Index Modulation for Modulation on Conjugate-Reciprocal Zeros (IM-MOCZ)

TL;DR

The proposed IM-MOCZ provides higher SE gains than conventional MOCZ, and simulations demonstrate improved bit error rate (BER) performance for larger $K$ relative to $N, and simulations demonstrate improved bit error rate (BER) performance for larger $K$ relative to $N.

Abstract

This paper investigates the application of Index Modulation (IM) to Modulation on Conjugate-Reciprocal Zeros (MOCZ) to enhance spectral efficiency (SE) in short packet communications. The proposed IM-MOCZ scheme splits an $N$-bit message into two streams: $N-K$ bits select one of $2^{N-K}$ uniquely designed codebooks, while the remaining $K$ bits are transmitted with conventional MOCZ using the selected codebook. At the receiver, Root Finding Minimum Distance (RFMD) and Direct Zero-Testing (DiZeT) detectors evaluate all candidate codebooks and compute penalty metrics, with a majority-vote rule selecting the most confident codebook and recovering the transmitted message. The proposed IM-MOCZ provides higher SE gains than conventional MOCZ, and simulations demonstrate improved bit error rate (BER) performance for larger $K$ relative to $N$.

Figures (4)

• Figure 1: A block diagram of the proposed baseband equivalent IM-MOCZ system.
• Figure 2: Complex zeros of the received signal for IM-MOCZ with $N=5$, $K=3$, $L_{\text{ch}}=3$, $E_b/N_0=10$ dB, $R=1.1974$, and message $10100_2$. Hollow black circles denote transmitted complex zeros of $\mathbf{x}$; magenta circles denote complex zeros of $\mathbf{y}$. Codebooks $\mathbf{\zeta}_1$–$\mathbf{\zeta}_4$ are shown in blue, orange, yellow, and purple, respectively. Received complex zeros are $\tilde{a}_1=0.9336+0.1417i$, $\tilde{a}_2=0.5958+1.3146i$, $\tilde{a}_3=-0.2978+0.3378i$, $\tilde{a}_4=-0.7922+0.0098i$, and $\tilde{a}_5=0.3106-0.6452i$.
• Figure 3: BER performance of IM-MOCZ and conventional MOCZ for $N=10$, $L_{\text{ch}}=3$, $R=1.1974$, and $K=10,8, 6, 4$ using RFMD and DiZeT detection.
• Figure 4: BER performance of IM-MOCZ and conventional MOCZ for $N=20$, $L_{\text{ch}}=6$, $R=1.1974$, and $K=20,18,16,14$ using RFMD and DiZeT detection.