Bit-Driven Spatial Modulation

• Bit-driven spatial modulation is a method where input bits select a single active antenna or beam, encoding information solely via spatial resource activation.
• It leverages RIS-enabled architectures for real-time phase configuration and dynamic signal routing, significantly reducing RF complexity and power consumption.
• Analytical studies show that increasing RIS elements enhances capacity and reliability while mitigating error rates through optimal index detection and coherent combining.

Bit-driven spatial modulation denotes schemes in which a set of input bits steers the reconfiguration of spatial resources—specifically antenna indices or dynamically controlled reflectors—so that the data is mapped solely to spatial patterns rather than traditional amplitude/phase constellations. Its canonical realization is space-shift keying (SSK) and its extensions, in which each symbol-period sees exactly one spatial pathway (e.g., transmit antenna, receive antenna, or beam direction via a reconfigurable surface) activated according to the data. Bit-driven SSK and its generalizations are of rising interest in the context of energy-efficient, ultra-low-complexity, and reconfigurable architectures, notably with multiple intelligent reflecting surfaces (RISs) acting as spatial routers.

1. Bit-Driven Spatial Modulation: Concept and Fundamentals

In bit-driven spatial modulation, a block of $\log_2M$ bits (for $M$ possible spatial branches) selects an element from a set of spatial resources—commonly transmit antennas or beam directions—as the sole "on" pathway for each symbol interval. The distinguishing feature is that no symbol information is conveyed via standard complex-valued modulation; all information is embedded in the spatial activation pattern, as controlled directly by the bits.

In received-spatial SSK systems with reconfigurable surfaces, bit-driven control extends to networked entities such as dynamically addressed RISs, where the bits determine which receiver or beam path is selected at the physical layer via modulation of the RIS reflection phases (Bayar et al., 23 Nov 2025).

This contrasts with classical spatial modulation (SM), in which both a conventional modulated symbol and the antenna index convey information, and with traditional MIMO, which typically activates all antennas simultaneously.

Key properties:

• Information is encoded purely in spatial resource selection, not in complex symbol constellations (Chang et al., 2013).
• At most a single RF chain or transmit chain is needed per transmission, independent of the number of spatial resources.
• Detection at the receiver is typically a discrete search for the maximally aligned spatial response (i.e., index detection).
• The number of spatial resources is a power of two to map bits bijectively.

2. System Architectures and Channel Models

Bit-driven spatial modulation schemes are realized in various hardware and propagation network topologies:

a) Classical SSK MIMO:

• Transmitter has $N_t$ antennas; exactly one is active per use.
• At each use, input bits select an antenna index $m$; the transmitted vector is $x = \mathbf{e}_m$ (the $m$th canonical basis vector).
• All RF power is focused on the selected antenna; others are silent.
• The receiver, with $N_r$ antennas, observes the signature response for each possible index.

b) RIS-Enabled and Dual-RIS Enabled SSK:

• Reconfigurable surfaces (RISs) act as passive (or semi-passive) routers.
• In a canonical dual-RIS—assisted SSK model (Bayar et al., 23 Nov 2025), a single-antenna Tx radiates to RIS$_1$, which statically reflects to RIS$_2$. Bits are mapped at the controller of RIS$_2$, which applies a data-driven phase profile to steer energy towards a designated receiver among $N_r$ candidates.
• The overall channel is a cascaded multi-hop path: $$\mathbf{h}_{\text{eff}}(m) = \mathbf{G} \, \mathbf{h}_m$$, where $\mathbf{G}$ models RIS$_1$–RIS$_2$ and $\mathbf{h}_m$ (row $m$ of $\mathbf{H}$) models RIS$_2$ to Rx $m$.

c) Bit-Driven Molecular SSK:

• Molecular communication analog: each input symbol's bits activate one nanomachine among $N$ for molecular emission; spatial decoding is at $N$ receivers (Huang et al., 2018).

d) Bit-Driven SSK with Dynamic RISs for Indoor Routing:

• RIS$_2$ at a branching point in an indoor network is configured in real time (driven by SSK mapping) to steer energy to specific zones or users (Bayar et al., 23 Nov 2025).

Channel models: Various fading conditions are analyzed—Rayleigh, Rician, shadowed Rician, and cascaded Rician for dual-RIS deployments—along with multi-hop pathloss effects. The spatial mapping at the controller leverages knowledge of the cascaded channel (or statistics), and bit-to-phase mapping is performed to maximize coherent combining at the target receiver.

3. Modulation, Phase Configuration, and Mapping

The core mapping step is bit-to-spatial-index association, which, in dual-RIS schemes, translates to a phase configuration map at the controlling RIS:

• Bit mapping: Input block $b_1,\dots,b_{\log_2N_r}$ is mapped to receive antenna index $m$.
• RIS phase design: For all $i=1,\dots,N$ (RIS elements), the reflecting phase is chosen according to

$$\phi_{2,i}^{\text{opt}}(m) = -\left(\psi_{k,i} + \theta_{i,m}\right)$$

where $\psi_{k,i}$ and $\theta_{i,m}$ are the phases of the channels from RIS$_1$ to RIS$_2$ and from RIS$_2$ to Rx antenna $m$, respectively (Bayar et al., 23 Nov 2025).

• Static phase at earlier RIS: RIS$_1$ is typically set statically, e.g., maximizing mean power in the RIS$_1$–RIS$_2$ link.
• No amplitude/phase modulation: The symbol $s$ transmitted by the source is a constant (e.g., $|s|^2=1$), with all data in the spatial mapping.
• Received signal: At Rx $m$, the signal is

$$y_m = \sqrt{E_s}\,\zeta\,\sum_{k=1}^N\sum_{i=1}^N \alpha_{k,i}\,\beta_{i,m} + n_m$$

where $\zeta$ aggregates path-loss terms, and the double sum aggregates the cascaded Rician or Rayleigh fading (Bayar et al., 23 Nov 2025).

Detection: The receiver implements a maximum-likelihood index detector: $\hat m = \arg\max_{p\in\{1,\dots,N_r\}} |y_p|^2$

4. Capacity and Error Rate Performance

Ergodic capacity and outage analysis rely on the statistical properties of the cascaded channel. For large numbers of RIS elements, the sum

$$Z = \sum_{k=1}^N \sum_{i=1}^N \alpha_{k,i}\,\beta_{i,m}$$

is approximately Gaussian via the central limit theorem. The received instantaneous SNR is

$\gamma_m = \frac{\zeta^2 E_s\,|Z|^2}{N_0}$

whose distribution is noncentral $\chi^2_1$ with parameters set by the means and variances of $\alpha_{k,i}, \beta_{i,m}$ (Bayar et al., 23 Nov 2025).

Outage probability at threshold $\gamma_{\rm out}$: $$P_{\rm out} = F_{\gamma_m}(\gamma_{\rm out}) = 1 - Q_1\left(\frac{\mu_Z}{\sigma_Z},\,\sqrt{\frac{\gamma_{\rm out}}{\zeta^2 E_s \sigma_Z^2/N_0}}\right)$$ where $Q_1$ denotes the first-order Marcum-$Q$ function.

Ergodic capacity: For large $N$ (channel hardening),

$$C_{\rm avg} \approx \log_2\left(1 + \frac{\zeta^2 E_s\,\mu_Z^2}{N_0}\right)$$

which highlights the key scaling: capacity increases with the squared mean of the effective composite channel (which itself grows as $N^2$ if both RISs are large) and decreases with compounded path-loss and thermal noise (Bayar et al., 23 Nov 2025).

Error performance: Bit-error rate is governed by the minimal distance among effective spatial signatures and is optimized by coherent RIS phase configuration. Analytical and simulation studies confirm that increasing $N$ or optimizing RIS placement/phase yields substantial gains in both capacity and error rates.

Engineering trade-off: While adding RIS stages can introduce additional path loss (as observed by higher outage in some dual-RIS vs. single-RIS scenarios for equivalent $N$), dual-RIS architectures uniquely support bit-driven dynamic routing and flexible indoor coverage (Bayar et al., 23 Nov 2025).

5. Implementation and Complexity

Bit-driven spatial modulation, including dual-RIS SSK, achieves notable hardware efficiency:

• Minimal RF hardware: Only one active hardware chain for a large number of spatial resources—even in dual-RIS systems, since the RISs are passive.
• RIS controller complexity: Bit-to-index map is a standard LUT; required phase calculation for each symbol is $O(N)$.
• Detection: The receiver performs a search over $N_r$ outputs, each involving a scalar energy computation.
• No high-order DAC or PA requirements: All amplitude/phase information is in the macro spatial structure. This lowers the precision requirements on RF hardware.

Key practical insights:

• Capacity and reliability grow rapidly as the size of either RIS grows, provided joint optimization is performed (or suboptimally, if phase quantization is coarse but sufficient) (Zhu et al., 1 Nov 2024).
• System performance degrades gracefully if per-element RIS phase precision is reduced; 2–3 bits of phase control suffices for nearly continuous performance (Zhu et al., 1 Nov 2024).
• System robustness to hardware impairments and distortion noise has also been quantified, showing error floors only emerge at very high SNR and for sizable system impairments (Basu et al., 7 Nov 2024).

6. Applications and Extensions

Bit-driven spatial modulation with RIS-driven routing finds application in:

• Indoor wireless signal routing: Dynamically steerable multi-zone coverage with minimal active RF resources (Bayar et al., 23 Nov 2025).
• Molecular or optical SSK analogs: Similar bit-to-spatial mapping in nanonetworks or optical arrays (Huang et al., 2018).
• Satellite and LEO multi-beam coverage: Beam steering in LEO satellites for ISAC functions, where SSK also provides link-layer robustness and hardware simplicity (Ngoufo et al., 17 Jul 2025).
• Low-complexity MIMO front-ends: Ubiquitous in IoT, green communications, and environments requiring strict power/complexity constraints (Chang et al., 2013).

Generalizations: The concept extends naturally to multi-branch activation (GSSK, HSSK), joint SSK-RPM (reflection phase modulation) for additional spectral efficiency, and multi-hop or mesh networks deploying multiple RIS planes.

7. Design Trade-offs and Future Directions

Bit-driven spatial modulation is subject to several engineering trade-offs:

• Spectral efficiency vs. spatial aperture: SSK (pure index) spectral efficiency increases logarithmically with the number of spatial branches; further efficiency necessitates either larger arrays/RISs or hybrid schemes.
• Path-loss aggregation: Multi-hop via several passive RISs can amplify path loss if not properly compensated by array gain or placement.
• Reconfiguration latency: Changing RIS$_2$ states must meet symbol-clock constraints; controller design is thus critical for high-data-rate deployments.
• Error floor management: Hardware impairments, channel estimation errors, and finite quantization in RIS phases impose error floors at high SNR; these can be mitigated via architecture scaling (e.g., increasing $N$), error-correcting code integration, or optimal phase design.
• Complexity scalability: While index detection complexity is modest, joint spatial–phase search (for extensions with reflection phase modulation or dual-role SSK+PSK RISs) grows linearly or polynomially with system size.

Promising research vectors include:

• Analytic optimization of joint RIS configurations over cascaded channels
• Ultra-low-overhead channel estimation and implicit feedback for bit-driven RIS control
• Integrated design of SSK mapping with beam allocation in multi-user and multi-zone environments
• Hardware-efficient implementation and bit-to-phase LUT compression for large $N$

Bit-driven spatial modulation, especially in RIS-enabled and multi-hop settings, presents a unified paradigm for energy-efficient, scalable, and flexible wireless signal routing, with rigorous analytical grounding of its capacity and error-rate behavior under practical impairments and network topologies (Bayar et al., 23 Nov 2025).