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A Novel Space-Time Coding Architecture for Rydberg Atomic Quantum Receiver-Based Systems
Asifa Zannat, Milad Abolpour, Dani Korpi, Mikko A. Uusitalo, Mikko Valkama, Ertugrul Basar
TL;DR
RAQR magnitude readout creates a nonlinear observation model that does not directly support conventional complex-valued MIMO processing. The paper addresses this with real orthogonal space-time coding and strong-reference heterodyne reception, deriving a real linear model with matched-filter symbol-wise detection. Analytical and simulation results show full transmit-receive diversity and improved performance over spatial-multiplexing benchmarks.
Problem
RAQR magnitude-based readout produces a nonlinear model incompatible with conventional complex-valued MIMO processing.
Method
The transmitter uses real orthogonal designs, while strong-reference heterodyne reception produces an equivalent real-valued linear model for matched-filter symbol-wise detection.
Results
The analytical BEP achieves diversity order NtNr, and simulations validate the analysis while showing improved BER performance over spatial-multiplexing-based benchmarks.
Takeaways & Limitations
Preserved orthogonality enables low-complexity independent symbol detection in point-to-point RAQR-assisted MIMO links.
Abstract
from arXiv · showhide
Rydberg atomic quantum receivers (RAQRs) offer high sensitivity and wide tunability, but their magnitude-based readout yields a nonlinear model incompatible with conventional complex-valued multi-input multi-output (MIMO) processing. We propose a low-complexity space-time coding framework for point-to-point RAQR-assisted MIMO links. Data symbols are encoded using real orthogonal designs, while strong-reference heterodyne reception yields an equivalent real-valued linear model. The preserved orthogonality enables matched filter symbol-wise detection without matrix inversion or vector search. An analytical bit error probability expression is derived, proving the proposed scheme achieves the full transmit-receive diversity. Simulations validate the analysis and demonstrate improved performance over spatial multiplexing benchmarks.
I. INTRODUCTION
RAQRs address sensitivity and frequency-coverage challenges in RF reception, but their observation model requires specialized processing. The paper proposes real-valued orthogonal space-time coding with heterodyne reception for low-complexity RAQR-assisted MIMO detection.
- Motivation: RAQRs use atom–light interactions to transduce incident electromagnetic fields into optical readouts.Their large dipole moments and rich energy-level structure motivate wireless communication and sensing applications.
- Related work: Prior RAQR studies considered atomic MIMO reception, spatial multiplexing, multi-user transmission, precoding, learning-based designs, and statistical detection.Phase-retrieval algorithms were proposed to recover transmitted signal vectors from RAQR-specific observations.
- Proposed approach: The proposed architecture encodes information using real orthogonal designs tailored to the RAQR real-valued observation model.It targets a point-to-point link between an Nt-antenna RF transmitter and an Nr-element RAQR.
- Proposed approach: Strong-reference heterodyne reception produces phase-sensitive measurements and an equivalent real-valued model that preserves codeword orthogonality.This allows received signals to be linearly combined for independent real-symbol detection.
- Results: The analytical BEP yields diversity order NtNr, while simulations report improved BER performance over spatial-multiplexing-based baselines.The receiver uses matched-filter-style linear processing without matrix inversion or vector search.
II. SYSTEM MODEL
The system models magnitude-dependent RAQR reception for an RF-to-RAQR MIMO link with a receiver-side reference. Under a strong-reference condition, first-order processing yields a real-valued linear model for subsequent coding and detection.
- System model: The considered link connects an Nt-antenna conventional RF transmitter to an RAQR with Nr vapor-cell receive elements.Each vapor-cell sensor converts the incident RF electric field into an optical readout.
- Reference signal: A receiver-side local oscillator supplies a constant reference vector b observed at the RAQR array.Its m-th entry depends on the reference polarization, channel gain, phase shift, transition dipole moment, and reduced Planck constant.
- Channel model: The effective channel is modeled over L propagation paths between each transmit antenna and receive vapor cell.The path coefficients are complex Gaussian, with polarization vectors and propagation-induced phase shifts; 1/√L normalizes average channel power.
- Linearization: When the reference dominates the signal-plus-noise magnitude, first-order approximation and reference-magnitude subtraction produce a real-valued observation with Gaussian noise.This real-valued linear model forms the basis for the OSTBC construction and detection framework.
A. Illustrative Example
For two transmit antennas, the paper constructs a four-channel-use codeword from four real information symbols mapped into the real and imaginary transmit dimensions. The resulting equivalent channel is orthogonal, enabling independent matched-filter detection.
- A. Illustrative Example: For Nt = 2, the real-equivalent model has four transmit dimensions corresponding to the real and imaginary parts of two complex signals.The codeword spans four consecutive channel uses and carries s1 through s4.
- A. Illustrative Example: The two-antenna codeword maps a real orthogonal design into the real and imaginary parts of a complex transmit block.Its rows correspond to transmit antennas and its columns to four channel uses.
- A. Illustrative Example: The receiver stacks the phase-compensated RAQR outputs and noise across the four channel uses into equivalent real vectors.The resulting equivalent channel matrix is built from the real and imaginary channel columns.
- A. Illustrative Example: G_eq^T G_eq = (1/4)||G||_F^2 I_4, so the four real information symbols decouple under matched-filter combining.Each symbol can therefore be detected independently.
B. OSTBC Construction
The general RAQR-OSTBC construction begins with a real orthogonal design over 2Nt transmit dimensions and maps it into a complex transmit matrix. Hurwitz–Radon constraints determine a suitable codeword length, while orthogonality enables linear symbol separation and energy normalization.
- B. OSTBC Construction: The codeword X ∈ C^(Nt×T) is constructed from a real design C ∈ R^(2Nt×T) whose rows represent real-equivalent transmit dimensions.The design carries T real symbols over T channel uses from an M-ary real constellation.
- B. OSTBC Construction: Real matrices A1 through A2Nt are selected with orthogonality constraints that produce C C^T = ||s||^2 I_(2Nt).These constraints allow real information symbols to be decoupled through linear processing.
- B. OSTBC Construction: The real design is split into C_R and C_I and then mapped to the complex OSTBC transmit matrix X.The construction separates the first Nt rows from the remaining Nt rows before recombination.
- B. OSTBC Construction: The normalization factor 1/√(2Nt) keeps average transmit energy per channel use from increasing with Nt.The resulting codewords support the subsequent RAQR detection process.
C. Detection Process
The received observations are stacked into a real-valued equivalent model whose orthogonal channel structure decouples the real information symbols. Matched filtering therefore enables independent nearest-neighbor detection without matrix inversion or vector search.
- Detection Process: Stacking all T channel-use observations and noise vectors yields the real-valued RAQR input-output relationship.The equivalent observation has dimension R^{N_rT}, while the equivalent channel maps the T real symbols.
- Detection Process: The equivalent channel matrix preserves orthogonality, with zero cross-correlations between distinct symbol dimensions.This orthogonality follows from the real orthogonal-design construction and the resulting equivalent channel structure.
- Detection Process: Matched filtering decouples the real information symbols after linear combining.Each combined output consists of the corresponding symbol plus a Gaussian noise term.
- Detection Process: Each real symbol is independently detected with a nearest-neighbor detector.The matched-filter output can alternatively feed a soft demapper for channel decoding.
III. PERFORMANCE ANALYSIS
The analysis derives the BEP from conditional symbol errors and the distribution of the effective channel gain. In the high-SNR regime, the BEP decays with an exponent equal to the full transmit-receive diversity order.
- PERFORMANCE ANALYSIS: The conditional SEP for an M-PAM constellation is averaged over the effective channel-gain distribution to obtain the SEP.The analysis uses Es = Eb log2(M), averages over Z, and applies Craig’s formula.
- PERFORMANCE ANALYSIS: Under rich scattering, the effective channel entries are modeled as i.i.d. complex Gaussian variables, making their squared magnitudes i.i.d. exponential variables.The common average channel power is obtained using the large-path approximation.
- PERFORMANCE ANALYSIS: The aggregate channel gain Z follows a Gamma distribution with shape parameter N_tN_r and scale parameter Ω_H.This distribution determines the averaging required for the analytical SEP.
- PERFORMANCE ANALYSIS: Gray-coded approximation gives BEP ≈ SEP/log2(M).The resulting expression is then examined in the high-SNR regime.
- PERFORMANCE ANALYSIS: At high SNR, BEP ≈ Cγ_b^-d, where d is the diversity order and equals N_tN_r.C is the coding gain, while the exponent establishes full transmit-receive diversity.
IV. NUMERICAL RESULTS
Numerical results validate the analytical BEP and real-valued RAQR-OSTBC model, while comparisons show how coding and diversity gains vary with spectral efficiency and SNR. The proposed scheme achieves full transmit-receive diversity with low-complexity symbol-wise detection, though it can sacrifice low-SNR coding gain.
- IV. NUMERICAL RESULTS: For N_r = 4 and η = 1 bpcu, analytical BEP and simulated BER closely match for N_t ∈ {1, 2, 3, 4}.The simulations use a multipath channel with 23 clusters and 20 paths per cluster at f_c = 5 GHz.
- IV. NUMERICAL RESULTS: Increasing N_t makes the BER curves steeper, confirming the transmit-diversity gain predicted by the analysis.This supports the analytical full-diversity behavior across the tested antenna configurations.
- IV. NUMERICAL RESULTS: At η = 1 bpcu, RAQR-OSTBC gains over SIMO because each real symbol experiences all N_tN_r transmit-receive links.The comparison includes SIMO, SMUX, and PRSS at equal spectral efficiency.
- IV. NUMERICAL RESULTS: At η = 2 bpcu, PRSS outperforms RAQR-OSTBC at low SNR, while RAQR-OSTBC has the steeper high-SNR BER decay.The low-SNR difference is attributed to higher-order real constellations and lower coding gain; the asymptotic slope retains full diversity.
- IV. NUMERICAL RESULTS: RAQR-OSTBC trades spectral efficiency for full transmit-receive diversity and low-complexity symbol-wise detection.SMUX and PRSS instead require joint vector processing, with PRSS also using a second channel use to reconstruct a complex-valued observation.
V. CONCLUSION
The paper proposes a low-complexity RAQR-assisted MIMO space-time coding framework using real orthogonal designs and strong-reference heterodyne reception. Its analytical and numerical results support full transmit-receive diversity and improved error performance over spatial-multiplexing benchmarks.
- V. CONCLUSION: Real information symbols are encoded into space-time codewords using real orthogonal designs to provide transmit diversity across multiple channel uses.The design is tailored to the real-valued RAQR observation model.
- V. CONCLUSION: A strong-reference heterodyne RAQR produces a real-valued linear observation model that supports matched-filter symbol-wise detection.This is the receiver-side basis of the proposed low-complexity framework.
- V. CONCLUSION: The analytical BEP shows full transmit-receive diversity, and simulations report improved error performance compared with spatial-multiplexing-based benchmarks.The conclusion identifies extensions to imperfect reference signals, neural receivers, multiuser transmission, and joint coding and precoding.