Autocorrelation matrix in Matlab & Python — build R for Wiener / MVDR

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Build the autocorrelation (covariance) matrix R from snapshots in Matlab or NumPy — including complex conjugate correlation — for Wiener, LMS, and MVDR beamformers.

QAM Modulation using Karnaugh-map walks

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This article focused on constructing constellation for rectangular QAM modulation using Karnaugh-map walks. Exploit inherent property of Karnaugh-maps to construct Gray coded QAM constellation points. M-ary Quadrature Amplitude Modulation (M-QAM) In MQAM modulations, the information bits are encoded as variations in the amplitude and the phase of the signal. The M-QAM modulator transmits a series … Read more

MIMO System Capacity: Unlocking Blazing-Fast Wireless Speeds

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MIMO — Capacity path 1. Intro → 2. Channel model → 3. SISO capacity → 4. Ergodic SISO → 5. MIMO capacity Tools: Shannon calculator Introduction Extend the scalar ergodic average to a matrix channel. With receiver CSI and equal power across transmit antennas, ergodic MIMO capacity is the expectation of a log-determinant—the expression Telatar … Read more

Understanding Ergodic Capacity: Testing Your Wireless Speed Calculator

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MIMO — Capacity path 1. Intro → 2. Channel model → 3. SISO capacity → 4. Ergodic SISO → 5. MIMO capacity Tools: Shannon calculator Introduction We already met ergodic capacity as an expectation. Now treat it as something you compute: how do you estimate it stably, and is there a closed form to check … Read more

Capacity of SISO system over a fading channel

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MIMO — Capacity path 1. Intro → 2. Channel model → 3. SISO capacity → 4. Ergodic SISO → 5. MIMO capacity Tools: Shannon calculator Introduction Shannon’s formula \(C=\log_2(1+\mathrm{SNR})\) shows up in every communications course. On a fading channel the SNR itself is random, so capacity becomes a random variable. What does that mean in … Read more

Model and characterize MIMO channels

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MIMO — Capacity path 1. Intro → 2. Channel model → 3. SISO capacity → 4. Ergodic SISO → 5. MIMO capacity Tools: Shannon calculator Introduction Capacity formulas and diversity analyses assume you already have a channel model. Skip that step, jump straight to \(\log\det\), and it is hard to see why correlated antennas multiplex … Read more