MOCZ Modulation

We introduce a novel blind (noncoherent) communication scheme, called modulation on conjugate-reciprocal zeros (MOCZ), to reliably transmit sporadic short binary packets over unknown finite impulse response systems as used, for example, to model underspread wireless multipath channels. In MOCZ, the information is modulated onto the zeros of the transmitted signals z-transform. In the absence of additive noise, the zero structure of the signal is perfectly preserved at the receiver, no matter what the channel impulse response (CIR) is. Furthermore, by a proper selection of the zeros, we show that MOCZ is not only invariant to the CIR, but also robust against additive noise. Starting with the maximum-likelihood estimator, we define a low complexity and reliable decoder and compare it to various state-of-the art noncoherent schemes, such as OFDM index modulation (IM), OFDM pilot aided, and orthogonal signaling. Our scheme outperforms OFDM-IM and maintains its performance even if the packet length becomes shorter than the CIR.

About MOCZ

The future generation of wireless networks faces a diversity of new challenges. Trends on the horizon – such as the emergence of the Internet of Things (IoT) and the tactile Internet – have radically changed our thinking about how to scale the wireless infrastructure. Among the main challenges new emerging technologies have to cope with is the support of a massive number (billions) of devices ranging from powerful smartphones and tablet computers to small and low-cost sensor nodes. These devices come with diverse and even contradicting types of traffic including high speed cellular links, device-to-device connections, and wireless links carrying short-packet sensor data. Short messages of sporadic nature will dominate in the future and the conventional cellular and centrally-managed wireless network infrastructure will not be flexible enough to keep pace with these demands. Although intensively discussed in the research community, the most fundamental question here on how we will communicate in the near future under such diverse requirements remains largely unresolved. A key problem is how to acquire, communicate, and process channel information. Conventional channel estimation procedures require a substantial amount of resources and overhead. This overhead can dominate the intended information exchange when the message is short and the traffic sporadic. Noncoherent and blind strategies, provide a potential way out of this dilemma. Classical approaches like blind equalization have been already investigated in the engineering literature, but new noncoherent modulation ideas which explicitly account for the short-message and sporadic type of data are required.


  • Walk, P., Jung, P., & Hassibi, B. (2019). “MOCZ for Blind Short-Packet Communication: Basic Principles”, IEEE Transactions on Wireless Communications, 18(11), 5080-5097

  • Walk, P., Jung, P., Hassibi, B., & Jafarkhani, H. (2019). “MOCZ for Blind Short-Packet Communication: Practical Aspects”, arXiv preprint