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## PA nonlinear compensation

As described above, the wireless system suffers from PA nonlinearities, when the power efficiency of this latter is high, i.e., it is operated with low IBO. Therefore, in order to increase the PA efficiency without damaging the system performance, several solutions are proposed. The techniques can be divided into two classess : 1) the pre-distortion (PD) module which is implemented before PA and 2) PAPR reduction module which is the signal adjustment. When pre-distorsion is applied on the base-band sampled digital signal we call it digtal pre-distorsion (DPD). This kind of predistosion will be used in the following of the presented work. These two complementary technique are always implemented together.

DPD technology was proposed by James K. Cavers et. al [66] in the 1990s. After more than 20 years of development, DPD has become one of the most basic blocks in current wireless communication systems. The core idea of DPD is to first extract an inverse model of RF PA, and then cascade the extracted inverse model before the input of PA, so that the cascaded system of DPD and PA is linear [67]. As shown before in FIGURE 1.5, When the input power of PA is small, its input-output gain is approximately constant. When the input signal power gradually increases, PA gradually enters the nonlinear region and exhibits strong nonlinear characteristics. In order to compensate for this negative effect, we insert a pre-distortion module before the input of PA. The gain of this pre-distortion module changes with the input signal power, and the trend is opposite to that of the PA, so that the final RF PA output signal is relative linear amplification to the original transmitted signal. The method is shown o FIGURE 1.6. Through the application of DPD technology, the linear working area of PA can be effectively extended, so that it can produce higher output power without obvious nonlinear distortion effects, and greatly improve the efficiency.

### Massive MIMO-OFDM downlink system model

We consider a massive MIMO-OFDM downlink scheme with various numerologies. The BS has Mt antennas that serve Mr single-antenna users with different numerologies over a frequency-selective channel, where Mt is far larger than Mr. NUM numerologies, represented by index num, where num = 1, …,NUM, can be used to divide the Mr users into NUM groups. Nnum and CPnum denote the IFFT/FFT size and CP size of group num, respectively. The proposed transceiver architecture differs from that of [86], in which we added zeros to each user’s signal structure to allow flexible INI management. Our transceiver can suppress Intra-NI by using several precoders in this way, and the added zeros enable INI cancellation, which will be addressed later. The BS sends data, over the mt-th antenna, to the mr-th user via channel √ αmrhtmr,mt , where αmr is the large-scale fading, htmr,mt ∈ C1×D is the channel impulse response between transmitting antenna mt and user mr, mt = 1…Mt, mr = 1…Mr and D is the number of taps. Then, hf(num) mr,mt = FFT(√ αmrhtmr,mt ,Nnum).

#### Massive MIMO-OFDM uplink : INI theoretical analysis

The uplink system is the reverse of the downlink system introduced in the previous section. We consider a single-cell massive MIMO-OFDM uplink system, where Mt single-antenna users that are

using different numerologies, transmit signals to a BS equipped with Mr antennas, over a frequencyselective channel. Note that in the uplink system, Mr is significantly larger than Mt due to the fact that now the BS is the receiver. The users can be also divided into NUM groups using NUM numerologies. Other definitions such as channel response remain the same with the previous section. We also use two users (Mt = 2) with two different numerologies, as shown on FIGURE 2.9. Considering the generalized synchronized scenario, similar as before, we assume that N1 = N × N2,CP1 = N × CP2 , where N = 2i and i is an integer [12]. At the BS side, the received signal is separated into two branches and the data stream are then detected through linear processing by two ZF detectors P ¯ (1) ∈ C2×Mr×N1 and P ¯ (2) ∈ C2×Mr×N2 .

**Downlink INI cancellation**

Only numerologies with large IFFT/FFT sizes suffer from INI as compared to numerologies with small IFFT/FFT sizes, as seen in the previous sections. In massive MIMO systems, only the uplink transmission estimates the maximum channel state. The uplink channel estimation is used for precoding in the downlink transmission, but discrepancies between the uplink and downlink channels are adjusted by a reciprocity adjustment method [90]. In this regard, the proposed INI cancellation approach is implemented at the BS side, so the receivers are not incredibly complex. At the BS side, FIGURE 2.10 illustrates the proposed INI cancellation method’s scheme. The key concept is to measure the INI from numerology 2 to numerology 1 ahead of time using knowledge of the MIMO channel response and signals following user 2’s precoding. Then, instead of transmitting s1, we transmit ˜︁s1 = s1 − ini(2,1) in the transmission part. As we demonstrated in section 2.2.2, this calibration does not introduce any INI at user 2, and our proposed transmission scheme perfectly protects the transmission of user 2. The transmit power with INI cancellation is pTx = pu + pini, where pu is the power allocated to users and pini is the power allocated to INI cancellation. It is worth noting that in equation (2.25), ρ is adjusted to fulfill the constraint imposed by the total transmit power pTx when taking the pini into account. According to some simulations, the pini is insignificant compared to the power allocated to users (pu), and it is worth noting that this would result in a minor.

**Table of contents :**

Acknowledgements

List of Tables

List of Figures

R´esum´e d´etaill´e de la th`ese

General Introduction of the thesis

**1 Technical background **

1.1 Wireless communication systems : 5G and beyond

1.2 Massive MIMO

1.2.1 Precoding

1.2.2 Null space

1.2.3 Degrees of freedom

1.3 Numerologies

1.4 Propagation channels

1.4.1 Channel characterization

1.4.2 Channel taps distribution

1.5 PA

1.5.1 PA characteristics

1.5.2 PA model

1.5.3 PA nonlinear compensation

**2 Massive MIMO for Inter-numerology interference cancellation **

2.1 Introduction

2.2 Massive MIMO-OFDM downlink : INI theoretical analysis

2.2.1 Massive MIMO-OFDM downlink system model

2.2.2 Inter-numerology interference analysis

2.3 Massive MIMO-OFDM uplink : INI theoretical analysis

2.3.1 Massive MIMO-OFDM uplink system model

2.3.2 Inter-numerology interference analysis

2.4 INI cancellation

2.4.1 Downlink INI cancellation

2.4.2 Uplink INI cancellation

2.5 Simulation results

2.5.1 Parameters

2.5.2 Downlink simulation results

2.5.3 Uplink simulation results

2.5.4 Multi-user cellular system

2.6 Conclusion

**3 NL Distortion-aware MU Precoding for massive MIMO Downlink under PA nonlinearities **

3.1 Introduction

3.2 Massive MIMO Dwonlink system model

3.3 Existing transmission schemes

3.3.1 Reference 1 and 2 :

3.3.2 Scheme 1 : ZF precoding + PAPR reduction using null-space + DPD

3.3.3 Scheme 2 : joint precoding and PAPR reduction using null-space [1]+ DPD . . 96

3.3.4 Scheme 3 : Joint precoding, PAPR reduction and DPD [2]

3.4 Proposed new scheme : Joint MU precoding and PAPR reduction without null-space + DPD

3.5 Complexity analysis

3.6 Simulation results

3.6.1 System parameters

3.6.2 Performance results

3.6.3 Complexity comparison

3.7 Conclusion

**4 End-to-end learning based massive MU-MIMO Downlink via deep autoprecoder **

4.1 Introduction

4.2 System model

4.3 Proposed autoprecoder structure and learning solution

4.3.1 Autoprecoder structure

4.3.2 Implementation details

4.4 Computational Complexity Analysis

4.5 Simulation Results

4.6 Conclusion

**5 Conclusion and Perspectives **

5.1 Conclusion

5.2 Perspectives

**Bibliographie **