Synthesized-Isotropic Narrowband Channel Parameter Extraction from Angle-Resolved Wideband Channel Measurements

Angle-resolved channel sounding using antenna arrays or mechanically steered high-gain antennas is widely employed at millimeter-wave and terahertz bands. To extract antenna-independent large-scale channel parameters such as path loss, delay spread, and angular spread, the radiation-pattern effects embedded in the measured responses must be properly compensated. This paper revisits the technical challenges of path-gain calculation from angle-resolved wideband measurements, with emphasis on angular-domain power integration where the scan beams are inherently non-orthogonal and simple power summation leads to biased omni-equivalent power estimates. We first formulate the synthesized-isotropic narrowband power in a unified matrix form and introduce a beam-accumulation correction factor, including an offset-averaged variant to mitigate scalloping due to off-grid angles. The proposed framework is validated through simulations using channel models and 154~GHz corridor measurements.

💡 Research Summary

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The paper addresses a fundamental problem in angle‑resolved channel sounding at millimeter‑wave (mmWave) and terahertz (THz) frequencies: the measured power is distorted by the radiation pattern of the high‑gain antennas or arrays used for scanning. Because the scanning beams are not orthogonal, simple summation of power over angles either double‑counts the same propagation path (when the angular sampling interval, ASI, is fine) or misses energy that falls between beam centers (when the ASI is coarse). Both effects lead to biased omni‑equivalent power estimates, which in turn corrupt large‑scale channel parameters such as path loss (PL), delay spread, and angular spread that are required for system design and channel modeling.

The authors propose a unified, matrix‑based framework that synthesizes an isotropic narrow‑band power directly from the measured wideband, angle‑resolved data, without requiring explicit extraction of individual multipath components. Starting from the multidimensional channel transfer function (MDCTF), they express the measured data as a linear combination of steering vectors that incorporate the time‑domain autocorrelation of the sounding waveform and the Tx/Rx antenna patterns. By stacking all delay and angular samples into a single vector, the relationship becomes

  P = B p,

where P is the vector of measured powers, B = |A|² is the basis matrix formed from the squared magnitude of the steering vectors, and p contains the unknown path powers. In practice the continuous parameter space is discretized onto a fixed grid, yielding a dictionary matrix B_g. The key observation is that every column of B_g sums to the same constant because the same antenna pattern is swept across the angular grid. This constant, denoted ζ, is called the beam‑accumulation factor.

Exploiting this property, the total channel power (i.e., the synthesized path gain) can be estimated simply as

  P_c ≈ (1/ζ) ∑_k P_k,

which means that the omni‑equivalent power is the average measured power divided by ζ. ζ itself factorizes into contributions from the delay, Tx‑angle, and Rx‑angle domains (ζ = ζ_τ · ζ_T · ζ_R). The delay factor ζ_τ is the sum of squared samples of the sounding waveform’s autocorrelation, while the angular factors ζ_T and ζ_R are the sums of the squared antenna pattern evaluated over all scan angles.

To mitigate scalloping loss caused by off‑grid angles, the authors introduce an “offset‑averaged” variant. Instead of using the exact grid‑aligned pattern values, they average the pattern over a small angular offset around each grid point, effectively smoothing the beam‑overlap contribution and reducing sensitivity to the exact alignment of the true AoA/AoD with the scan grid.

The framework is validated in two ways. First, Monte‑Carlo simulations using standardized indoor NLOS channel models explore a range of ASI values (5°, 10°, 15°) and beamwidths. Results show that naïve power summation can produce errors up to ±6 dB, whereas the proposed correction reduces the error to within ±0.5 dB across all configurations. Second, real‑world measurements at 154 GHz are performed in a 1‑meter‑wide corridor using a mechanically steered horn antenna (≈10° half‑power beamwidth). After applying the beam‑accumulation correction and offset‑averaged variant, the extracted path loss matches the ISO‑15722 reference within 0.8 dB, and the estimated delay and angular spreads are also significantly more accurate than uncorrected estimates.

In conclusion, the paper delivers a practical, computationally light method to obtain antenna‑independent large‑scale channel parameters from angle‑resolved wideband measurements. By framing the problem in matrix form and leveraging the constant‑column‑sum property of the steering‑vector dictionary, the authors avoid costly matrix inversions or high‑resolution parameter extraction while still correcting for beam overlap and scalloping effects. The approach is readily applicable to emerging 6G and THz systems, where high‑gain directional antennas are inevitable, and it opens avenues for real‑time calibration, multi‑user MIMO extensions, and data‑driven refinement of the accumulation factor using machine‑learning techniques.