Spatial Lattice Modulation for MIMO Systems

Abstract

This paper proposes spatial lattice modulation (SLM), a spatial modulation method for multipleinput-multiple-output (MIMO) systems. The key idea of SLM is to jointly exploit spatial, in-phase, and quadrature dimensions to modulate information bits into a multi-dimensional signal set that consists of lattice points. One major finding is that SLM achieves a higher spectral efficiency than the existing spatial modulation and spatial multiplexing methods for the MIMO channel under the constraint of M -ary pulseamplitude-modulation (PAM) input signaling per dimension. In particular, it is shown that when the SLM signal set is constructed by using dense lattices, a significant signal-to-noise-ratio (SNR) gain, i.e., a nominal coding gain, is attainable compared to the existing methods. In addition, closed-form expressions for both the average mutual information and average symbol-vector-error-probability (ASVEP) of generic SLM are derived under Rayleigh-fading environments. To reduce detection complexity, a low-complexity detection method for SLM, which is referred to as lattice sphere decoding, is developed by exploiting lattice theory. Simulation results verify the accuracy of the conducted analysis and demonstrate that the proposed SLM techniques achieve higher average mutual information and lower ASVEP than do existing methods. Index TermsMultiple-input-multiple-output (MIMO), spatial modulation (SM), lattice modulation.

Signal Shaping for Generalized Spatial Modulation and Generalized Quadrature Spatial Modulation

“…However, the arXiv:1901.09318v1 [eess.SP] 27 Jan 2019 design for more spectral-efficient multiple-data-stream GenSM was left unconsidered. Besides, little work is known on the constellation design for GenQSM other than [16] proposed a heuristic signal constellation optimization for QSM and [17] studied a lattice-code-based constellation optimization strategy for GenQSM. These are based on predefined codebooks and can be viewed as an optimization strategy in the discrete space.…”

On the Capacity of MISO Channels With One-Bit ADCs and DACs

“…In addition, the major limitation of the works in [19], [20] is the assumption of BPSK signaling per transmit antenna as channel inputs. This assumption excludes the possibility of using spatial modulation methods [22]- [27], where information bits are jointly mapped across a set of activated indices of spatial, in-phase, and quadrature dimensions Fig. 1.…”

“…and the BPSK symbols of the activated dimensions. Under the one-bit DACs constraint, a set of all possible channel inputs is generated using spatial lattice modulation (SLM) method [27], which is known as a generalization of spatial modulation techniques [22]- [26]. Since the joint information mapping by SLM maximizes the number of possible input alphabets, in general, it might achieve higher transmission rates compared to the case when using the BPSK signaling per transmit antennas as in [19], [20].…”

“…In particular, we characterize the capacity expression with a closed form for the MISO channel with one-bit ADCs and DACs. The key idea to find the capacity expression is to construct the channel input vectors in an 2M-dimensional input space {−1, 0, 1} 2M by the joint information mapping across the transmit antennas, the real and the imaginary components [27]. Then, we optimize the input distribution to maximize the mutual information between the channel inputs and outputs.…”

“…We extend the results of the SISO case into the MISO case. For the MISO channel, it is possible to construct the channel input set with 9 M − 1 different non-zero input vectors by the joint information mapping rule in [27]. Using this channel input set, we characterize the channel capacity by deriving the capacity-achieving input distribution under the average transmit power constraint.…”