# Recent Progress on Novel DSP Techniques for Mode Division Multiplexing Systems: A Review
## 4 DSP Techniques on Compensation of MDL Effects in FMF Links
### Space-Time Coding Technique (STC)  
A few studies have also shown that STC technique in transmitter can effectively suppress MDL effects in SDM systems, which was originally proposed to suppress spatial  
Figure 11: (**a**) Required OSNR to achieve HD-FEC limit BER under FMF links with various DMD values. And \(\text{LP}_{11\text{a}}\)-X signals detected through a linear MIMO equalization (**b**) or through a U-SIC scheme (**c**) after transmission over 15-km FMF at OSNR of 8 dB. Figure 10: Schematic structures of U-SIC detectors comprising two stages. channel fading in wireless MIMO communications [62]. Instead of directly multiplexing different \(M\) modes to transmit independent symbols stream \(\mathbf{S}_{M\times 1}\). MIMO scheme could be beneficial from the space and time degrees of freedom at once by making multiple copies of an input symbol over different channels at different time slots. Naturally, through various channel propagation, these copies could be exploited to have a better estimation of the transmitted symbols at receiver side and the MDL effect would be further mitigated. The schematic structure of SDM MIMO system applying STC technique is shown in Figure 12, where \(\mathbf{X}_{M\times T}\) is a space-time transmitted codeword. \(\mathbf{Y}_{M\times T}\) is the codeword at receiver side where \(M\) denotes the number of channels and \(T\) is the length of the code. \(\mathbf{N}_{M\times T}\) denotes a white Gaussian noise. The effectiveness of STC for MDL suppression in SDM systems has already been demonstrated by various simulations and subsequent experiments. In [63] and [64], it was shown that the combination of redundancy-free STC with inline mode scramblers and ML detector can thoroughly eliminate the SNR penalties caused by the MDL at most 10 dB. Moreover, two reduced-complexity STC detectors achieving a near-ML performance were also proposed: a sub-optimal decoding scheme and a multiblock STC approach in [64]. What's more, two more simple schemes were proposed for STC applications to decrease coding complexity in SDM systems. In [65], Hadamard transform (HT) was utilized in STC technique to disperse the power of each symbol over all modes for identical channel equalization performance. Then, a dense 627-km SDM transmission experiment were demonstrated to prove the HT's advantage of improving MDL tolerance, where the transmission distance was increased by 20%. While in [66], a mode-interleaving method was also presented to simplify STC schemes, which method could improve the transmission reach by 40% through simulation, as well as saving \(\mathrm{O}\big{(}M^{2}\big{)}\) computation complexity compared with conventional space-time block coding (STBC) method. The numerical conclusions of the benefits of STC were soon confirmed in [67] through experimental measurements, where lower BER at the same OSNR condition was achieved and the Q-factor in FMF transmission systems was improved by 3.4 dB in an absence of 10-dB MDL as shown in Figure 13a,b, respectively. Figure 12: SDM transmission system with STC technique. Figure 13: (a) BER vs. OSNR for ST coded and uncoded transmission for MDL = 0, 6, 10 dB (b). Q penalty vs. MDL at OSNR = 14 dB with regards to the MDL-free transmission. Since STC with mode scramblers was shown to be a powerful tool to mitigate MDL effect, more efforts were adopted to explore possible techniques for further improved performance of the SDM systems that apply STC technique. In [68], an upper bound of the error probability of the optical channel induced by MDL was derived, this upper bound leads to a design criterion of space-time codes which is able to totally mitigate MDL in SDM systems. In [69] and [70], the combination of STC and FEC was studied to suppress the MDL effect. Numerical simulation results showed that, through guidance of the aforementioned upper bound of error probability, the obtained gain of the combination is equal to the summation of both coding gain.