Space Shift Keying (SSK) Overview

• SSK is a spatial modulation technique that encodes data solely via the activated transmit antenna index, eliminating conventional amplitude or phase modulation.
• It offers energy-efficient, low-complexity MIMO communication by activating only one antenna per symbol, reducing hardware requirements and power consumption.
• SSK has been extended to applications like RIS-assisted networks, molecular communications, and LEO satellite systems, with advanced optimization enhancing performance under practical constraints.

Space Shift Keying (SSK) is a spatial index modulation technique whereby information is conveyed solely by the index of the activated transmit antenna in each symbol interval. In SSK, no conventional amplitude or phase modulation is employed; the entire message is embedded in the spatial activation pattern, i.e., which transmit antenna is used. This approach enables energy-efficient, low-complexity multiple-input multiple-output (MIMO) communication, and has been extended to molecular, wireless, satellite, and reconfigurable intelligent surface (RIS)-assisted networks, with extensive analytical frameworks developed for performance characterization and optimization.

1. Principle of Operation and System Model

In canonical SSK, an array of $N_t$ transmit antennas is available, but exactly one antenna is activated per channel use, governed by $\log_2 N_t$ bits of input data. The transmitted vector is $\mathbf{x} = \mathbf{e}_k$ where $\mathbf{e}_k$ is the $k$th standard basis vector, and the corresponding channel output is $\mathbf{y} = \mathbf{H} \mathbf{x} + \mathbf{n}$, with $\mathbf{H}$ the $N_r \times N_t$ channel matrix and $\mathbf{n}$ additive noise. No baseband amplitude or phase modulation is applied; all signaling is through the antenna index. The receiver's task is to estimate which antenna transmitted, typically via maximum-likelihood (ML) or energy-comparison rules, exploiting the distinct spatial signatures of each channel vector (Chang et al., 2013, Bayar et al., 23 Nov 2025, Zhang et al., 26 Sep 2024).

Key extensions include:

• RIS/IRS-aided SSK: Antenna excitation is routed through reconfigurable surfaces, which apply controlled phase shifts to maximize the receive signal or spatial separation (Canbilen et al., 2020, Zhu et al., 1 Nov 2024, Li et al., 2021, Zhu et al., 2023, Zhu et al., 2023, Basu et al., 7 Nov 2024, Bayar et al., 23 Nov 2025).
• SSK with multilevel coding: Information is mapped not only to the antenna index but also combined with effective coding for each "spatial bit" (Hasan et al., 2021).

2. Fundamental Properties and Analytical Framework

2.1 Spectral Efficiency and Minimum Energy

• Spectral efficiency: Each SSK symbol encodes $m = \log_2 N_t$ bits; thus, the spectral efficiency of SSK is $\log_2 N_t$ bits per channel use (bpcu) (Chang et al., 2013, Zhang et al., 26 Sep 2024).
• Energy efficiency: Since only one antenna is active, the total transmit energy per symbol is constant and minimal—theoretically, SSK achieves the minimum possible average symbol power among schemes in which each codeword has a fixed Hamming weight of one (Chang et al., 2013).
• Diversity: The diversity order under ML detection is $N_r$ (number of receive antennas), with pairwise error rates scaling as $(E_s/N_0)^{-N_r}$ at high SNR (Chang et al., 2013).

2.2 Error Probability and Union Bounds

The pairwise error probability (PEP) for mistaking antenna $i$ for $j$ under ML detection is:

$$P\{i \to j\} = Q\left(\sqrt{\frac{E_s}{2N_0} \|\mathbf{h}_i - \mathbf{h}_j\|^2}\right),$$

with $Q$ the standard Gaussian tail and $\mathbf{h}_i$ the channel from antenna $i$ (Ngoufo et al., 17 Jul 2025, Raj et al., 10 Apr 2024, Chang et al., 2013, Zhang et al., 26 Sep 2024). The bit error rate (BER) is then upper-bounded by a union over all candidate pairs, weighted by their Hamming distance.

3. Comparison with Related Spatial Modulation Schemes

3.1 Spatial Modulation (SM)

• SM generalizes SSK by conveying additional information via an $M$-ary modulation symbol, with spectral efficiency $\log_2 N_t + \log_2 M$ bpcu (Zhang et al., 26 Sep 2024).
• SM achieves higher BER performance and SE than SSK at equal hardware complexity if moderate $M$ is feasible (Zhang et al., 26 Sep 2024).
• SSK is a special case of SM with $M=1$.

3.2 Time-Orthogonal SSK (TOSD-SSK)

• TOSD-SSK exploits time-orthogonal pulse waveforms per transmit antenna, yielding an intrinsic transmit diversity gain of $2N_r$ (Renzo et al., 2011, Renzo et al., 2012).
• At high SNR and with sufficient pilots, TOSD-SSK outperforms both conventional SSK and the Alamouti code in robustness against channel estimation errors.

4. SSK in Nonconventional Channels

4.1 Molecular Communication (SSK-MC)

• SSK principles have been applied in molecular nanoscale MIMO systems, where information is encoded in the choice of a transmitter-releasing nanomachine (Huang et al., 2018).
• The received molecule count is modeled through a diffusion channel, with closed-form symbol error rates confirming superior energy efficiency and performance compared to MIMO-On-Off Keying or SISO- CSK at equivalent bit rates (Huang et al., 2018).

4.2 LEO Satellite, ISAC, and Sensing

• In Low Earth Orbit satellite systems, SSK offers attractive hardware and complexity savings for both data communication and integrated sensing-and-communication (ISAC) architectures (Ngoufo et al., 17 Jul 2025, Zhang et al., 26 Sep 2024).
• Analytical and simulation studies confirm that while SSK incurs an SE penalty versus SM, it remains competitive in constrained RF-chain environments and offers robust performance in joint radar-communication tasks (Ngoufo et al., 17 Jul 2025).

5. SSK with Reconfigurable Intelligent Surfaces (RIS) and Beamforming

5.1 System Architectures and Signal Modeling

RIS/IRS-aided SSK leverages programmable metasurfaces to intelligently alter the propagation environment, achieving large array gains and new diversity mechanisms:

• Passive/Intelligent beamforming: RIS elements coherently align the phases of impinging waves, maximizing the minimum Euclidean distance between spatial codewords at the receiver and thereby minimizing BER (Canbilen et al., 2020, Zhu et al., 1 Nov 2024, Li et al., 2021).
• The received signal is typically modeled as

$y = \sum_{l=1}^N g_{l,i} e^{j\phi_l} h_l + n,$

where $g_{l,i}$ denotes the channel from transmit antenna $i$ to RIS element $l$, $h_l$ the RIS-to-RX link, $\phi_l$ the controllable RIS phase, and $n$ noise (Canbilen et al., 2020, Zhu et al., 1 Nov 2024).

5.2 Optimization under Discrete Phase Constraints

Realistic RISs implement discrete (quantized) phase shifts, making the phase design problem a non-convex combinatorial optimization. Successive convex approximation and penalty-alternating methods have been proposed to maximize the minimum pairwise distance between spatial codewords, yielding significant improvements in reliability (Zhu et al., 1 Nov 2024).

5.3 Performance Analysis with Imperfect CSI and Hardware Impairments

• Imperfect channel knowledge (whether due to estimation error or delayed feedback) introduces error floors at high SNR, but increasing RIS size ($N$) and the number of pilots substantially mitigates this effect (Zhu et al., 2023, Zhu et al., 2023).
• Hardware impairments (modeled with EVM-like additive noise) lead to SNR-independent BER floors that decay with increased $N$ and higher fading order $m$ (Basu et al., 7 Nov 2024).

5.4 Dual-RIS and Full-Duplex SSK

Cascaded (dual) RIS deployments amplify SSK performance by compounding array gains ($\sim N^2$), enabling increased coverage, higher ergodic capacity, and improved outage performance, especially in multi-zone or blocked environments (Bayar et al., 23 Nov 2025). In full-duplex scenarios, RIS helps suppress self-interference, and closed-form ML detectors with Gauss-Chebyshev quadrature provide tight BER estimates (Zhu et al., 2023).

6. Coding and Hybrid/Extended SSK Schemes

6.1 Multilevel and Polar-Coded SSK

Bit-level capacity variation among "spatial bits" in SSK warrants customized coding. Multilevel coded SSK with polar codes matches code rates to the capacity of each spatial bit, providing substantial SNR and BER gains over bit-interleaved approaches (e.g., 2.9 dB at BER $=10^{-4}$) (Hasan et al., 2021).

6.2 Generalized SSK (GSSK) and Energy-Efficient Extensions

Allowing multiple antennas to be active per symbol and optimizing the symbol probabilities (via convex programming and Huffman coding), the energy-efficient Hamming code-aided SSK (HSSK) can approach the theoretical minimum power for a given rate, outperforming conventional SSK by $1$–$2$ dB (Chang et al., 2013).

6.3 Code Index Modulation (CIM) and SSK

Integrating SSK with code-spreading (e.g., Hadamard codes) further increases passive information throughput and is robust in RIS-assisted deployments. Low-complexity detectors and joint SSK-CIM schemes exhibit enhanced spectral efficiency and diversity (Bayar et al., 8 Jul 2025).

7. Design Trade-offs, Applications, and Guidelines

7.1 Hardware and Complexity

• SSK requires only one transmit RF chain, with simple switching logic, drastically reducing hardware cost, heat, and power consumption relative to conventional MIMO (Ngoufo et al., 17 Jul 2025, Chang et al., 2013, Zhang et al., 26 Sep 2024).
• The receiver complexity is linear in $N_r$ and $N_t$ for ML detection, sublinear with further code or channel structure (Bayar et al., 8 Jul 2025).

7.2 Performance under Practical Constraints

• Inter-link interference (ILI): SSK eliminates intra-symbol ILI since only one transmitter is active per symbol. Inter-symbol interference (ISI), however, still constrains performance in some physical channels (e.g., molecular), mitigated through guard intervals or ISI-aware design (Huang et al., 2018).
• Channel estimation: SSK (and especially TOSD-SSK) is robust to imperfect channel knowledge, needing only a handful of pilots to closely approach coherent bounds (Renzo et al., 2012, Renzo et al., 2011).
• Phase quantization: RIS-SSK remains resilient with 2–3 bits of phase resolution; the performance gap to continuous-phase operation is minimal for moderate-to-large $N$ (Zhu et al., 2023, Zhu et al., 1 Nov 2024).

7.3 Application Domains

• LEO satellite and ISAC: SSK supports cost- and power-constrained payloads, integrated sensing, and streamlined handover in clustered multi-satellite topologies (Zhang et al., 26 Sep 2024, Ngoufo et al., 17 Jul 2025).
• Molecular communication: SSK achieves superior symbol error rates and energy-per-bit metrics over traditional CSK/OOK, provided receiver geometry enables strong spatial signature separation (Huang et al., 2018).
• RIS/IRS-enhanced terrestrial and indoor networks: Passive metasurfaces combined with SSK offer energy-efficient, coverage-boosted, and interference-robust physical layers, even in full-duplex regimes (Canbilen et al., 2020, Li et al., 2021, Basu et al., 7 Nov 2024, Bayar et al., 23 Nov 2025).

7.4 Guidelines

• SSK is preferable in applications constrained by hardware complexity, energy, or where only modest spectral efficiency is required.
• For higher SE, SSK can be augmented with advanced coding or code index modulation.
• RIS- or IRS-assisted SSK should employ phase optimization algorithms, ensure up-to-date channel information, and balance quantization resolution with system cost and feedback overhead.
• In interference- or ISI-limited environments, system geometry (spacing, alignment), RIS placement, and symbol timing must be engineered to leverage the full energy and diversity benefits of SSK.

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References:

• (Chang et al., 2013): Energy Efficient Transmission over Space Shift Keying Modulated MIMO Channels
• (Huang et al., 2018): Spatial Modulation for Molecular Communication
• (Zhang et al., 26 Sep 2024): What Roles Can Spatial Modulation and Space Shift Keying Play in LEO Satellite-Assisted Communications?
• (Hasan et al., 2021): Multilevel Polar Coded Space-Shift Keying
• (Canbilen et al., 2020): Reconfigurable Intelligent Surface-Assisted Space Shift Keying
• (Zhu et al., 1 Nov 2024): Discrete RIS Enhanced Space Shift Keying MIMO System via Reflecting Beamforming Optimization
• (Zhu et al., 2023): Performance Analysis of RIS-Aided Space Shift Keying With Channel Estimation Errors
• (Zhu et al., 2023): Reconfigurable Intelligent Surface Aided Space Shift Keying With Imperfect CSI
• (Li et al., 2021): Space Shift Keying with Reconfigurable Intelligent Surfaces: Phase Configuration Designs and Performance Analysis
• (Basu et al., 7 Nov 2024): RIS-Assisted Space Shift Keying with Non-Ideal Transceivers and Greedy Detection
• (Bayar et al., 23 Nov 2025): Performance Evaluation of Dual RIS-Assisted Received Space Shift Keying Modulation
• (Renzo et al., 2012): Space Shift Keying (SSK-) MIMO with Practical Channel Estimates
• (Renzo et al., 2011): On the Performance of Space Shift Keying (SSK) Modulation with Imperfect Channel Knowledge
• (Ngoufo et al., 17 Jul 2025): Space Shift Keying-Enabled ISAC for Efficient Debris Detection and Communication in LEO Satellite Networks
• (Bayar et al., 8 Jul 2025): Adaptive Communication Through Exploiting RIS, SSK, and CIM for Improved Reliability and Efficiency
• (Zhu et al., 2023): Performance of RIS-Assisted Full-Duplex Space Shift Keying With Imperfect Self-Interference Cancellation
• (Raj et al., 10 Apr 2024): On the Performance of IRS-Assisted SSK and RPM over Rician Fading Channels
• (Rajashekar et al., 2012): Structured Dispersion Matrices from Space-Time Block Codes for Space-Time Shift Keying