(Peer-Reviewed) Direct detection with an optimal transfer function: toward the electrical spectral efficiency of coherent homodyne detection
	
		Xingfeng Li 李星峰 ¹, Jingchi Li 李靖驰 ¹, Xiong Ni 倪雄 ¹, Hudi Liu 刘虎迪 ¹, Qunbi Zhuge 诸葛群碧 ¹, Haoshuo Chen 陈昊硕 ², William Shieh 谢伟 ³, Yikai Su 苏翼凯 ¹
			
				¹ State Key Lab of Advanced Optical Communication Systems and Networks, Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
中国 上海 上海交通大学电子工程系 区域光纤通信网与新型光通信系统国家重点实验室
² Nokia Bell Labs, 600 Mountain Ave, Murray Hill, NJ 07974, USA
³ School of Engineering, Westlake University, Hangzhou 310030, China
中国 杭州 西湖大学工学院
			
			
				Opto-Electronic Science, 2024-12-24
			
		
		
			
		
		
	 
	
	
	Abstract
Complex-valued double-sideband direct detection (DD) can reconstruct the optical field and achieve a high electrical spectral efficiency (ESE) comparable to that of a coherent homodyne receiver, and DD does not require a costly local oscillator laser. However, a fundamental question remains if there is an optimal DD receiver structure with the simplest design to approach the performance of the coherent homodyne detection. 
This study derives the optimal DD receiver structure with an optimal transfer function to recover a quadrature amplitude modulation (QAM) signal with a near-zero guard band at the central frequency of the signal. We derive the theoretical ESE limit for various detection schemes by invoking Shannon’s formula. Our proposed scheme is closest to coherent homodyne detection in terms of the theoretical ESE limit. 
By leveraging a WaveShaper to construct the optimal transfer function, we conduct a proof-of-concept experiment to transmit a net 228.85-Gb/s 64-QAM signal over an 80-km single-mode fiber with a net ESE of 8.76 b/s/Hz. To the best of our knowledge, this study reports the highest net ESE per polarization per wavelength for DD transmission beyond 40-km single-mode fiber. For a comprehensive metric, denoted as 2ᴱˢᴱ×Reach, we achieve the highest 2ᴱˢᴱ×Reach per polarization per wavelength for DD transmission.
	
	
	
	
	
	
		    
		    
    			
		    
    			
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