This technical document gives complementary results to deliverable D2.1, regarding the definition and test of innovative energy-efficient sub-THz  modulation schemes (index modulation in the filter domain).

In the previous deliverable D2.1, we investigated the spatial Index Modulation (IM) domain and mainly Generalized Spatial Modulation (GSM)-based schemes to achieve low-power ultra-high wireless rates in sub-THz bands. In addition, the GSM Multiple-Input Multiple-Output (MIMO) system performances using spatial IM domain are presented with the achieved link budged, and the proposed Enhanced Generalized Spatial Modulation (EGSM) in high correlated channels is also analyzed. In addition, the study is completed by proposing Dual Polarized Generalized Spatial Modulation (DP-GSM) with its low-complexity detector where an additional layer for indexation is added to enhance the performance and the Spectral Efficiency (SE).

It is worth recalling that the spectral-efficient spatial IM scheme with power-efficient modulation scheme (e.g., GSM-QPSK) is shown to be more advantageous in sub-THz bands than the systems used in recent standards (e.g., IEEE 802.11ax) where Spatial Multiplexing (SMX) with high order Quadrature Amplitude Modulation (QAM) is adopted, this comparison with their optimal detectors is shown in this article. However, GSM requires a full-RF transmitter architecture (i.e., higher transmitter cost) to maintain its SE while using only few Transmit Antennas (TAs) for multiplexing Amplitude-Phase Modulation (APM) symbols, and it suffers from performance degradation when a Transmit Antenna combination (TAC) index is misdetected due to error propagation to all APM symbols. Consequently, these results and drawbacks motivate us to propose a novel IM domain that provides even higher SE/Energy Efficiency (EE) in Single-Input Single-Output (SISO) prior to its MIMO exploitation. It is worth mentioning that each single bit SE enhancement in the SISO context will be multiplied by the multiplexing order in the MIMO context and leads to important SE gain, especially with larger-scale MIMO. Hence, an intelligent strategy that should significantly impact the overall MIMO system design is to enhance the SE of SISO systems while using power-efficient low-order APMs suitable for sub-THz bands with the current technological limitation and RF impairments. This deliverable D2.1-addendum completes the previously cited work by introducing a novel indexation dimension and a novel modulation scheme in SISO and MIMO.

As a first important achievement in this deliverable, a novel domain for IM, named Filter Domain (FD), is proposed where another degree of freedom for IM is presented. In contrast to existing time, frequency, and spatial IM domains that don’t use all the available resources efficiently (e.g., time slots, frequency bands, antennas), the proposed filter IM domain allows to overcome this drawback and reach higher SE and EE gains. Within the filter IM domain/dimension, a novel modulation scheme named Filter Shape Index Modulation (FSIM) is proposed. To the best of our knowledge, this is the first time such an indexing dimension is used as a method for SE and EE enhancement purposes. The pulse-shaping filter is indexed to convey additional information bits to those transmitted in the APM data symbols. The information bits in FSIM are mapped into both signal domain (any M-ary APM) and filter domain. We consider a filter bank with different shapes as a new approach rather than a single pulse shaping filter to further explore the indexation gain. Compared to the joint Maximum Likelihood (ML) detection that considers the joint detection of both filter shape index and APM symbols, we proposed a low-complexity Matched Filter (MF) detector that detects firstly the filter shape being used at the transmitter and then the APM symbols being received. A prominent computational complexity reduction is obtained by MF detector while reaching the optimal performance.

The proposed scheme demonstrates that Inter-Symbol Interference (ISI) is not necessarily undesirable while it is controllable and predictable since it permits to achieve a higher system capacity compared to systems that enforce zero interference. It is worth mentioning that FSIM maintains its superiority in a frequency selective channel compared to existing QAM or Single Carrier (SC) SISO-IM scheme where FSIM achieves a minimum gain of 4 to 6 dB. Second important achievement is the development of a generalized MIMO SMX system by incorporating FSIM scheme to achieve high SE and EE gain. A simple linear receiver for SMX-FSIM is presented, which is based on Zero Forcing (ZF) sample level equalizer followed by a parallel MF-based detector (any other equalizer can be used if it conserves the indexed information). The proposed parallel detection for SMX-FSIM provides good performance with prominent complexity reduction.

Finally, it is worth mentioning that SMX FSIM has better performance, higher robustness to Phase Noise (PN), lower transceiver cost, higher SE/EE gains, and less power consumption compared to other spectral efficient MIMO candidates. However, these advantages come with a slight receiver complexity increase which is in order of L times higher than other candidates, and this complexity can be reduced by proper design of filter bank with a shorter filter of length L while respecting FSIM scheme filter requirements, and it will be shown in our future filter bank design publication.

For instance, the proposed SMX FSIM in sub-Terahertz (THz) channel requires much lower signal-to-noise ratio (SNR) (4 -18 dB less than other candidates SMX-QAM and GSM), which is crucial for sub-THz systems with limited output power, and it is the only scheme among the (Dual-Polarized (DP))-GSM and (DP)-SMX-QAM systems that can operate in a medium PN level with linear low complexity receiver. More details about the performance assessment of the proposed uncoded/coded FSIM based system will be presented in the future deliverable D3.1.