Short Frame Transmission at Very Low SNR by Associating CCSK Modulation With NB-Code

Abstract

In this paper, we present a frame structure that can be viewed as a preamble for the detection and synchronization process (leading to low cost receiver) and as an encoded codeword carrying the transmitted message (leading to reliable transmission). This duality facilitates an ALOHA protocol avoiding preamble overhead. The frame structure, named Quasi-Cyclic Short Packet (QCSP), is based on the association of a Cyclic Code Shift Keying (CCSK) modulation and a non-binary error control code. The detection/correction algorithm of the QCSP system is presented, its performance is theoretically derived and discussed for different parameters. A QCSP frame can be transmitted and received correctly with an error probability of 10 −4 , distanced by 1.2 dB from Polyanskiy's bound (an estimated Shannon's limit for small packet size) at -11 dB of SNR for a payload of 360 bits. Compared to a classical preamble-based frame using a modern binary error control code, the size of a QCSP frame is reduced by 23%. Moreover, detecting a QCSP frame requires a lower complexity than detecting a longer classical preamble.

Phase Synchronization for Non-Binary Coded CCSK Short Frames

“…For the grid of ω, it is more convenient to specify the final phase (9). In the worst cases, θ = +π (respectively −π) and f r = +10 −3 (respectively, −10 −3 ), leading to the final phase…”

“…In [9], a Quasi Cyclic Short Packet (QCSP) frame structure has been proposed based on the combinations of Cyclic Code Shift Keying (CCSK) [10] of length q chips and a Non-Binary (NB) error control code [11] over GF(q). The key idea is to design a preamble-less frame, where the whole payload is used to perform both detection and timing synchronization processes from the first side, and Forward Error Correction (FEC) decoding process to recover the conveyed data from the other side.…”

“…The method uses the structural properties of the QCSP frame to detect the exact time of arrival of the frame. In the continuity of the workflow initiated in [9], [12] and [13], this paper presents the final step of the synchronization process, i.e., the suppression of the remaining residual frequency and initial phase offsets. Once the frame fully synchronized, coherent demodulation can be performed to generate the symbol Log-Likelihood Ratio required by the non-binary decoder.…”

Weighted Coherent Detection of QCSP frames

“…Recently, a new preamble-free frame, called Quasi-cyclic Short Packet (QCSP), has been proposed [8]. The QCSP frame is based on the association of a Cyclic Code Shift Keying (CCSK) modulation and a Non-Binary Forward Error Control (NB-FEC) code.…”

“…Moreover, the proposed method which is presented in [8] is based on a theoretical Gaussian channel with a calibrated level of noise and signal. In a real radio receiver, the amplitude of the signal is subjected to an unknown multiplicative factor due to the front end of the radio frequency stage in general, and the behavior of the automatic gain control in particular.…”