4.3 Spectrum Shaping by CPS-OFDM
4.4.1 Simulation Setup
The system parameters chosen from the 4G LTE specification [3] are listed in Table 4.4.1.
The allocation of LB, BB, and RB is in accordance with the subcarrier indices inI, ¯I, and J as shown in Fig. 4.3. For the setting of CPS-OFDM in the BB, the used parameters are listed in Table 4.4.1. The signal processes of synchronization and channel estimation are assumed to be perfect.
4.4.2 Performance Evaluations
We first evaluate the spectral leakage performance only for the downlink transmission in the BB (i.e., S = 0). In Fig. 4.5, from the simulated PSD results, it can be found that the proposed CPS-OFDM waveform inherits the low-OOBE characterization from
Figure 4.5: Tight spectral containment achieved by CPS-OFDM with Kg = 1 and Mg = 2 for the downlink transmission in the BB.
the GFDM modulation with one guard subcarrier and two guard sub-blocks. In this case, the transmission efficiency γ is 77.78%. Compare to the use of OFDMA with the same number of null subcarriers (i.e., Nnc = 32), the proposed waveform evidently achieves larger sidelobe attenuation.
Then, we consider the joint downlink transmissions of the legacy OFDMA and the CPS-OFDM in the LB and the BB, respectively. As shown in Fig. 4.6, observed from J = {801, 802, · · · , 812}, the CPS-OFDM corresponding to the BB acts as a functionality of spectrum shaping to prevent the adjacent RB used for the 5GRAT from receiving severe sidelobe interference caused by the legacy OFDMA transmission. Moreover, the level of spectrum shaping can be enhanced by increasing the frequency range of the BB as displayed in Fig. 4.7.
The operation of spectrum shaping can satisfy the OOBE criterion stated in (4.8). For λ = −34dB, as shown in Fig. 4.6, the legacy OFDMA transmission requires 144 null subcarriers. In the proposed scheme, equivalently, only 32 null subcarriers are needed. It obviously gains much more SE for heterogeneous LTE downlink spectrum access. Note that the legacy sidelobe leakage level can be found in [108] and the value of λ shall be determined according to future 5G radio frequency requirements.
For the transmitter implementation, PAPR is a critical factor that highly correlates with the PA efficiency [109]. The PAPR of the proposed downlink transmission can be evalu-ated by showing its complementary cumulative distribution function (CCDF) defined as CCDF = 1− Pr {PAPR ≤ PAPR0}, where Pr {PAPR ≤ PAPR0} indicates the proba-bility of PAPR that does not exceed a given threshold denoted by PAPR0. As shown in Fig. 4.8, the PAPR performance of additionally using CPS-OFDM is very close to that of the legacy OFDMA transmission. Hence, no additional processing of PAPR reduction is needed for the legacy BS.
The uncoded BER performance is analyzed to validate the feasibility of integrating the proposed CPS-OFDM, namely, embedded-GFDM, with the legacy OFDMA. The legacy UE and the advanced UE are assumed to have the same noise variance and receive the downlink signals via two distinct Extended Pedestrian A (EPA) channels. As shown in Fig. 4.9, compared with the legacy UE, the advanced UE suffers from about 2 dB detection performance degradation given a fixed BER (e.g., 10−2). The reason behind this is that the ZF decoder Q results in noise enhancement penalty (NEP). The legacy UE remains the same detection performance because of the preservation of orthogonality among the subcarriers indexed by I and ¯I. It is important to notice that there is no NEP, if the precoding matrix P is designed to be unitary as indicated by Chapter 2.
Figure 4.6: CPS-OFDM functioning as the spectrum shaping of legacy OFDMA trans-mission gaining much more spectrum efficiency compared to GB utilization.
Figure 4.7: Illustration of the flexibility of CPS-OFDM that the level of spectrum shaping depends on the frequency range of the BB
Figure 4.8: No additional PA burden for the legacy BS when introducing the proposed CPS-OFDM to the BB.
Figure 4.9: No detection performance degradation for the legacy UE due to orthogonality preservation with the advanced UE and only 2 dB BER gap for the advanced UE due to the additional precoder P being non-unitary causing NEP.
4.5 Concluding Remarks
In this chapter, the idea of spectrum shaping using CPS-OFDM (a.k.a. embedded-GFDM) is proposed to facilitate heterogeneous LTE downlink spectrum access. CPS-OFDM wave-form can be easily multiplexed with OFDMA-based signaling with tight spectral contain-ment. Simulations results demonstrate that the proposed scheme enjoys the flexibility of reusing the guard band resided in the 4G licensed transmission band and also warrants no impact on the legacy UE receivers. It is worthy to emphasize that using the proposed CPS precoding technique intelligently enables smooth migration from 4G to 5G in the view of spectrum engineering.
Chapter 5
Conclusions and Future Work
A new waveform called circularly pulse-shaped OFDM (CPS-OFDM), along with its transceiver optimization design and practical applications, is proposed in this dissertation for 5G New Radio (NR) and beyond.
In Chapter 2, we justified that CPS-OFDM possesses the advantages of both low out-of-subband emission (OSBE) and low peak-to-average power ratio (PAPR). Thus, the spectral regrowth and the signal distortion caused by power amplifier (PA) nonlinearity can be substantially alleviated. Benefited from the design flexibility, CPS-OFDM can further reduce the PAPR and so enhance the PA efficiency by allowing little noise en-hancement penalty (NEP). In addition, the proposed CPS precoder is able to be efficiently realized with linearithmic-order complexity through the characteristic-matrix-domain im-plementation method. The optimal prototype shaping vector built in the CPS precoder is obtained by the proposed optimization algorithm based on majorization-minimization (MM) and convex-iteration (CI) iteration processes. Simulation results demonstrate the performance gains in detection reliability and spectral efficiency (SE) of applying the pro-posed schemes to three practical sub-6 GHz uplink cases specified by 3GPP. The supe-riority of CPS-OFDM over the existing waveform candidates is very evident. Therefore, the proposed CPS-OFDM is considered to be one of the most promising technologies in 5G NR and beyond.
In Chapter 3, we proposed a constellation shaping optimization method to reduce the cubic metric (CM) of CPS-OFDM signals. The optimized offset data symbols also
pre-serve the original low-OSBE property of CPS-OFDM. Benefited from the extremely low CM, the spectral regrowth and the signal distortion caused by severe power amplifier (PA) nonlinearity can be significantly alleviated. Therefore, with the proposed scheme, the CPS-OFDM system can earn more SE.
In Chapter 4, we introduced the idea of spectrum shaping using CPS-OFDM to facili-tate heterogeneous LTE downlink spectrum access. The proposed CPS-OFDM waveform can be easily multiplexed with OFDMA-based signaling. Simulations results demonstrate that the proposed scheme enjoys the flexibility of reusing the guard band resided in the 4G licensed transmission band and also warrants no impact on the legacy receivers. Therefore, adopting the proposed CPS precoding technique intelligently enables smooth migration from 4G to 5G in the views of spectrum engineering and commercial cellular operators.
In the future, there are some remaining issues related to the use of CPS-OFDM and its optimization procedure for further study. The criteria to decide the parameters K, M ,K, M, β, ϵ, and w adapting to various application scenarios are of interest. The downlink us-age relying on multiple user-specific CPS precoders at the transmitter is to be investigated.
Although the optimized prototype shaping vector obtained from the proposed algorithm can be offline computed and saved into a lookup table, one may accelerate the conver-gence rate of the MM process by finding a more suitable surrogate function alternative to (2.41). A proof to the existence of the optimal rank-one solution of Problem (2.44) is anticipated. It is worthy to analyze the signal-to-interference-plus-noise ratio (SINR) of CPS-OFDM subject to multiuser interference arising from spectral regrowth, synchro-nization mismatch, and different subcarrier spacing for its advanced receiver development.
Moreover, designing dedicated pilot sequences for CPS-OFDM channel estimation might be needed. Integrating the proposed CPS-OFDM system with MIMO technologies in an efficient way is strongly desirable and also essential to 5G NR and beyond.
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