[통산 250편 금자탑 🏆] 초·중·고 물리(파동·전자기학)·수학(선형대수) 교육과 국방 첨단 다기능 위상배열 레이더(AESA) 디지털 빔포밍(DBF): ZeliDesk의 온디바이스 순수 C# 송수신 모듈(TRM) 공간 위상 제어, 적응형 부엽 제거(Adaptive Nulling / LCMV), 0-Alloc AVX-512 SIMD 복소 빔가중치 합성, 120fps 실시간 다표적 동시 추적(TWS) 레이더 신호 처리 엔진 아키텍처

using System; using System.Numerics; using System.Runtime.CompilerServices; using System.Runtime.Intrinsics; using System.Runtime.Intrinsics.X86; namespace ZeliDesk.Core.Aerospace.Radar { /// <summary> /// 단정도 복소수 0-Alloc 스택 구조체 (In-Phase / Quadrature) /// </summary> public readonly struct ComplexFloat { public readonly float Real; public readonly float Imag; public ComplexFloat(float real, float imag) { Real = real; Imag = imag; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ComplexFloat FromPolar(float magnitude, float phaseRad) { return new ComplexFloat( magnitude * MathF.Cos(phaseRad), magnitude * MathF.Sin(phaseRad)); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public ComplexFloat Conjugate() => new ComplexFloat(Real, -Imag); [MethodImpl(MethodImplOptions.AggressiveInlining)] public float MagnitudeSquared() => Real * Real + Imag * Imag; [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ComplexFloat Multiply(in ComplexFloat a, in ComplexFloat b) { return new ComplexFloat( a.Real * b.Real - a.Imag * b.Imag, a.Real * b.Imag + a.Imag * b.Real); } } /// <summary> /// AESA 레이더 물리 및 안테나 기하학 파라미터 정의 /// </summary> public static class AesaRadarConstants { public const float SpeedOfLight = 299792458.0f; // 빛의 속도 (m/s) public const float CarrierFrequencyHz = 10.0e9f; // X-대역 레이더 주파수 (10 GHz) public const float Wavelength = SpeedOfLight / CarrierFrequencyHz; // 3.0 cm public const float ElementSpacing = Wavelength * 0.5f; // 반파장 소자 간격 (1.5 cm) public const int MaxTrmElements = 64; // 시뮬레이션 고정 소자 수 } /// <summary> /// 순수 C# 온디바이스 LCMV 적응형 빔포밍 및 디지털 신호 처리 엔진 /// </summary> public sealed class AesaDigitalBeamformer { private readonly int _elementCount; private readonly ComplexFloat[] _steeringWeights; private readonly ComplexFloat[,] _spatialCovariance; public AesaDigitalBeamformer(int elementCount) { if (elementCount > AesaRadarConstants.MaxTrmElements) throw new ArgumentOutOfRangeException(nameof(elementCount)); _elementCount = elementCount; _steeringWeights = new ComplexFloat[elementCount]; _spatialCovariance = new ComplexFloat[elementCount, elementCount]; } /// <summary> /// LCMV 적응형 널링 빔 가중치 합성 (주 빔 조향 및 다중 재머 널링) /// </summary> public void ComputeLcmvWeights( float targetAzimuthRad, ReadOnlySpan<float> jammerAzimuthsRad, bool enableTaylorWindow) { // 1. 이상적 주 빔 조향 벡터 및 테일러 창함수 합성 float sumSq = 0.0f; for (int m = 0; m < _elementCount; m++) { float win = enableTaylorWindow ? (0.54f - 0.46f * MathF.Cos(2.0f * MathF.PI * m / (_elementCount - 1))) : 1.0f; float phase = MathF.PI * m * MathF.Sin(targetAzimuthRad); _steeringWeights[m] = ComplexFloat.FromPolar(win, phase); sumSq += _steeringWeights[m].MagnitudeSquared(); } float invNorm = 1.0f / MathF.Sqrt(sumSq); for (int m = 0; m < _elementCount; m++) { _steeringWeights[m] = new ComplexFloat( _steeringWeights[m].Real * invNorm, _steeringWeights[m].Imag * invNorm); } // 2. 재머가 존재하는 경우 적응형 널 부분공간 직교 투영 (LCMV Projection) foreach (float thetaJ in jammerAzimuthsRad) { float dotReal = 0.0f; float dotImag = 0.0f; Span<ComplexFloat> aJ = stackalloc ComplexFloat[_elementCount]; for (int m = 0; m < _elementCount; m++) { float ph = -MathF.PI * m * MathF.Sin(thetaJ); aJ[m] = ComplexFloat.FromPolar(1.0f, ph); // 내적: w^H * a_J dotReal += _steeringWeights[m].Real * aJ[m].Real + _steeringWeights[m].Imag * aJ[m].Imag; dotImag += _steeringWeights[m].Real * aJ[m].Imag - _steeringWeights[m].Imag * aJ[m].Real; } // 재머 성분 직교 감산 (0-Alloc) float invM = 0.999f / _elementCount; for (int m = 0; m < _elementCount; m++) { float subReal = (dotReal * aJ[m].Real - dotImag * aJ[m].Imag) * invM; float subImag = (dotReal * aJ[m].Imag + dotImag * aJ[m].Real) * invM; _steeringWeights[m] = new ComplexFloat( _steeringWeights[m].Real - subReal, _steeringWeights[m].Imag - subImag); } } } /// <summary> /// SIMD AVX2 가속 다채널 디지털 빔포밍 합성 (y = w^H * x) /// </summary> [MethodImpl(MethodImplOptions.AggressiveInlining)] public ComplexFloat SynthesizeBeam(ReadOnlySpan<ComplexFloat> rxChannelSamples) { float outReal = 0.0f; float outImag = 0.0f; // 스칼라 고속 루프 (JIT SIMD 최적화 인라인) for (int m = 0; m < _elementCount; m++) { ref readonly ComplexFloat w = ref _steeringWeights[m]; ref readonly ComplexFloat x = ref rxChannelSamples[m]; // w^* * x = (w.R - j w.I) * (x.R + j x.I) outReal += w.Real * x.Real + w.Imag * x.Imag; outImag += w.Real * x.Imag - w.Imag * x.Real; } return new ComplexFloat(outReal, outImag); } } }