PaperlayerView exact revision on arXiv

Source-linked AI summary

Noncoherent MIMO in the FR3 Upper Mid-Band Using Grassmannian Signaling: Prototype and Experimental Evaluation

Álvaro Pendás-Recondo, Enrique Pendás-Recondo, Álvaro F. Vaquero, Marcos R. Pino, Jesús Alberto López-Fernández

arXiv:2610.08056v1eess.SPmath.DG

TL;DR

Pilot-based channel-state acquisition trades spectral efficiency against estimation accuracy, motivating communication without transmitter or receiver CSI. This paper prototypes 15 GHz Grassmannian MIMO with OFDM and reports close agreement between measured and simulated SER, validating its block-fading operation.

  • Problem

    Pilot-based CSI acquisition trades estimation accuracy against spectral efficiency, and acquiring transmitter CSI is especially challenging.

    Source: §I · p. 1

  • Method

    The paper combines Grassmannian signaling and OFDM in a 15 GHz noncoherent MIMO prototype, using a receiver decoder that does not require channel knowledge.

    Source: C. Contributions · p. 3, B. Narrowband Channel Model · p. 4

  • Results

    Measured NLoS SER agrees well with Monte Carlo simulations, validating the prototype under block-fading conditions.

    Source: A. NLoS Measurements · p. 11

  • Takeaways & Limitations

    The design targets LoS and NLoS operation across urban, rural, and vehicular scenarios, while Grassmannian signaling avoids phase-coherence requirements across RF chains.

    Source: §VI · p. 12

Abstract

from arXiv · show

This work presents a prototype implementation of a noncoherent multiple-input multiple-output (MIMO) system based on Grassmannian signalling, where neither the transmitter nor receiver requires channel state information (CSI), operating at a carrier frequency of 15 GHz in the frequency range 3 (FR3) upper mid-band envisioned for 6G. To the best of our knowledge, this is the first prototype implementation of Grassmannian signaling reported in the literature beyond sub-6 GHz bands. We identify the motivation of applying Grassmannian signaling, a form of unitary space-time modulation (USTM), in this band for wireless and mobile applications with low spectral-efficiency requirements but strict reliability and power-efficiency demands. With this idea in mind, we present a system design integrated with orthogonal frequency-division multiplexing (OFDM) that addresses the challenges associated with the higher carrier frequencies of FR3 while providing reliable operation across a broad range of scenarios, including urban and rural environments as well as vehicular communications. We then present the prototype implementation of the proposed design, based on software-defined radio (SDR) devices integrated with radio-frequency (RF) mixers, filters, and power amplifiers to ensure adequate operation in the targeted band. Over-the-air (OTA) experiments based on symbol error rate (SER) measurements under non-line-of-sight (NLoS) and line-of-sight (LoS) scenarios, and across different data rates, show good agreement with software simulations, thereby validating the prototype implementation.

I. INTRODUCTION

CSI acquisition becomes harder as antenna counts and operating frequencies rise, while pilot-based methods trade spectral efficiency for estimation accuracy. The introduction motivates Grassmannian signaling for CSI-free communication and describes its potential in FR3 and the limited prototype work preceding this study.

I. INTRODUCTION

  • Pilot-based CSIR trades estimation accuracy against spectral efficiency, while CSIT acquisition is more challenging, particularly as antenna counts and operating frequencies increase,.Pilot periodicity and frequency distribution, feedback limits and delays, and channel aging affect CSI acquisition.Source: §I · p. 1
  • Grassmannian signaling suits short coherence blocks and burst transmissions where CSI acquisition is costly or unreliable.It uses USTM codewords as Stiefel representatives of Grassmannian points and assumes the channel remains constant over a coherence block.Source: §I · pp. 1–2

A. Grassmannian and USTM Prototype Implementations

  • Earlier experimental prototypes were few, and prior MIMO-OFDM implementations operated below 6 GHz; this work reports the first Grassmannian or USTM prototype beyond 6 GHz.The cited prototype survey distinguishes earlier single-carrier and MIMO-OFDM implementations.Source: A. Grassmannian and USTM Prototype… · p. 2

B. Motivation: Noncoherent MIMO in the FR3 Upper Mid-Band

  • FR3 may suit small-antenna MIMO under rapidly varying conditions, including UAV control and V2V/V2X links without guaranteed LoS, though the proposed constellations operate at 0.25–1 bps/Hz.Grassmannian signaling removes phase-coherence constraints between RF chains; in strong-LoS scenarios, channel tracking with limited pilots can favor conventional pilot-based schemes.Source: B. Motivation: Noncoherent MIMO in the… · pp. 2–3

C. Contributions

The paper presents a 15 GHz Grassmannian-signaling MIMO prototype integrated with OFDM and evaluates it over the air. Measured SER agrees closely with software simulations across propagation scenarios and constellation sizes, validating the implementation.

C. Contributions

  • The prototype combines Grassmannian signaling with OFDM at 15 GHz, which the authors describe as the first such implementation beyond sub-6 GHz.The system is designed for noncoherent MIMO operation.Source: C. Contributions · p. 3
  • The design targets both LoS and NLoS, a 955 ns RMS delay spread, and Doppler shifts up to 35 m/s at transmitter and receiver.The delay-spread target corresponds to the 3GPP UMa scenario at 15 GHz; design choices are detailed to support adaptation.Source: C. Contributions · p. 3
  • SDR devices with digital synchronization and decoding blocks are integrated with RF mixers, power amplifiers, and filters for FR3 operation.The prototype is limited in part by hardware to 5 MHz bandwidth and two transmit and two receive antennas; larger matrix dimensions may make ML-decoding complexity limiting.Source: C. Contributions · p. 3
  • Measured SER agrees closely with software simulations across propagation scenarios and constellation sizes, validating the prototype implementation.The OTA evaluation includes NLoS Rayleigh block-fading and LoS strong-dominant-path scenarios.Source: C. Contributions · p. 3

II. SYSTEM MODEL

The system model introduces Grassmannian signaling through subspaces represented by orthonormal-basis matrices. It explains how the received signal can retain the transmitted subspace despite an unknown channel.

A. Grassmannian Signaling Preliminaries

  • The complex Grassmannian is the set of M-dimensional complex subspaces of C^T, represented by orthonormal-basis matrices in the complex Stiefel manifold.Different Stiefel matrices can represent the same subspace when related by a unitary right multiplication.Source: A. Grassmannian Signaling Preliminaries · p. 4
  • The orthogonal projector onto a subspace uniquely characterizes it and is independent of the chosen Stiefel representative.For a representative U, the projector is formed as U Uᴴ.Source: A. Grassmannian Signaling Preliminaries · p. 4
  • With an unknown channel, the noiseless received signal remains in the subspace associated with the transmitted Grassmannian point.Each received column is a linear combination of columns of the transmitted matrix.Source: A. Grassmannian Signaling Preliminaries · p. 4

B. Narrowband Channel Model

The narrowband model assumes an unknown channel that stays constant over a coherence block and transmits unitary space-time matrices. Detection uses the received subspace without channel knowledge, with maximum-likelihood status under isotropic channel fading.

B. Narrowband Channel Model

  • The channel is unknown to both ends but remains constant over a coherence block, and each transmitted T×M matrix has orthonormal columns.The model requires T_ch ≥ 2M and uses blocks of T ≤ T_ch symbols.Source: B. Narrowband Channel Model · p. 4
  • The constellation contains L codewords, with rate R = log2(L)/T bps/Hz and log2(L) information bits per block.The received signal is represented by a matrix Y over the time block.Source: B. Narrowband Channel Model · p. 4
  • The additive white Gaussian noise matrix W has i.i.d. entries distributed as CN(0, 1), and ρ denotes the signal-to-noise ratio (SNR).Source: B. Narrowband Channel Model · p. 4
  • The receiver detects without H by choosing a transmitted subspace; this decoder is ML for isotropically distributed channels and performs well in both LoS and NLoS scenarios.The decoder need not exploit favored spatial directions, which would require at least statistical CSI.Source: B. Narrowband Channel Model · p. 4

C. Broadband Channel Model

The design integrates a narrowband noncoherent system with OFDM to handle broadband channels, carrying parallel noncoherent links on separate subcarriers while requiring each channel to remain approximately constant across a codeword.

C. Broadband Channel Model

  • OFDM uses cyclic-prefix insertion to mitigate multipath-caused inter-symbol and inter-carrier interference while maintaining an approximately flat response within each subcarrier.Source: C. Broadband Channel Model · p. 4
  • Each of K subcarriers carries a parallel noncoherent communication, with T complete OFDM symbols needed before independently decoding its constellation symbol.Source: C. Broadband Channel Model · p. 4
  • The channel must remain quasi-constant over T complete OFDM symbols, including the cyclic-prefix duration.Source: C. Broadband Channel Model · pp. 4–5

D. Discrete and Continuous Time-Frequency Parameters

III. SYSTEM DESIGN

  • The design choices are presented as a flexible case study whose parameters can be adapted to the application.Source: §III · p. 5

A. Input Parameters

The design targets terrestrial use at 15 GHz across diverse channel and mobility conditions. Its parameter choices address multipath, Doppler, and phase-shift effects while keeping the prototype scalable within practical limits.

A. Input Parameters

  • Two transmit and two receive antennas suffice to validate operation, while adding antennas requires common frequency and clock references and may make ML decoding prohibitive.For arbitrary Grassmannian constellations, decoder complexity is O(TMNL).Source: A. Input Parameters · p. 5
  • At 15 GHz, noncoherent MIMO is framed as practically applicable to terrestrial scenarios, unlike higher-frequency cases that tend to rely on LoS conditions.At 25 GHz and 100 GHz, channel correlation can simplify CSI acquisition, but those advantages arise from restricting operation to LoS.Source: A. Input Parameters · p. 5
  • The design covers urban and rural terrestrial conditions, LoS and NLoS channels, a 955 ns RMS delay spread, and speeds up to 35 m/s.Source: A. Input Parameters · p. 5

B. Explicit Choices for System Parameters

  • With K = 64 and Kcp = 20, the design uses Δf = 78.125 kHz and tcp = 4 μs, keeping the cyclic prefix above 4τrms and spacing above the 70 kHz Doppler rule of thumb.Source: B. Explicit Choices for System… · pp. 5–6
  • The block length is T = 4, the minimum for this Grassmannian design, balancing decoding complexity and the quasi-static channel requirement.The resulting block duration is 67.2 μs; the channel is assumed approximately constant over that interval.Source: B. Explicit Choices for System… · p. 6
  • For L = 4, a phase shift of 20° degrades SER by only about 2.5 dB; for L = 16, shifts up to 10° are well tolerated.The latter corresponds to an uncorrected frequency shift of 1.6531 kHz in this scenario.Source: B. Explicit Choices for System… · p. 6

C. NLoS vs LoS Conditions

The section evaluates noncoherent signaling under NLoS and LoS conditions, including phase shifts and Rician fading. Its analysis connects the LoS trend to the diversity strategy used by Grassmannian signaling.

C. NLoS vs LoS Conditions

  • Even under LoS, abrupt trajectories such as UAV links may require substantial pilot overhead to track phase changes.Source: C. NLoS vs LoS Conditions · p. 7
  • For T = 4, M = N = 2, and L = 16, simulated SER improves as the Rician K-factor increases and the LoS component becomes more dominant.Source: C. NLoS vs LoS Conditions · p. 7, Figure 2 · p. 7
  • Grassmannian signaling sends one data stream through different fading channels for diversity gain, so a deterministic LoS component provides a more stable link than Rayleigh fading.Source: C. NLoS vs LoS Conditions · p. 7
  • This LoS trend is opposite to spatial multiplexing, where a dominant path can collapse singular modes and make stream separation ill-conditioned.Source: C. NLoS vs LoS Conditions · p. 7

IV. PROTOTYPE IMPLEMENTATION

The prototype combines GNU Radio and USRP equipment with external RF components to operate at 15 GHz. Its OFDM packet design supports two constellation sizes and uses SER measurements derived from packet CRC fields.

A. General Aspects

  • The transmitter and receiver use GNU Radio with USRP X310 units, while external mixers, amplifiers, and waveguide filters extend operation to 15 GHz.Source: A. General Aspects · pp. 7–8
  • Four-centimeter antenna spacing, equal to 2λc, is chosen to enhance NLoS diversity while keeping the design compact.Source: A. General Aspects · p. 8
  • The 5 Msps, 64-subcarrier OFDM setup uses 56 active subcarriers and sends one synchronization symbol per 32 data symbols, with no pilot symbols.Source: A. General Aspects · p. 8
  • With L = 2 and L = 16 at T = 4, the data rates are 0.1616 and 0.6465 bps/Hz, respectively.Across 5 MHz, those rates correspond to 0.8081 and 3.2323 Mbps.Source: A. General Aspects · p. 8
  • SER is measured instead of BER because BER estimation from the CRC32 header is more complex and potentially less accurate, though SER upper-bounds BER.Source: A. General Aspects · p. 8
  • Only one antenna transmits power per subcarrier, reducing ML decoder complexity by a factor of M, although OFDM still requires M RF chains.The implementation can support other USTM or Grassmannian designs, with decoder complexity the main real-time OTA constraint.Source: A. General Aspects · p. 8

B. Time and Frequency Synchronization

The design uses one synchronization symbol per packet for timing and frequency correction without estimating the channel or transmitting pilots. Packets contain eight space-time matrices per active subcarrier, and the transmitter combines OFDM processing with an RF hardware chain for 15 GHz operation.

B. Time and Frequency Synchronization

  • One synchronization symbol enables frame detection, symbol-timing synchronization, and carrier-frequency-offset estimation and correction before each packet.The system sends 32 OFDM symbols, or eight space-time matrices per active subcarrier; a common time and frequency reference reduces hardware-induced frequency offset.Source: B. Time and Frequency Synchronization · p. 8, Figure 3 · p. 9
  • The receiver decodes without channel estimates or pilots, requiring each subcarrier’s channel to remain quasi-static only over a 67.2 µs block.Synchronization parameters need remain quasi-constant over the 554.4 µs packet; packet length can be adjusted in multiples of four OFDM symbols.Source: B. Time and Frequency Synchronization · p. 9

C. Transmitter

  • The transmitter maps encoded space-time matrices across 64 IFFT inputs, then upconverts to 15 GHz, filters, and amplifies the signal.The RF chain uses WR42 waveguide filters to suppress spectral images; average power per antenna is about −10 dBm.Source: C. Transmitter · p. 9

D. Receiver

The receiver synchronizes and OFDM-processes each antenna chain before decoding space-time matrices and checking a CRC32 header for SER estimation. NLoS measurements use transmitter-side digital channel distortion and artificial noise to reproduce Rayleigh block fading; measured and simulated SER agree well, with identified boundaries from hardware noise and large frequency shifts.

D. Receiver

  • The receiver synchronizes, applies OFDM processing per antenna chain, decodes space-time matrices, and checks CRC32 for SER estimation.Processing includes cyclic-prefix removal, FFT computation, and serialization before decoding.Source: D. Receiver · p. 10

A. NLoS Measurements

  • Rayleigh block fading is emulated by decoupling the antenna links and applying random channel distortion and artificial noise to transmitter samples before OTA transmission.The physical channel is made approximately diagonal using polarization discrimination and absorber foam; the added digital channel effects are therefore present in the radiated signal.Source: A. NLoS Measurements · p. 10
  • Measured and Monte Carlo simulated SER values for L = 2 and L = 16 agree well under block-fading conditions, validating the prototype.Around 20 dB SNR, measured SER is slightly higher than simulated SER because hardware noise becomes non-negligible relative to added artificial noise.Source: A. NLoS Measurements · p. 11
  • A 50 kHz frequency shift causes severe intercarrier interference and strong performance degradation because one synchronization symbol cannot correct it.Shifts up to 3.5 kHz are corrected by frequency synchronization without affecting measured SER; the design also accounts for delay spread up to τrms = 955 ns.Source: A. NLoS Measurements · p. 11

B. LoS Measurements

In the LoS setup, the measured channel phase varies across the 5 MHz bandwidth, supporting the use of OFDM rather than a single channel coefficient. Measured and simulated SER agree for both tested constellation sizes, with a slight high-SNR deviation for L = 16.

B. LoS Measurements

  • The LoS setup places the transmit and receive antenna pairs 20 cm apart in the same plane, with 2λc = 4 cm antenna spacing.A strong dominant path is present; multipath effects are expected to be negligible at 15 GHz over this short separation.Source: B. LoS Measurements · p. 11
  • Measured and simulated SER show good agreement for L = 2 and L = 16 in the LoS scenario.For L = 16, a deviation of about 1 dB appears as SNR increases, at lower SNR than the deviation observed in the NLoS measurements.Source: B. LoS Measurements · p. 11, Figure 9 · p. 12
  • The measured S21 phase varies by up to 8° across the 5 MHz bandwidth, which would make a single channel coefficient inaccurate without OFDM.The reported measurement is between the left transmit and left receive antennas.Source: B. LoS Measurements · p. 11, Figure 8 · p. 12

VI. CONCLUSION

The paper demonstrates a Grassmannian noncoherent MIMO prototype at 15 GHz, a band beyond the reported range of earlier Grassmannian or USTM prototypes. OTA SER measurements across LoS and NLoS conditions agree with simulations; the authors identify higher-rate detection complexity and operation above 15 GHz as open boundaries.

VI. CONCLUSION

  • The prototype operates at 15 GHz and is, to the authors’ knowledge, the first Grassmannian or USTM prototype reported beyond 6 GHz.The design targets LoS and NLoS operation without CSI, including conditions associated with urban delay spreads and rural velocities.Source: §VI · p. 12
  • OTA SER measurements under LoS and NLoS conditions and across constellation sizes show good agreement with software simulations.The authors regard this agreement as validation of the prototype implementation.Source: §VI · p. 12
  • At increasing data rates, maximum-likelihood detection can become prohibitively complex; reduced-complexity USTM decoders trade some SER performance.The potential use of these or similar noncoherent schemes above the paper’s 15 GHz working assumptions remains an open question.Source: §VI · p. 12
Loading 2610.08056v1…