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Practical Implementation of Spatial Modulation
N. Serafimovski, A. Younis, R. Mesleh, P. Chambers, M. Di Renzo, C. X. Wang, P. M. Grant, M. A. Beach, H. Haas
TL;DR
The paper addresses the need to characterise practical SM and SMX performance, including effects from real transmission hardware. It builds an NI-PXIe testbed with digital encoding and decoding, then compares experimental ABER with analytical and simulation results under LoS conditions. The study reports validated agreement among these approaches and identifies hardware power imbalances as relevant to observed performance.
Problem
The paper asks how SM and SMX perform in a practical experimental testbed, including the effects of wireless channels and transmitter and receiver RF-chain power imbalances.
Method
The authors implement NI-PXIe transmitter and receiver hardware with DSP encoding and decoding, then evaluate SM and SMX using experimental, simulation, and analytical approaches.
Results
Experimental ABER results for SM and SMX agree closely with simulations incorporating power imbalances and with analytical upper bounds at low ABER.
Takeaways & Limitations
SM is presented as a simple, low-cost practical MIMO approach requiring one RF chain while achieving enhanced performance in a LoS wireless channel.
Abstract
from arXiv · showhide
In this work we seek to characterise the performance of spatial modulation (SM) and spatial multiplexing (SMX) with an experimental test bed. Two National Instruments (NI)-PXIe devices are used for the system testing, one for the transmitter and one for the receiver. The digital signal processing that formats the information data in preparation of transmission is described along with the digital signal processing that recovers the information data. In addition, the hardware limitations of the system are also analysed. The average bit error ratio (ABER) of the system is validated through both theoretical analysis and simulation results for SM and SMX under line of sight (LoS) channel conditions.
I. INTRODUCTION
This work examines spatial modulation (SM) in a practical testbed, comparing its average bit error ratio (ABER) with spatial multiplexing (SMX) while analysing transmission-chain effects and hardware constraints.
- SM motivation: SM activates one antenna per symbol and encodes information through both the active antenna index and transmitted constellation symbol.The spatial and signal components are jointly represented in the modulation scheme.
- SM motivation: SM can reduce hardware complexity and energy consumption because only one RF chain is needed at each transmission instance.The stated energy reduction scales linearly with the number of transmit antennas.
- Study scope: The paper analyses SM ABER in a practical testbed and compares it with SMX using NI-PXIe-1075 hardware and associated transmission-chain processing.The study examines RF chains, the wireless channel, power imbalances, and software processing.
- Study scope: The work derives an analytical upper bound for SM over NLoS channels with power imbalance and compares it with experimental and simulation results.The paper reports that the experimental results validate the analytical bound and simulations.
II. TESTBED SET–UP AND SYSTEM MODEL
The testbed combines NI-PXIe transmitter and receiver hardware with transmitter- and receiver-side digital signal processing to send and recover binary data.
- System architecture: The experiment separates the transmission chain into PXIe hardware and DSP-Tx/DSP-Rx software at the transmitter and receiver.DSP-Tx prepares binary files for transmission, while DSP-Rx processes received data to recover the original stream.
- Antenna configuration: The system uses two transmit antennas and two receive antennas, with vertically polarised dipole elements having 7 dBi peak azimuth gain.The antennas have an omnidirectional radiation pattern in the azimuth plane.
- Transmitter hardware: The transmitter includes an I/Q signal generator, an RF signal generator, and an IF-to-carrier RF up-converter.The PXIe-Tx operates from 85 MHz to 6.6 GHz, supports 100 MHz bandwidth, and reaches 5 dBm maximum transmission power.
- Transmitter hardware: The transmitter maps signed 16-bit transmission-vector values linearly to output voltage amplitude before producing a 2.3 GHz analogue waveform.The signal generator output is passed through the RF signal generator and up-converter.
2) Receiver hardware (PXIe–Rx):
The receiver uses dedicated RF chains, down-conversion, digitisation, filtering, clock synchronisation, and maximum-likelihood processing to recover SM and SMX signals.
- Receiver chain: Each receive antenna has a complete RF chain consisting of down-conversion followed by dedicated 16-bit digitisation.The receiver records the signals from the antenna paths simultaneously.
- Filtering and sampling: The receiver samples at 10 Ms/s and applies a real flat bandwidth of B_f = 0.4 × f_s = 4 MHz.The bandwidth may produce frequency-selective fading, but equalisation is not required in this setup.
- Detection: Maximum-likelihood detection jointly decodes the spatial and signal symbols for both SM and SMX.The experimental setup has no multi-tap delays because the transmit and receive antennas are very close.
- Receiver chain: The receiver digitiser synchronises with the RF generator reference clock before writing the received binary files for DSP-Rx processing.The hardware and software processing are presented as a step-by-step encoder-decoder chain.
B. Testbed Software
The testbed software uses DSP–Tx to frame and modulate binary data for SM or SMX, then DSP–Rx synchronises, estimates channel and SNR, and recovers the data for ABER evaluation.
- DSP–Tx: DSP–Tx splits incoming binary information into 100-symbol frames and modulates each frame using SM or SMX.
- SM modulation: SM maps log2(Nt M) bits into a transmit antenna index and an M-QAM symbol, activating one antenna while the others remain silent.This transmit-vector structure avoids ICI and supports single-stream ML decoding with one active RF chain.
- SMX modulation: SMX divides the bit stream into blocks of Nt log2(M) bits and transmits symbols simultaneously from the Nt transmit antennas.
- Frame construction: Pilot sequences, zero padding, frequency-offset sequences, and synchronization pulses are inserted to support channel estimation, inter-frame separation, frequency correction, and peak detection.Each pilot sequence has length NΘ = 10, while 50 zero-valued symbols are added at both frame ends; synchronization uses maximum-power pulses separated by zero-valued symbols.
- Performance evaluation: Recovered binary data and estimated SNR are used to obtain ABER performance for both SM and SMX.
C. Propagation Environment (Channel)
The experiment uses a short-distance, direct-LoS two-by-two antenna arrangement at 2.3 GHz, producing channels modeled as Rician fading with distinct measured statistics.
- Channel characterization: Wireless-channel mean values range from 1.3 mV to 3.6 mV.
- Channel characterization: Channel measurements are collected using 105 pulse samples at 10 Ms/s and 2.3 GHz, then fitted with maximum-likelihood approximations and checked for a Rician distribution.
- Channel characterization: The four fast-fading channel coefficients are modeled by Rician distributions with unique K-factors and distinct means.
III. EQUIPMENT CONSTRAINTS
The testbed measurements account for physical hardware and channel-imbalance effects rather than assuming identical links. These effects are characterized through calibrated attenuation coefficients and swapped RF-chain configurations.
- Hardware imperfections include connector losses, RF-chain differences, phase responses, and attenuations across the transmission path.
- The experiment uses 2.3 GHz transmission with 10 dB attenuation on each transmit–receive RF coaxial link.
- Channel CDFs are measured for each transmit–receive antenna pair to characterize unequal fading-coefficient distributions.
- The channel model incorporates a pair-specific attenuation coefficient α(r,nt) for each receive- and transmit-antenna pair.The coefficient represents attenuation from receive antenna r to transmit antenna nt.
- Swapping receiver RF chains between configurations tests whether channel-attenuation discrepancies originate in the NI modules or chassis.
- Measured attenuation coefficients differ between configurations, with values ranging from 0 dB to 1.1 dB in one configuration and up to 1.17 dB in the other.
IV. ANALYTICAL MODELING
The analytical model derives ABER expressions for SM and SMX in the experimental system under noise-limited, strong-LoS conditions. It models each link with Rician fading and incorporates measured hardware power imbalances.
- The ABER model characterizes SM and SMX over a single link in a noise-limited scenario.
- ABER averages the bit errors between transmitted and decided vectors over channel realizations and conditional pairwise error probabilities.
- The strong LoS experimental channel is modeled using Rician fading for each transmit–receive antenna pair.
- The model redefines fast-fading coefficients using measured power-imbalance attenuation factors to account for hardware imperfections.
- The derived analytical bound is validated against experimental and simulation results.
V. COMPLEXITY ANALYSIS
The complexity analysis compares maximum-likelihood receivers for SM and SMX using real multiplicative operations. SM receiver complexity is independent of transmit-antenna count, producing larger relative savings as antenna count increases.
- Receiver complexity is measured by counting real multiplicative operations required by the ML detection algorithms.
- The SMX–ML detector complexity increases linearly with the number of transmit antennas.
- SM–ML complexity does not depend on transmit-antenna count and equals the complexity of SIMO systems.
- For Nt = 4, SM provides a 60% reduction in receiver complexity relative to SMX.
- For Nt = 128, SM provides a 98% reduction in receiver complexity relative to SMX.
A. Measurement Campaign
The measurement campaign transmits 10^5 information bits using two transmit antennas and BPSK over a 4 MHz real flat bandwidth, with repeated frame-level channel estimation.
- 10^5 information bits are transmitted in 50 frames of 2000 bits each.
- The campaign uses two transmit antennas, BPSK, and a 4 MHz real flat bandwidth.
- The channel is estimated at the beginning and end of every frame, producing 100 channel estimations per transmission vector.
B. Results
The testbed results validate analytical and simulation models for SM and SMX under LoS conditions, while showing how channel separability and hardware power imbalances affect ABER. SM achieves substantial coding gains over SMX with many transmit antennas, although large-array experimental validation remains unavailable.
- SM in LoS: Experimental SM results approximate simulations with power imbalances and closely follow the derived upper bound at low ABER in LoS channels.The comparison uses 2 transmit antennas, 2 receive antennas, and 2 bits/s/Hz.
- SM in LoS: Similar channels degrade SM ABER because they reduce the separability of spatial constellation points.SM performs best when channels are unique, such as in rich scattering environments.
- SM in LoS: Power imbalances increase the Euclidean distance between channel signatures, reducing the spatial-error contribution when channel estimation is nearly perfect.At sufficiently high SNR, the remaining bound is associated with the signal component under the stated detection discussion.
- SMX in LoS: Approximately 3 dB coding gain favors SMX over SM at an ABER of 10^-4 in the reported 2-antenna LoS comparison.The same gain is also observed at an ABER of 10^-3 without power imbalances.
- Large-array comparison: SM with Nt = 64 offers coding gains of up to 4 dB over SMX with Nt = 8 and 6 dB over SMX with Nt = 4.These results use Rayleigh fading, 8 bits/s/Hz, and four receive antennas; SM requires one RF chain but 64 unique channels.
- Scope and conclusion: The study concludes that practical hardware tolerances benefit ABER for both schemes, while limited RF chains prevent experimental validation with larger antenna arrays.The larger-array empirical results are left for future research.
VII. SUMMARY AND CONCLUSION
The work experimentally validates SM and SMX in a practical LoS testbed, finding that hardware-induced power imbalances help explain observed performance. SM shows promising practical performance with low complexity and power consumption, while broader validation remains needed.
- SM and SMX ABER performance was experimentally validated in a practical testbed and compared with simulation and analytical approaches.The study reports first-time experimental validation under the tested conditions.
- Rician channels with different attenuations closely described the physical behavior of SM and SMX.The attenuation differences were attributed to hardware imperfections in the transmitter and receiver RF chains.
- Power imbalances produced significant coding gains relative to theoretical predictions that omitted those imbalances.Introducing the imbalances into the analytical model brought SM and SMX into agreement with theoretical expectations.
- Validation remains incomplete for larger antenna configurations, channel imperfections, interference, capacity, energy efficiency, and DSP or FPGA deployment.The authors identify these areas as extensions needed to broaden the work’s applicability.
- SM demonstrated excellent performance in a LoS wireless channel as a simple, low-cost MIMO technique.The paper presents SM as a practical approach to enhanced spatial-multiplexing performance without high processor complexity or power consumption.