Virtual Labs

Which of the following statements is true about ZF and MMSE?

a: ZF always outperforms MMSE Explanation

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b: MMSE and ZF perform equally at high noise Explanation

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c: MMSE performs better than ZF at low SNR Explanation

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d: MMSE is a linear approximation of ZF Explanation

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What is the major drawback of the Zero Forcing (ZF) equalizer?

a: It requires channel state information Explanation

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b: It amplifies noise in channels with deep fades or low singular values Explanation

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c: It has high computational complexity Explanation

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d: It does not work with MIMO systems Explanation

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Which equalizer is computationally simpler but less robust to noise?

a: MMSE Explanation

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b: ZF Explanation

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c: Maximum Likelihood Explanation

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d: Sphere Decoder Explanation

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The MMSE equalizer reduces to the Zero Forcing equalizer in which case?

a: High noise power Explanation

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b: Low signal power Explanation

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c: Infinite SNR (i.e., noise → 0) Explanation

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d: Infinite bandwidth Explanation

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What is the effect of MMSE regularization compared to ZF?

a: It reduces inter-symbol interference but increases complexity Explanation

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b: It adds a noise-dependent regularization term to reduce noise amplification Explanation

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c: It ignores the channel matrix Explanation

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d: It increases the condition number of the matrix Explanation

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Which matrix operation is used in the ZF equalizer for a MIMO channel with matrix Hᴴ?

a: Hᴴ Explanation

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b: (Hᴴ H)⁻¹ Hᴴ Explanation

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c: H Hᴴ Explanation

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d: H⁻¹ Explanation

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In a system where H is the channel matrix and σ² is the noise variance, what is the MMSE equalizer matrix?

a: H⁻¹ Explanation

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b: (Hᴴ H)⁻¹ Hᴴ Explanation

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c: (Hᴴ H + σ² I)⁻¹ Hᴴ Explanation

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d: Hᴴ (H Hᴴ + σ² I)⁻¹ Explanation

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What happens when the MIMO channel matrix Hᴴ is not full-rank?

a: ZF works perfectly Explanation

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b: MMSE and ZF perform the same Explanation

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c: ZF becomes ill-conditioned and performs poorly Explanation

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d: Both ZF and MMSE are optimal Explanation

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Which equalizer performs best in terms of Bit Error Rate (BER) in a noisy and ill-conditioned channel?

a: Zero Forcing Explanation

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b: MMSE Explanation

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c: Maximum Likelihood Detection Explanation

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d: Matched Filter Explanation

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Reciever Architecture: ZF and MMSE