[Paper Review] Diversity Multiplexing Trade-off and Selection Gain in Media-Based Modulation

Ehsan Seifi, Amir K. Khandani|arXiv (Cornell University)|Feb 6, 2022

Advanced Wireless Communication Technologies4 citations

TL;DR

This paper analyzes the diversity-multiplexing trade-off (DMT) and selection gain in Media-Based Modulation (MBM), a novel transmission scheme that encodes data in the state of RF mirrors rather than the signal waveform. By leveraging independent fading across receive antennas due to multipath-induced channel state variations, MBM achieves superior performance: a 1×N_r SIMO-MBM system with an MDS code significantly outperforms an N_r×N_r legacy MIMO in both diversity and multiplexing gains.

ABSTRACT

The idea of Media-based Modulation (MBM) is to embed information in the variations of the transmission media (channel states). Using an RF closure with $w$ RF walls, MBM creates a set of $2^w$ select-able states for the end-to-end channel. Each state represents an index of an MBM constellation point. In each state, the wave (tone) emanating from the transmit antenna experiences many pseudo-random back-and-forth reflections within the RF closure. The RF signal, upon finally leaving the RF closure, further propagates in the rich scattering environment to reach the receiver. This results in an independent complex channel gain to each receive antenna. As a result, coordinates of different MBM constellation points (vectors of channel gains formed over received antennas) will be independent of each other. This is unlike legacy transmission schemes where a fixed constellation structure used at the transmitter will be multiplied by a fixed, but random, channel gain. Due to this independence property, MBM offers several advantages vs. legacy systems, including "additivity of information over multiple receive antennas (regardless of the number of transmit antennas)", and "inherent diversity over a static fading channel". This work studies the Diversity-Multiplexing Trade-off of an MBM constellation. Analytical expressions are provided that demonstrate the advantages of MBM vs. legacy systems. In particular, it is shown that a $1 imes N_r$ SIMO-MBM constellation equipped with an MDS code (even with a relatively small code length) significantly outperforms an $N_r imes N_r$ legacy MIMO.

Motivation & Objective

• To analyze the diversity-multiplexing trade-off (DMT) in Media-Based Modulation (MBM), a novel transmission scheme that encodes data in the state of RF mirrors.
• To investigate how coding with Maximum Distance Separable (MDS) codes enhances diversity gain in MBM while minimizing multiplexing gain reduction.
• To quantify the selection gain achievable through transmitter feedback that selects only high-energy MBM constellation points.
• To compare the performance of MBM with conventional SISO, SIMO, and MIMO systems in terms of error probability and spectral efficiency.
• To derive analytical expressions for pairwise error probability and word error probability in MBM under various channel and coding conditions.

Proposed method

• Models a 1×N_r SIMO-MBM system where each of 2^w RF mirror states creates a distinct channel state vector at the receiver, with independent complex fading per receive antenna.
• Derives the pairwise error probability (PEP) for MBM using the non-central chi-squared distribution of the squared Euclidean distance between constellation points.
• Establishes that un-coded MBM achieves a diversity gain of d = N_r - r for spatial multiplexing gain r, based on the high-SNR asymptotic behavior of error probability.
• Applies MDS coding to MBM with parameters (N, K, D = N - K + 1) over GF(q), deriving a word error probability bound involving the hypergeometric function and SNR dependence.
• Introduces a selection gain mechanism where the transmitter removes low-energy constellation points based on feedback, reducing average error probability.
• Uses the incomplete gamma function and chi-squared tail probabilities to model the reduction in error probability and the required number of additional RF mirrors to maintain rate.

Experimental results

Research questions

• RQ1 What is the diversity-multiplexing trade-off (DMT) of an un-coded 1×N_r SIMO-MBM system?
• RQ2 How does MDS coding affect the diversity gain in MBM, and what is the trade-off with multiplexing gain?
• RQ3 What is the achievable selection gain in MBM when the transmitter uses feedback to select only high-energy channel states?
• RQ4 How many additional RF mirrors are required to maintain the same transmission rate after applying selection gain via energy thresholding?
• RQ5 How does the error probability of MBM scale with SNR, and how does it compare to legacy MIMO systems in high-SNR regimes?

Key findings

• Un-coded MBM achieves a diversity gain of d = N_r - r for spatial multiplexing gain r, demonstrating inherent diversity over static fading channels.
• Coded MBM using an MDS code with minimum distance D achieves a diversity gain of d = D N_r - r/τ, where τ is the code rate, significantly outperforming uncoded systems.
• The word error probability for coded MBM is bounded by P_w ≤ (2^N / √(2πN_r)) × (1 + SNR/2)^(- (D N_r - r/τ)), showing a diversity gain proportional to D.
• Selection gain via feedback reduces the required SNR by a factor of approximately γ_c ≈ (Γ(n/2, nE/2) / Γ(n/2, nE))^(2/n), where E is the energy threshold.
• The number of additional RF mirrors needed to maintain rate after selection is δ = log₂(1 - F(nE; n)), where F is the chi-squared CDF with n degrees of freedom.
• A 1×N_r SIMO-MBM system with MDS coding significantly outperforms an N_r×N_r legacy MIMO system in both diversity and multiplexing gains, even with short code lengths.