5G Bi-Directional Beamforming & SINR Lab 5G BEAM STEERING SYSTEM BS & MS Joint Steering + Interference Cancellation System SINR -- dB RX Power -- dBm 1. gNodeB (Base Station) Antennas ($N_{BS}$): 16 Large arrays at the tower create narrow "Pencil Beams" to maximize range. 2. UE (Mobile Station) Antennas ($N_{MS}$): 4 ...

  Understanding Clarke-Jakes Model: The Foundation of Rayleigh Fading A comprehensive guide to the Clarke-Jakes model, the Doppler Bathtub Spectrum, and precision Coherence Time calculations in wireless communications. What is Clarke’s Model? Clarke’s Model (often called the Clarke-Jakes model) is the mathematical framework used to describe small-scale fading in mobile wireless channels. It explains how a signal behaves when a receiver moves through a dense multipath environment where there is no direct Line-of-Sight (NLOS). Key Assumptions: A fixed transmitter and a moving receiver. An infinite number of scatterers (rich multipath). Signals arrive from all horizontal directions (360°) with equal probability. The received signal envelope follows a Rayle...

  Is the -174 dBm/Hz Noise Floor Formula Universal? Understanding the limits of thermal noise calculations in RF engineering. In the world of RF engineering and wireless communication, the formula for calculating the noise floor is treated as gospel. For most terrestrial applications, we use the standard benchmark: P noise (dBm) = -174 + 10 * log 10 (Bandwidth) + NF While this equation is incredibly robust for designing cellular networks, Wi-Fi systems, and satellite links, it is not a universal law of physics applicable to every frequency. Depending on your environment and operating frequency, this formula can lead to significant errors. Where Does the "-174" Come From? The value -174 dBm/Hz is derived from the thermal noise power spectral density equation, P = kTB . Under standard conditions: k: Boltzmann’s Constant (1.38 × 10 -23 J/K). T: Absolute temperature, traditionally set at 290 K (Standard Room Temperature). When you convert this to dBm per 1 Hz of bandwidth...

RF Noise Floor Simulation Master the formula: P noise = 10log 10 (kTB) + NF Noise Floor: -100 dBm System Parameters Bandwidth (B) in MHz 20 Noise Figure (NF) in dB 5 Temperature (T) in Kelvin 290 Wi-Fi (20MHz) LoRa (125kHz) LTE (10MHz) Cryo-SDR (10K) Calculated Noise Floor -100.0 dBm Calculation breakdown will appear here... Sensitivity Tip Total Noise Floor represents the poi...

  For electron diffusion in a semiconductor, the excess electron concentration decays exponentially with distance: Δ n ( x ) = Δ n ( 0 ) e − x / L n \Delta n(x)=\Delta n(0)e^{-x/L_n} ​ where: Δ n ( x ) \Delta n(x) Δ n ( x ) = excess electron concentration at distance x x x Δ n ( 0 ) \Delta n(0) Δ n ( 0 ) = excess electron concentration at x = 0 x=0 x = 0 L n L_n L n ​ = electron diffusion length At the diffusion length x=L_n x =2 micrometer ​10^14 * e^(2/2) = .367 * 10^14 cm^-3 Option (1) GATE EC Previous Year Papers with Solutions → Electronics and Communication Study Material →

  Fourier Transform of \(x(t)=\dfrac{t}{(1+t^2)^2}\) We want to determine the Fourier transform of $$ x(t)=\frac{t}{(1+t^2)^2} $$ using the Fourier transform definition $$ X(\omega)=\int_{-\infty}^{\infty}x(t)e^{-j\omega t}\,dt $$ Step 1 : Let $$ x_1(t)=\frac{1}{1+t^2} $$ Then $$ X_1(\omega)=\pi e^{-|\omega|}. $$ Proof: $$ \int_{-\infty}^{\infty}\frac{1}{1+t^2}e^{-j\omega t}\,dt $$ Use the Residue Theorem. $$ \int_{-\infty}^{\infty}\frac{1}{1+z^2}e^{-j\omega z}\,dz $$ Or, $$ \int_{-\infty}^{\infty}\frac{1}{(z+j)(z-j)}e^{-j\omega z}\,dz $$ Poles are at \(z=-j\) and \(z=j\). For the pole at \(z=-j\): $$ \operatorname*{Res}_{z=-j}\left(\frac{e^{-j\omega z}}{(z+j)(z-j)}\right) = \lim_{z\to -j}(z+j)\frac{e^{-j\omega z}}{(z+j)(z-j)} = \frac{e^{-\omega}}{-2j}. $$ Therefore, $$ -2\pi j\left(\frac{e^{-\omega}}{-2j}\right) = \pi e^{-\omega}. $$ For the pole at \(z=j\): $$ \operatorname*{Res}_{z=j}\left(\frac{e^{-j\omega z}}{(z+j)(z-j)}\righ...

  Effect of Noise in Amplitude Modulation (AM)  Understanding the effect of noise in amplitude modulation (AM) is one of the most important topics in Analog Communication Systems.  This article explains the complete derivation step by step, including: Transmitted AM signal Received signal equation Why noise is written in envelope-phase form Difference between r(t) and y(t) Envelope detector output Threshold effect Step 1: Transmitted AM Signal The transmitted amplitude modulated (AM) signal is s(t)=A c [1+k a m(t)]cos(2πf c t) where A c = Carrier amplitude m(t) = Message signal k a = Amplitude sensitivity f c = Carrier frequency Step 2: Noise is Added by the Channel Every communication channel introduces random noise. Let the channel noise be n(t) The received signal becomes r(t)=s(t)+n(t) This is the most fundamental equation in communication systems. Received Signal = Transmitted...

BER vs SNR: Constellation Analysis BER Derivation from Constellation Points The probability of a bit error in an AWGN channel is determined by the minimum Euclidean distance (\(d_{min}\)) between symbols in a constellation. The generic formula for Bit Error Rate (BER) is: \[ BER = Q \left( \frac{d_{min}}{\sqrt{2N_0}} \right) \] 1. Binary PSK (BPSK) BPSK is antipodal . The points are located at \(+\sqrt{E_b}\) and \(-\sqrt{E_b}\). Because the carrier is always "on" at full strength, the Peak Power equals the Average Power . Distance (\(d_{min}\)): \(2\sqrt{E_b}\) BER Formula: \(Q(\sqrt{2E_b/N_0})\) At 0 dB SNR: \(Q(\sqrt{2}) \approx 0.078\) 2. Orthogonal FSK FSK symbols are perpendicular in signal space. Like PSK, FSK has a constant envelope , meaning the power never fluctuates regardless of which frequency is sent. Distance (\(d_{min}\)): \(\sqrt{2E_b}\) BER Formula: \(Q(\sqrt{E_b/N_0...