ILSA

System Analysis & Formulation

The ILSA stack is partitioned by core: Cortex-M4 handles RF capture and spectral primitives, while the Cortex-A7 manages feature synthesis, classification, and UI rendering.

Target Latency: < 50 ms•RAM Budget: < 30 kB•AoA Error: < 10°

A. Pre-Processing (Cortex-M4)

Baseband Capture
x[n]=I[n]+jQ[n]x[n] = I[n] + jQ[n]
DC Removal
x~[n]=x[n]−1N∑i=0N−1x[i]\tilde{x}[n] = x[n] - \frac{1}{N} \sum_{i=0}^{N-1} x[i]
Short-Time Fourier Transform
X(k,m)=∑nx[n+mH]w[n]e−j2πkn/NX(k,m) = \sum_{n} x[n+mH] w[n] e^{-j2\pi kn/N}
Cyclostationary Feature
Rxα(τ)=1T∑tx(t)x∗(t−τ)e−j2παtR_x^\alpha(\tau) = \frac{1}{T} \sum_{t} x(t) x^*(t-\tau) e^{-j2\pi\alpha t}

B. Feature Extraction (Cortex-A7)

Power Spectral Density (PSD)
Sxx(k)=1Nfs∣∑nx[n]w[n]e−j2πkn/N∣2S_{xx}(k) = \frac{1}{N f_s} \left| \sum_{n} x[n] w[n] e^{-j2\pi kn/N} \right|^2
Spectral Moments
μ1=∑kpk,μ2=∑(k−μ1)2pk\mu_1 = \sum k p_k, \quad \mu_2 = \sum (k-\mu_1)^2 p_k
Skewness & Kurtosis
Skew=∑(k−μ1)3pkμ23/2,Kurt=[1N∑(Sxx−μ)4σ4]−3\text{Skew} = \frac{\sum (k-\mu_1)^3 p_k}{\mu_2^{3/2}}, \quad \text{Kurt} = \left[ \frac{1}{N} \sum \frac{(S_{xx}-\mu)^4}{\sigma^4} \right] - 3
Spectral Entropy
H=−∑pklog⁡pkH = -\sum p_k \log p_k

C. Tiny ILSA Head (Classifier)

Input Vector
f=[PSDbands,μ1,μ2,skew,kurt,H,SFM,ρ,Lb]f = [PSD_{bands}, \mu_1, \mu_2, \text{skew}, \text{kurt}, H, SFM, \rho, L_b]
Cost Function (Softmax)
J(Θ)=−∑log⁡(exp⁡(θyTf)∑cexp⁡(θcTf))+λ∣∣Θ∣∣2J(\Theta) = -\sum \log \left( \frac{\exp(\theta_y^T f)}{\sum_c \exp(\theta_c^T f)} \right) + \lambda ||\Theta||^2
Standardization
f^=f−μfσf\hat{f} = \frac{f - \mu_f}{\sigma_f}

D. Angle of Arrival (Dual-Antenna)

Phase Difference
θ^=arcsin⁡(Δϕkλ2πd)\hat{\theta} = \arcsin \left( \frac{\Delta\phi_k \lambda}{2\pi d} \right)
SNR Weighting
wk=max⁡(0,∣X1(k)∣∣X2(k)∣−η)w_k = \max(0, |X_1(k)||X_2(k)| - \eta)
Optimization Objective
θ^=argmax∑wkcos⁡(Δϕk−2πdλsin⁡θ)\hat{\theta} = \text{argmax} \sum w_k \cos(\Delta\phi_k - \frac{2\pi d}{\lambda} \sin\theta)

System Architecture Visualization

ILSA System Architecture
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