Differential Encoding by a Look-Up Table for Quadrature-Amplitude Modulation

In this paper, we propose a novel differential encoder for QAM (quadrature-amplitude modulation), by a look-up table instead of a rule. Using a table for differential encoding has the advantages of both low complexity and good error performance. We propose algorithms to construct the table for maximizing the minimum noncoherent distance and minimizing the number of different data bits between two codewords with small noncoherent distance. For 16QAM and 32QAM, we show that the differential encoders obtained by the proposed algorithms are optimal in terms of minimum noncoherent distance. Differential detectors for QAM, including a reduced-complexity two-symbol detector and multiple-symbol detectors, are proposed as well. Simulation results of 16QAM show that the proposed differential encoder provides significant gain over existent differential encoders as expected by distance analysis, and the proposed low-complexity multiple-symbol differential detector can further improve the error performance.

I Introduction

Differentially encoded MPSK (-ary PSK), called differential phase-shift keying (DPSK), is a well-known simple noncoherent modulation. However, DPSK is not bandwidth efficient when is small and has poor error performance when is large. To achieve satisfactory error performance at high transmission rate, differential encoding for QAM (quadrature-amplitude modulation) were considered in [1] and [2], in which rules of differential encoding based on different divisions of the signal spaces were proposed. Differentially encoded 16QAM serially concatenated with an outer code for the block fading channel was considered in [3].