NLP) scheme for downlink multi-user multiple-input multiple-output (DL-MU-MIMO) transmission has received much attention as a promising technology to achieve high capacity within the limited bandwidths available to radio access systems. In order to minimize the required transmission power for DL-MU-MIMO and achieve high spectrum efficiency, Vector Perturbation (VP) was proposed as an optimal NLP scheme. Unfortunately, the original VP suffers from significant computation complexity in detecting the optimal perturbation vector from an infinite number of the candidates. To reduce the complexity with near transmission performance of VP, several recent studies investigated various efficient NLP schemes based on the concept of Tomlinson-Harashima precoding (THP) that applies successive pre-cancellation of inter-user interference (IUI) and offsets the transmission vector based on a modulo operation. In order to attain transmission performance improvement over the original THP, a previous work proposed Minimum Mean Square Error based THP (MMSE-THP) employing IUI successive pre-cancellation based on MMSE criteria. On the other hand, to improve the transmission performance of MMSE-THP, other previous works proposed Ordered MMSE-THP and Lattice-Reduction-Aided MMSE-THP (LRA MMSE-THP). This paper investigates the further transmission performance improvement of Ordered MMSE-THP and LRA MMSE-THP. This paper starts by proposing an extension of MMSE-THP employing a perturbation vector search (PVS), called PVS MMSE-THP as a novel NLP scheme, where the modulo operation is substituted by PVS and a subtraction operation from the transmit signal vector. Then, it introduces an efficient search algorithm of appropriate perturbation vector based on a depth-first branch-and-bound search for PVS MMSE-THP. Next, it also evaluates the transmission performance of PVS MMSE-THP with the appropriate perturbation vector detected by the efficient search algorithm. Computer simulations quantitatively clarify that PVS MMSE-THP achieves better transmission performance than the conventional NLP schemes. Moreover, it also clarifies that PVS MMSE-THP increases the effect of required transmission power reduction with the number of transmit antennas compared to the conventional NLP schemes.

In this paper, we propose a modified Tomlinson Harashima precoding (THP) method with less increase of computational complexity for the multi-user MIMO downlink system. The proposed THP scheme minimizes the influence of noise enhancement at the receivers by placing the diagonal weighted filters at both transmitter side and receiver side with square root. Compared to previously proposed non-linear precoding methods including vector perturbation (VP), the proposed THP achieves high BER performance. Furthermore, we show that the proposed THP method is implemented with lower computational complexity than that of existing modified THP and VP in literature.

Precoding is an excellent choice for complementing the MIMO systems. Linear precoding techniques offer better performance at low signal-to-noise ratios (SNRs) while non-linear techniques perform better at higher SNRs. In addition, the non-linear techniques can achieve near optimal capacity at the expense of reasonable levels of complexity. However, precoding depends on the knowledge of the wireless channel. Recent work on MIMO systems have shown that channel-knowledge at the transmitter, in either full or partial forms, can increase the channel capacity and system performance considerably. Therefore, hybrid techniques should be deployed in order to obtain a better trade-off in terms of complexity and performance. In this paper, we present a hybrid precoding technique which deals with the condition of partial channel-knowledge while offering robustness against the effects of correlation and poorly scattered channels while at the same time keeping low levels of complexity and high performance.