2.6 Appendix
2.6.5 Other 5G OFDM-Based System Models
The baseband transceiver system implementations of OFDM, WOLA-OFDM, UF-OFDM, f-OFDM, DFT-S-OFDM, SS-SC-FDMA, ZT DFT-S-OFDM, and CPS-OFDM with NoGI are briefly sketched in this subsection.
Most of the parameters labeled on Figs. 2.29-2.36 conform to the usage defined in Section 2.1. In Fig. 2.29, a basic OFDM system with either CP or ZP, HN is able to be an N×N diagonal matrix whose diagonal elements corresponding to the N complex-valued channel frequency response taps [58, 59]. The frequency-domain equalization (FDE) ma-trix can then be easily chosen as H−1N to compensate the channel effect in zero forcing (ZF) sense. For WOLA-OFDM shown in Fig. 2.30, the notations z and z−1 represent the advance operator and the delay operator, respectively. The CP and cyclic suffix (CS) insertion matrix is given by
Gcpcs =
where W is the number of extended samples overlapping with the previous (or next) block.
The (N′ + 2W )× 1 vector w is composed of windowing coefficients. For UF-OFDM shown in Fig. 2.31, the S× 1 vector p = [WN[hTf 0T(N−L
f−1)×1]T]◦−1I is to pre-equalize the frequency response of the FIR filter to make the passband flat. As for f-OFDM shown in Fig. 2.32, the passband of the FIR filter is basically designed to be flat and so no pre-equalization is needed. Note that in Section 2.4 the WOLA processing and the filtering at the receiver are omitted. For SS-SC-FDMA shown in Fig. 2.34, the use of S× 1 shaping vector p is transparent to the receiver, M ≤ S ≤ N. For ZT DFT-S-OFDM shown in Fig. 2.35, several zeros are placed in front of the M -point DFT to make the power of each block tail small enough such that the IBI can be alleviated. It is usually said that the block tail serves as an internal GI. In Fig. 2.36, the proposed CPS-OFDM system without GI utilization is presented and highly recommended for 5G NR and beyond.
Figure 2.29: OFDM baseband transceiver system model.
Figure 2.30: WOLA-OFDM baseband transceiver system model.
Figure 2.31: UF-OFDM baseband transceiver system model.
Figure 2.32: f-OFDM baseband transceiver system model.
Figure 2.33: DFT-S-OFDM (a.k.a. SC-FDMA) baseband transceiver system model.
Figure 2.34: SS-SC-FDMA baseband transceiver system model.
Figure 2.35: ZT DFT-S-OFDM baseband transceiver system model.
Figure 2.36: CPS-OFDM baseband transceiver system model with NoGI.
Chapter 3
Reducing Cubic Metric of Circularly Pulse-Shaped OFDM Signals Through Constellation Shaping Optimization With Performance Constraints
Circularly pulse-shaped orthogonal frequency division multiplexing (CPS-OFDM) is one of the most promising 5G waveforms that addresses two physical layer signal requirements of low out-of-subband emission (OSBE) and low peak-to-average power ratio (PAPR) with flexibility in parameter adaptation. In this chapter, a constellation shaping optimiza-tion method is proposed to further reduce the cubic metric (CM) of CPS-OFDM signals for the case that demands rather high power amplifier (PA) efficiency at the transmitter.
Simulation results demonstrate the superiority of the proposed scheme in CM reduction, and the corresponding benefits of spectral regrowth mitigation and spectral efficiency (SE) improvement. Most of the contents in this chapter were presented in [56]
3.1 Introduction of This Work
The fifth generation wireless systems (5G), named as New Radio (NR), are envisioned to support various innovative service-oriented applications in manifold usage scenarios [1],
e.g., machine type device-to-device communications [89], grant-free asynchronous trans-missions [4], and coexistence of heterogeneous spectrum access with different numerolo-gies [39]. The physical-layer signal formats of 5G NR, on basis of OFDM [2], additionally demand low OSBE, low PAPR, flexibility in parameter adaptation, backward and for-ward compatibility [7, 8, 11]. As indicated by Chapter 2, CPS-OFDM is one of the most promising waveforms that addresses these requirements simultaneously with SE improve-ment [48]. In contrary to a number of existing waveform schemes relying on windowing or filtering techniques [14], CPS-OFDM exploits a subband-wise precoder characterized by a prototype vector and its circularly time-frequency shifted versions without imposing guard interval (GI) burden [48]. Besides, CPS-OFDM can be regarded as a generalized DFT-S-OFDM implemented with linearithmic-order complexity [48]. As CPS-OFDM has been demonstrated to bring such attractive advantages into upcoming 5G NR, it is wor-thy to study some auxiliary techniques that can further enhance the CPS-OFDM system performance in certain cases.
Considering the case that demands high PA efficiency at the transmitter (e.g., a smart factory with intercommunicating machinery [89]), this work intends to further reduce the CM of CPS-OFDM signals through a constellation shaping technique. CM is known as a more accurate indicator to quantify envelope fluctuations than PAPR [13,90–94]. The rea-son behind this is that CM closely relates to the third-order intermodulation product of PA nonlinearity, which dominates the distortion of the transmitted signals [13, 90]. The key idea of constellation shaping is to introduce offset values to input quadrature amplitude modulation (QAM) symbols so that CM (or PAPR) can be greatly reduced [13,94,95]. The use of this approach is usually accompanied with an error vector magnitude (EVM) con-straint that confines the resulting detection performance degradation within an acceptable range. Moreover, the inherent property of low OSBE of CPS-OFDM must be carefully preserved to facilitate asynchronous transmissions and mixed numerologies for lack of frequency-domain user orthogonality.
In this chapter, we propose a constellation shaping optimization method for CPS-OFDM according to the aforementioned design aspects. Specifically, the proposed
op-timization problem is formulated to minimize the CM subject to two constraints on the EVM and the OSBE. The optimized offset values imposed on the transmitted QAM sym-bols are transparent to the receiver, i.e., no additional side information about applying constellation shaping to the transmitter is required by the receiver. Although the real-time optimization may encounter some challenges such as high computational complexity and algorithm reliability, we believe that the advances in electronic technology can afford high computing power for signal processing in devices in the near future [95, 96].
The rest of this chapter is organized as follows. In Section 3.2, a CPS-OFDM baseband transceiver system model and its design problem are described. In Section 3.3, the pro-posed constellation shaping optimization method for CPS-OFDM is introduced. In Sec-tion 3.4, simulaSec-tion results show the performance gains of applying the proposed scheme to 5G NR. Finally, the contributions of this work are summarized in Section 3.5.