Eric Pierre Simon
email: eric.simon@univ-lille.fr.

Joumana Farah
email: joumana-farah@ul.edu.lb.

Pierre Laly

Performance Evaluation of Massive MIMO with Beamforming and Non Orthogonal Multiple Access based on Practical Channel Measurements

Keywords: Massive MIMO, NOMA, Zero-Forcing Beamforming, Maximum Ratio Transmission Beamforming, Power Allocation, Channel sounding

This paper presents a comprehensive performance analysis of a massive multiple-input multiple-output (MIMO) system using non-orthogonal multiple access (NOMA) in both indoor and outdoor environments, based on practical channel measurements. The latter are performed using frequency-domain channel sounding experiments conducted at 3.5 GHz with 18 MHz bandwidth. Multi-user beamforming and NOMA clustering are used in the massive MIMO system. The system performance is evaluated in terms of sum-rate capacity for two precoding schemes: zero-forcing (ZF) and maximum ratio transmission (MRT). Two inter-beam power allocation (PA) schemes are investigated: equal PA and water filling. Fractional transmit PA (FTPA) is used to perform intra-cluster PA between paired users. The study allows the identification of practical scenarios that are propitious to NOMA with beamforming. Results show that NOMA is particularly interesting with MRT, compared to ZF, especially when combined with water filling. However, ZF generally outperforms MRT for all system configurations.

I. INTRODUCTION

With the advent of 5G communications, Non Orthogonal Multiple Access (NOMA) has recently spurred a large amount of research work in a broad range of applications [START_REF] Liu | Non orthogonal multiple access for 5G and beyond[END_REF]. By a judicious power multiplexing, NOMA greatly outstrips the performance of its predecessor OMA (Orthogonal Multiple Access), widely used in 4G systems. It has also proved to be an important ally of multi-antenna transceivers in leveraging both energy and spectral efficiency of wireless systems, either in collocated [START_REF] Sun | Joint beamforming and power allocation design in downlink non-orthogonal multiple access systems[END_REF] [START_REF] Youssef | Waterfillingbased resource allocation techniques in downlink non-orthogonal multiple access (NOMA) with single-user MIMO[END_REF] or distributed antenna configurations [START_REF] Farah | Power minimization in distributed antenna systems using non-orthogonal multiple access and mutual successive interference cancellation[END_REF]. Power-domain NOMA allows multiplexing two or several users on the same frequency subband by taking advantage of their channel gain difference [START_REF] Benjebbour | System-level performance of downlink NOMA for future LTE enhancements[END_REF]. At the receiver, user separation is done using successive interference cancellation (SIC). The use of NOMA in MIMO systems with zero-forcing (ZF) beamforming (BF) is explored in [START_REF] Kim | Non-orthogonal multiple access in a downlink multiuser beamforming system[END_REF] where clustering and PA are done so as to minimize inter-cluster and interuser interference. In [START_REF] Sun | Joint beamforming and power allocation design in downlink non-orthogonal multiple access systems[END_REF], joint optimization of BF and power allocation (PA) is considered for both best-effort and rateconstrained users, with random user pairing. [START_REF] Xiao | Joint power allocation and beamforming for non-orthogonal multiple access (NOMA) in 5G millimeter-wave communications[END_REF] considers a two-user single-beam MIMO system with intra-beam PA for sum-rate maximization. In [START_REF] Ali | Non-orthogonal multiple access (NOMA) for downlink multiuser MIMO systems: User clustering, beamforming, and power allocation[END_REF], a ZF BF technique is proposed for downlink MIMO-NOMA, with dynamic PA and userclustering so as to mitigate inter-cluster interference. [START_REF] Sun | Joint beamforming and power allocation design in downlink non-orthogonal multiple access systems[END_REF] [6] [START_REF] Xiao | Joint power allocation and beamforming for non-orthogonal multiple access (NOMA) in 5G millimeter-wave communications[END_REF] [START_REF] Ali | Non-orthogonal multiple access (NOMA) for downlink multiuser MIMO systems: User clustering, beamforming, and power allocation[END_REF] show the important gain obtained with NOMA vs. OMA in the MIMO-BF context; nevertheless, these works are based on simulated transmission environments. It is not straightforward to validate their results in practical scenarios; more specifically, the design of user clustering and BF in indoor and outdoor is essential to confirm the viability of NOMA with massive MIMO in realistic environments. In [START_REF] Mart´inez | An experimental study of massive MIMO properties in 5G scenarios[END_REF], the results of channel measurement campaigns for massive MIMO with OMA are analyzed to validate three theoretical characteristics of massive MIMO systems: channel hardening, user orthogonality, and spatial covariance matrix rank. In [START_REF] Benjebbour | Combination of NOMA and MIMO: concept and experimental trials[END_REF], experimental measurements of user throughput are conducted in outdoor, for NOMA with open-loop 2x2 or 4x2 MIMO, to validate the system-level performance of MIMO-NOMA for two or three users in the system. To the best of our knowledge, no previous work has tackled the validation of NOMA clustering and BF in massive antenna transmission through practical channel sounding techniques. This paper aims at studying the viability of NOMA when combined with massive MIMO, by drawing important conclusions on the user positions propitious for clustering, depending on the environment and the PA and BF techniques. To this aim, this letter is organized as follows:

In section II, we start by describing the experimental setup used in our channel measurement campaign. Then, section III is dedicated to the system model adopted for the integration of channel measurements. Section IV describes the NOMA clustering and PA techniques used in our system. Throughput analysis is conducted in section V for different transmission scenarios and environments.

II. CHANNEL MEASUREMENTS

In this section, we present the measurement campaigns performed on massive MIMO channels, on which we base our study to assess the system performance with different BF and PA strategies. We start by introducing the measurement equipment. Then, we describe the outdoor and indoor environments where measurements are carried out.

A. Measurement setup

Narrowband frequency-domain channel sounding measurements [START_REF] Sanchis-Borras | Performance evaluation of MIMO-OFDM in tunnels[END_REF] are performed in indoor and outdoor. A vector network analyzer (VNA) of type Agilent Technologies E5071C is used to probe the radio channel in an 18 MHz bandwidth centered at 3.5 GHz. In this frequency band, 1200 uniformly spaced frequency points (subcarriers) are sampled with a frequency spacing of 15 KHz, corresponding to the LTE/LTE Advanced mobile system parameters [START_REF]Physical Layer Aspects for Evolved UTRA[END_REF]. The feeder cables for the transmitting and receiving antennas are MegaPhase high performance RF coaxial cables. They are included in the VNA calibration so that their effect is canceled in the channel measurement. At the transmitter, a virtual 2-D patch antenna array is created by an automated displacement system driven by a stepper motor. The virtual array is a vertical uniform rectangular array (URA), where measurements are performed over a 10 × 10 rectangular grid with 0.5λ spacing along X and Y, λ being the wavelength at 3.5 GHz. For each antenna position, the VNA acquires 10 successive realizations of the whole frequency range, which are then averaged for the reduction of measurement noise. The receiver is equipped with a single fixed antenna. This antenna is the EM-6116 omnidirectional antenna in our outdoor measurements, whereas a patch antenna is used for indoor. In indoor, both transmit and receiver antennas are positioned at 1.50m above ground level. In outdoor, the transmitter is positioned at a height of approximately 10m in order to imitate a cellular configuration with a base station. Fig. 1 shows the transmitter (Tx) and receiver (Rx) in the outdoor environment. Note that the measurement campaign is carried out outside the regular working hours, because channel sounding with virtual antenna arrays requires a static radio channel without motion. The set of measurements is constituted by fixing the Tx position while moving Rx at different positions.

B. Measurement Environments

The outdoor environment considered in this study is a semiurban area located at the campus of the university of Lille, France. Fig. 2 presents the measurement environment with the Tx (in red) and Rx antenna locations. A total of 8 Tx-Rx links is measured in outdoor, corresponding to Rx i

(i = 1, • • • , 8) in

III. SYSTEM MODEL

Consider a downlink massive MIMO system with K users. The Tx plays the role of a base station (BS) equipped with M = 100 antennas, while each position of the Rx corresponds to a different user equipped with a single antenna. The BS performs BF with N beams (N ≤ K ≤ M ). The grouping of multiple users within the same beam using NOMA is defined as a cluster. In this study, the maximum number of users per cluster is two. Let h n,1 and h n,2 denote their 1 × M channel vectors. In each cluster, the user having the higher (resp. lower) channel gain h n,1 (resp. h n,2 ) is defined as the strong (resp. weak) user, and is referred to by index 1 (resp. 2). The number of clusters is C ≤ N , i.e., some of the beams support single users. Hereafter, we describe the transceiver system for a given frequency subband. Nevertheless, for the sake of notation concision, the subband index is dropped in the following expressions. Let x n be the signal transmitted on beam n with power P n . The signal transmitted by the multiantenna system is an M × 1 vector defined as follows:

x = N n=1 P n w n x n , (1)
where w n is the n th row of the M × N precoding matrix W.

In a two-user beam, x n is decomposed as

x n = √ α n,1 s n,1 + √ α n,2
y n,i = h n,i x + n n,i , i = 1, 2 and n = 1, • • • , C, (2)
where y n,1 and y n,2 are the received signals for the strong and the weak users, respectively. n n,i is an i.i.d. additive white complex Gaussian noise (AWGN) with zero mean and variance σ 2 n . For single-user beams:

y n = h n x + n n , n = C + 1, • • • N. (3)
Similarly to [START_REF] Kim | Non-orthogonal multiple access in a downlink multiuser beamforming system[END_REF], BF is performed based on the channel gains of the strong users in clusters. An N × M channel matrix H is constituted by the channel vectors of the strong users within clusters and unique users of single-user beams:

H = h T 1,1 , • • • , h T C,1 , h T C+1 , • • • , h T N T . (4)
For ZF BF, precoding is done using W = H H (HH H ) -1 , while for MRT W = H H . Then, the beams precoding vectors are obtained by normalizing each column of W, i.e. w n = wn wn , where wn is the n th column of W.

The received signal of the strong user in a cluster can be decomposed as:

y n,1 = g n,1,n P n α n,1 s n,1 + g n,1,n P n α n,2 s n,2 + N k=1,k =n g n,1,k P k x k + n n,1 , n = 1, • • • , C (5)
where the equivalent channel gains are given by g n,1,k = h n,1 w k . The first three terms in (5) correspond respectively to the useful signal, intra-cluster interference (ICI) and interbeam interference (IBI). As in classical single-input singleoutput (SISO) NOMA, the strong user can remove ICI by SIC. In the case of ZF BF, IBI can be canceled since g n,1,k = 0 for k = n. The received signal of a weak user is similar to [START_REF] Benjebbour | System-level performance of downlink NOMA for future LTE enhancements[END_REF]. However, ICI is not canceled at the level of weak users. Assuming perfect SIC, the received SINRs are:

SINR n,1 = |g n,1,n | 2 P n α n,1 N k=1,k =n |g n,1,k | 2 P k + σ 2 n (6) SINR n,2 = |g n,2,n | 2 P n α n,2 |g n,2,n | 2 P n α n,1 + N k=1,k =n |g n,2,k | 2 P k + σ 2 n (7) For a user in beam n = C + 1, . . . , N , g n,k = h n w k : SINR n = |g n,n | 2 P n N k=1,k =n |g n,k | 2 P k + σ 2 n . (8)

IV. CLUSTERING TECHNIQUE AND POWER ALLOCATION

The NOMA clustering technique used in this work is inspired from [START_REF] Kim | Non-orthogonal multiple access in a downlink multiuser beamforming system[END_REF], where a correlation threshold ρ is used. However, unlike [START_REF] Kim | Non-orthogonal multiple access in a downlink multiuser beamforming system[END_REF] which considers a fixed number of clusters regardless of the number of active users in the system, here all users are served simultaneously on all subbands. More specifically, our clustering algorithm starts by identifying the set of user pairs that present a channel correlation exceeding ρ. From this set, the user pair that presents the highest channel difference (estimated by h n,1 -h n,2 ) is selected to constitute the first beam. These users are then removed from the user set. The search is iterated until no more user pair has a correlation higher than ρ. The remaining users are then allocated to separate beams. As for PA, it is performed in two steps. First, inter-beam PA is realized to determine P n , n = 1, . . . , N . Two different schemes are studied in this context: equal power and waterfilling inter-beam PA. Inspired from the work in [START_REF] Hojeij | Resource allocation in downlink non-orthogonal multiple access (NOMA) for future radio access[END_REF], where water-filling is used for inter-subband allocation in SISO NOMA, in this work, P n , n = 1, . . . , C, is determined by the channel gain of the strong user in cluster n. Then, in a second step, intra-beam PA is performed, where α n,i , i = 1, 2, are determined using Fractional Transmit Power Allocation (FTPA) [START_REF] Benjebbour | System-level performance of downlink NOMA for future LTE enhancements[END_REF].

V. PERFORMANCE EVALUATION AND CONCLUSION

In this section, we assess the performance of the studied massive MIMO NOMA system with our channel measurements, under different PA and BF strategies. 12 frequency subbands of 100 subcarriers are considered. BF and PA are performed separately on each subband, and the obtained spectral efficiency (calculated using Shannon capacity, based on the estimated SINRs) is averaged over all subbands. As our main goal is to assess the practical performance of NOMA in massive MIMO, each studied user set configuration is taken such that at least one NOMA pair can be formed among the considered users, i.e., at least one user pair fulfills the clustering requirements. For the outdoor scenario, two user sets are defined: O 1 = {Rx 1, Rx 2, Rx 4, Rx 8} and O 2 = {Rx i, i = 1, . . . , 8}. For indoor, we consider: I 1 = {Rx 1, Rx 2, Rx 3, Rx 7}, I 2 = {Rx 5, Rx 6, Rx 7, Rx 9}, and

I 3 = {Rx 1, Rx 2, Rx 3, Rx 5, Rx 7, Rx 8}.
Fig. 3 shows the channel correlation of some user pairs examples as a function of the subcarrier index. The pairs selected for NOMA clustering are those presenting a correlation greater than the threshold ρ, fixed at 0.7 in this work: Rx2-Rx4 in outdoor, Rx1-Rx2 and Rx5-Rx6 in indoor, for most of the subbands. Indeed, as the correlation is subband dependent, user grouping can vary from a subband to another. As can be seen in Fig. 2, both outdoor Rx2-Rx4 and indoor Rx1-Rx2 NOMA pairs correspond to users sharing the same line of sight (Los), whereas the Rx5-Rx6 pair corresponds to users in two adjacent rooms, only separated by a plaster wall. This shows that, in addition to LoS users, NOMA clustering can be efficiently applied to users in different indoor conditions. Fig. 4 and Fig. 5 show the average throughput obtained for outdoor and indoor user sets respectively, for ZF and MRT BF, and equal power (EP) PA. The performance of OMA is also shown for comparison, where all beams are constituted by single users. The same behaviour is observed in both environments. Regarding MRT, NOMA outperforms OMA for the whole receive SNR (Signal to Noise Ratio) range and all user sets. This is due to the fact that NOMA groups users having strongly correlated channels. It is known that MRT performs well when users in different beams present a low correlation, and its performance quickly degrades when user correlation increases, due to inter-beam interference [START_REF] Larsson | Massive MIMO for next generation wireless systems[END_REF]. Therefore, by grouping the most correlated users within the same beam, NOMA is highly favorable to MRT.

When it comes to ZF, NOMA performs similarly or slightly better than OMA at low SNR, while OMA outperforms NOMA at high SNR. When NOMA is employed with ZF, two contradictory phenomena occur. On the one hand, the grouping of users reduces the number of beams compared to OMA. Recall that for ZF, h n w n = 1 wn . Due to Cauchy-Schwartz inequality [START_REF] Wolniansky | V-BLAST: An architecture for realizing very high data rates over the rich-scattering wireless channel[END_REF], the fewer rows of H that a particular wn is constrained to be orthogonal to, the smaller its norm, and thus the larger the equivalent channel gains g n,n , which is favorable for throughput performance. On the other hand, when NOMA clustering is applied, the weak user suffers from IBI and ICI, which degrades its performance compared to the case where this user occupies a single-user beam. At low SNR, the ICI and IBI powers are negligible with respect to the additive noise variance. Thus, the first phenomenon dominates. However, when the SNR increases, the ICI and IBI are no longer negligible and the second phenomenon dominates, resulting in a poor throughput for the weak user. To illustrate this, we report in Table I the throughput of each user in the set O 1 at SNR=10 and 40 dB, for the first subband. The loss of the weak user Rx 4 penalizes the performance of NOMA at SNR=40 dB compared to OMA. Globally, MRT is significantly outperformed by ZF for all SNR values, in both indoor and outdoor environments. This is due to the fact that MRT aims at maximizing the receive SNR while ZF aims at annihilating the correlation between beams. However, ZF necessitates a pseudo inverse of the channel matrix (H H (HH H ) -1 ) which has a complexity by the order of O(M 3 ). Therefore, an efficient implementation of ZF on transmitters with low resources and computational capacities may be unfeasible. When MRT is used in low-complexity transmitters, our study shows that NOMA can significantly increase the system performance.

When using water filling (WF) instead of EP, it is known that subbands having inverse channel gains above the water line are not allocated any power. Therefore, the number of useful beams varies with the SNR and it is inconvenient to show throughput curves in terms of SNR. Instead, some throughput values are reported in Table II. It is clear that the gain obtained with WF towards EP is particularly significant with NOMA for a low SNR.

In conclusion, several beamforming and power allocation scenarios are studied in this letter for a massive MIMO system, under practical channel measurements. The study shows that NOMA with ZF is especially interesting in low SNR regimes. In MRT, NOMA allows an important performance gain in all SNR regions, by judiciously clustering highly correlated users. However, MRT is significantly outperformed by ZF BF for all SNR values, in both indoor and outdoor environments. These conclusions are validated in both outdoor and indoor environments.

Fig. 1 :

 1 Fig. 1: Practical setup for channel measurements

  Fig. 2 left. The indoor environment is the first floor of a typical office building on the campus. Two rows of rooms are situated on both sides of a 40m long corridor. The office rooms are separated by plaster walls. A map of this scenario is shown

Fig. 2 :

 2 Fig. 2: Outdoor (left) and indoor (right) environments with Tx and Rx locations

  s n,2 , where s n,1 and s n,2 are the transmitted signals of the strong and weak users respectively, with α n,1 + α n,2 = 1. Without loss of generality, the first C beams are clusters, while the subsequent ones are single-user beams. E[|s n,i | 2 ] = 1, n = 1, • • • , C, i = 1, 2, and E[|x n | 2 ] = 1, n = 1, • • • , N . The received signals for the users belonging to clusters are:

1 Fig. 3 :Fig. 4 :Fig. 5 :

 1345 Fig. 3: Channel correlation for different user pairs as a function of the subcarrier index

TABLE I :

 I Throughput of EP in bits/s/Hz for users in O1.

			ZF			MRT
			OMA	NOMA	OMA	NOMA
	O 1	SNR=10 dB SNR=30 dB	9.3-8.2 28.6-27.4 23.2-22.3 10-8.7	5.6-5.2 6.1-6.2 11.8-10.8 8.8-7.5
	I 1	SNR=10 dB SNR=30 dB	5.4-3.9 21.3-21.2 18.2-18.1 6.9-5.1	2.2-2.1 6.3-6.4	6.9-3 8.4-8.1

TABLE II :

 II Throughput of WF vs. EP in bits/s/Hz, for O1 and I1.


L Romero-Resendiz

I A Figueroa

C Reyes-Ruiz

J M Cabrera

C Braham

G Gonzalez

Residual stresses and microstructural evolution of ECAPed AA2017

Keywords:

The mechanical behavior and microstructural evolution of an AA2017 aluminum alloy processed by ECAP with an equivalent simple shear deformation of ∼6 at 200 °C were studied. Samples were characterized by means of scanning electron microscopy (SEM-EDS-EBSD), image-assisted by focus ion beam (FIB), Vickers microhardness and X-ray diffraction (XRD) techniques. During the deformation process, the Al 2 Cu precipitates did not get fragmented or re-absorbed in the Al matrix. After the first ECAP pass, at least 50% of grains displayed an ultrafine size. The EBSD analysis showed an increment of the misorientation angle immediately after the first ECAP pass. The macrotexture evolution was explained in terms of the formation of f1:

* and f3: C θ , B θ , θ , A θ , Ā θ , A 2θ * fibers. The macro-residual stress measurements of the highly deformed samples showed linear sin 2 ψ profiles. The micro and macro-residual stresses were compatible with dislocation rearrangement, in which the annihilation and formation were in quasi-equilibrium. It was found that the highest microhardness value (1176 MPa) and grain refinement (at least 20% of grains showed a size smaller than 100 μm 2 ) appeared after the first extrusion pass. The decrease in hardness, after the second pass and the residual stress stability, could be associated to a dynamic recovery phenomenon.

Introduction

One of the most recurrent techniques of severe plastic deformation for obtaining grain refinement and nanostructures is the equal channel angular pressing (ECAP) [START_REF] Figueiredo | Fabricating ultrafine-grained materials through the application of severe plastic deformation: a review of developments in Brazil[END_REF][START_REF] Valiev | Bulk nanostructured materials from severe plastic deformation[END_REF]. The importance of ECAP process is related to many factors such as the feasibility of implementation, the possibility of using the process in several alloys and the improvement of some mechanical properties without, significantly, deteriorating the thermal or electrical properties [START_REF] Higuera | Microstructure influencing physical and mechanical properties of electrolytic tough pitch copper produced by equal channel angular pressing[END_REF]. It is well known that important microstructural changes occur after the firsts ECAP passes, for instance, Iwahashi et al. [START_REF] Iwahashi | An investigation of microstructural evolution during equal-channel angular pressing[END_REF] reported a grain refinement from 1 mm to 4 μm with a single ECAP pass. However, the subsequent passes are necessary to achieve large grain misorientation angles [START_REF] Mazurina | Effect of deformation temperature on microstructure evolution in aluminum alloy 2219 during hot ECAP[END_REF][START_REF] Golobororodko | Effect of pressing temperature on fine-grained structure formation in 7475 aluminum alloy during ECAP[END_REF] and to improve the microstructural homogeneity of the alloy. It was also reported that the microstructure could vary on the highly deformed samples as a function of the processing route [START_REF] Iwahashi | Factors influencing the equilibrium grain size in Equal-Channel angular pressing: role of mg additions to aluminum[END_REF]. Other reports have identified that among the different processing routes, the route named Bc, generates a greater homogeneity of crystalline orientations [START_REF] Kim | Effect of equal channel angular pressing routes on high-strain-rate deformation behavior of ultra-fine-grained aluminum alloy[END_REF] and equiaxed microstructure in the extruded products [START_REF] Venkatachalam | Effect of processing routes on microstructure and mechanical properties of 2014 Al alloy processed by equal channel angular pressing[END_REF][START_REF] Langdon | Using Equal-Channel angular pressing for refining grain size[END_REF].

A number of aluminum (Al) alloys have been processed by ECAP, but specifically for the 2017 Al alloy (AA2017), the number of reports are very scarce, even though this alloy is widely used in the automotive and aeronautical sectors (due to their high fracture toughness and corrosion resistance). Because of the cracking phenomenon that occurs at room temperature extrusion of this alloy [START_REF] Rekik | Recovery of industrial and recycled Al-Cu alloys subjected to severe plastic deformation[END_REF], there is only one report that has succeeded in ECAPing the AA2017, but in an overaged condition (350 °C for 1 h), resulting in a decrease in hardness due to recrystallization [START_REF] Rekik | Recovery of industrial and recycled Al-Cu alloys subjected to severe plastic deformation[END_REF]. In addition to the above-mentioned AA2017 report, other studies of Al-4 wt% Cu alloys, deformed by ECAP, have been reported. These focused on the precipitates morphology after the ECAP process and the subsequent hardening [START_REF] Prados | The effect of Al2Cu precipitates on the microstructural evolution, tensile strength, ductility and work-hardening behaviour of a Al-4 wt% Cu alloy processed by equal-channel angular pressing[END_REF][START_REF] Xiao-Chang | Evolution of precipitates of Al-Cu alloy during equal-channel angular pressing at room temperature[END_REF][START_REF] Liu | On strain-induced dissolution of θ´and θ particles in Al-Cu binary alloy during equal channel angular pressing[END_REF].

Other Al-Cu based alloy compositions processed by ECAP have also been studied with the aim of reporting the fracture behavior, i.e. the transformation of a brittle fracture to ductile mode [START_REF] Aal | The effect of the pre-homogenization treatment on the fracture characteristics and wear properties of ECAPed Al-Cu alloys[END_REF][START_REF] Zhang | Cyclic deformation and fatigue properties of Al-0.7 wt.% Cu alloy produced by equal channel angular pressing[END_REF]. For instance, the 2219, 2024 and 2014 alloys were ECAPed, and the effect of the process on 2219 alloy was reported in terms of the microstructural changes that can be subdivided into three stages: 1) an incubation period for new grain evolution, 2) grain fragmentation by frequent formation of deformation bands and 3) full development of new fine grains [START_REF] Mazurina | Grain refinement in aluminum alloy 2219 during ECAP at 250°C[END_REF]. Besides, the results for the 2024 and 2014 alloys reported a considerable improvement in mechanical properties as a consequence of the ECAP passes [START_REF] Kim | Optimization of strength and ductility of 2024 Al by equal channel angular pressing (ECAP) and post-ECAP aging[END_REF][START_REF] Kaibyshev | Effect of ECAP on mechanical properties of an AA2014 alloy[END_REF][START_REF] Ventakatachalam | Effect of processing routes on microstructure and mechanical properties of 2014 Al alloy processed by equal channel angular pressing[END_REF].

Reports on the residual stress generated by ECAP are also rare. Previous results [START_REF] Reyes-Ruiz | Residual stress distribution of a 6061-T6 aluminum alloy under shear deformation[END_REF] showed that the residual stress values strongly depend on the inner or outer faces and the friction effects between the die-set and the sample in the study. On the other hand, there are some reports, in ECAPed Al alloys, related to texture analysis. For instance, El-Danaf reported the effect of extrusion die-angles on the texture after a single ECAP pass [START_REF] El-Danaf | Mechanical properties, microstructure and texture of single pass equal channel angular pressed 1050, 5083, 6082 and 7010 aluminum alloys with different dies[END_REF]. Similarly, Hoseini et al. compared different processing routes [START_REF] Hoseini | Texture contribution in grain refinement effectiveness of different routes during ECAP[END_REF], indicating that the grain refinement effectiveness during ECAP depends on the die angle and the sample rotation between passes.

Due to the lack of information related to residual stresses, hardness and texture on this particular alloy, the objective of this work was to evaluate the ECAP effects on the microstructural evolution, including the grains morphology and size, precipitates and texture in an AA2017. The residual stresses and hardness profile as a measure of strain homogeneity were also assessed. This work introduces the measurement of near surface residual stresses in order to evaluate the importance of friction between the ECAP die and the sample.

Experimental procedure

Commercially available AA2017-T6 (Al-3.83Cu-0.62Mn-0.58 Mg-0.55Si-0.51Fe-0.08Zn-0.04Cr-0.04Ti-0.11other, in wt%) bars were used as starting material. The alloy was annealed at 400 °C for 1 h and then furnace-cooled. The particular process was carried out in order to facilitate the extrusion by partial over-aging of the Al 2 Cu precipitates. A D2 steel die was used for the ECAP process. Samples with dimensions of 60 mm in length and 10 mm in diameter were used for the extrusion process at room temperature. The die has an inner angle of ϕ = 90°, an outer curvature Ψ = 37°and a channel diameter of 10 mm. This die geometry generates a shear strain of ∼0.99 for every ECAP pass, as previously reported [START_REF] Reyes-Ruiz | Residual stress distribution of a 6061-T6 aluminum alloy under shear deformation[END_REF]. The schematic representation of the experimental setup and the place where the samples were taken for the different characterization are shown in Fig. 1. It is worthy to note that the ECAP die set was placed inside an electrically heated furnace in order to keep a constant working temperature of 200 °C. The Bc route (rotation along its longitudinal axis by 90°clockwise between each pass) was carried out. MoS 2 lubricant was used for reducing the friction between the sample and the die walls.

The samples were identified as 0P, 1P, 2P, 3P, 4P, 5P and 6P, where the prefix corresponds to the number of ECAP passes when completed. Previous to the microstructural examination, the surface of the samples was prepared, starting with SiC sandpaper of 800, 1200 and 2000, then diamond solutions of 0.3 and 0.1 μm were used to obtain a mirror appearance. A Focus Ion Beam apparatus (model JEM-9320FIB) was used for metallographic observation, as conventional etching did not reveal the sub-grain microstructure in optical microscopy. Grain size observation was performed on the extrusion plane (EP -Fig. 1). The XRD measurements were performed using a Rigaku Ultima IV diffractometer, with Cu-Kα radiation, crossbeam optics (CBO), 40 kV and 44 mA, with a step size of 0.02°and a scanning speed of 0.07°min -1 . For the texture analysis, Al pole figures of (111), ( 200) and (220) planes were obtained by employing a scanning range of α(0°-90°) and β (0°-360°). The 3D Explore 2.5 software and MTEX (MATLAB toolbox R2014b) were used for calculating the orientation distribution functions (ODF) and data displaying. For Electron Backscattering Diffraction (EBSD) the material was prepared using conventional metallographic preparation, then colloidal silica of 0.1 μm for the final stage. Ultrasonic cleaning was used for removing surface impurities. The EBSD analysis was carried out with a Jeol 7600F scanning electron microscope (15 kV) with a Bruker Quantax EBSD detector.

The macro residual strains and stresses (type I) were evaluated on the internal surface (IS) (Fig. 1), using the sin 2 ψ method, in which the stress is calculated using the slope of the graph epsilon versus sin 2 ψ (where ψ is the angle formed between the normal of the sample and the normal of the diffraction plane). The working (422) plane was used with at least 10 experimental ψ values (from -60°to 54°). The macroresidual stresses were evaluated on the internal surface, without any surface preparation. This is important to retain the residual stresses produced during the process.

Microresidual strain (type II) was performed in the normal plane (NP) (Fig. 1). The microstrains (Ɛ) were evaluated using a Williamson-Hall plot based on the reflection peaks (111), ( 200), ( 220), (311), ( 222) and (400). Profile matching with a constant scale factor method (FullProf released 2017) was used for calculating the peak broadening. The instrumental peak width was calculated using a LaB 6 standard Fig. 1. Schematic representation of the ECAP system used in this study and planes where the samples were taken for the characterization. ND, TD and ED are the normal, transversal and extrusion directions, and TP, EP and NP are the transversal, extrusion and normal planes, respectively. powder. The working method assumes a Lorentzian XRD peak profile, within this approximation; it is possible to separate the strain (ε) and crystallite size (D) effects from the integral breadth (β) peak, following Eq. ( 1):

= + cos D 1 4 sin (1)
Although the Williamson-Hall model is merely qualitatively, it can evidence the tendency between the number of ECAP passes and the accumulated strain and/or crystallite size. The plot of cos versus 2 sin gives directly the crystallite size and the strain from the ordinate intersection and the slope of the linear fit of the experimental points. Within this approach, a slope closed to zero means that the strain is negligible, however, if the slope values are different from zero, they represent the strain contribution to the broadening [START_REF] Gonzalez | Microstructure and texture of Al-2Si-xSn (x = 0, 4, 8 mass%) alloys processed by equal channel angular pressing[END_REF].

A Shimadzu microdurometer model HMV-G was used for the microhardness measurements; the load was 100 g for 10 s on the normal plane (NP) (Fig. 1). A standard of medium-carbon steel was used for calibrating the microhardness tester. Taking into account that 55 measurements were taken per sample, the experimental error was calculated using the standard deviation.

Results and discussion

In this study, the Al 2 Cu precipitates and the presence of Mg and Sirich compounds were observed as demonstrated in the micrographs obtained by SEM (Fig. 2a). From the EDS analysis (Fig. 2b), the black dots in the micrographs were identified as the Mg 2 Si phase, and the presence of these dots was mainly found at the center of Al 2 Cu precipitates. The Mg 2 Si precipitates were always observed independently of the degree of deformation applied. These precipitates have been seen in Al alloys with even lower contents of Mg and Si [START_REF] Cabibbo | A TEM study of the combined effect of severe plastic deformation and (Zr), (Sc + Zr)-containing dispersoids on an Al-Mg-Si alloy[END_REF]. Fig. 2c shows the identified characteristic phases for 1P sample, similar results were also found for 0P and 6P samples.

The presence of Al 2 Cu in 0P, 1P and 6P passes was confirmed by XRD, as shown in Fig. 3. The most intense peaks corresponded to Al and the weakest to the Al-Cu phase. Complementary, further evaluation of grain morphology, misorientation and size were carried out for a better understanding of the microstructural evolution of this alloy.

The ECAP process generated a substantial grain refinement. Fig. 4 shows the corresponding micrographs for 0P, 1P, 5P, and 6P obtained by FIB. With this technique, the erosion of Ga ions on the sample surface generated an orientation contrast. For the last ECAP passes, it was possible to observe zones with weak contrast. It is though that these zones were produced due to the existence of dislocations tangles, where grain misorientation is < 3°, coexisting with high angle grain boundary (HAGB). The grain refinement was clear, since the grain size dropped from 4 μm for 0P to 0.3 μm for 6P.

Fig. 5 shows the misorientation histogram of the highly deformed samples, for 1P and 6P. For samples 1P to 6P the tendency for subgrains formation with low angle grain boundaries (LAGB) was observed. The subsequent formation of HAGB was also corroborated by electron backscattering diffraction (EBSD). The micrographs obtained by EBSD indicated substantial grain refinement after the first ECAP pass, producing ultrafine grain sizes, as expected for Al alloys processed by ECAP. It is worthy to note that after the 1P sample the grain refinement was rather small. Fig. 6 shows the grain size histogram from 0P, 1P, and 6P samples, assuming for the histogram calculation, an equivalent radius. According to the data obtained, and as already mentioned, the grain refinement was observed for the first ECAP pass. For the initial condition (0P), a grain area smaller than 10,000 μm 2 , which corresponds to 30% of the studied zone, was determined. Similarly, for 1P and 6P samples, the results showed an area smaller than 100 μm 2 , corresponding to 23% and 15%, respectively. These results indicated a drop in grain size of two orders of magnitude.

At this stage, it can be assumed that the success of the severe plastic deformation process reported in this work was due to the over-aging of the Al 2 Cu precipitates. As it will be explained later, the Al 2 Cu phase effect on the hardening process can be considered negligible. Thus, the ECAP hardening could be exclusively attributed to grain refinement [START_REF] Kang | Microstructure evolution and hardening behavior of 2024 aluminum alloy processed by the severe plastic deformation[END_REF]. Furthermore, the ECAP process did not generate any re-absorption of Al 2 Cu precipitates, but it cannot be denied that other precipitates could have partially disappeared during the process, although further investigation is highly pertinent to confirm this point. On the other hand, the increase of low angle grain boundaries could also be associated with the dislocation density, which was produced by the shear deformation process. The dislocation cells tended to accommodate in such fashion that produced high angle grain boundaries, as it has already been reported [START_REF] Hernández | Microstructure and texture evolution of the Al-20Sn alloy processed by Equal-Channel angular pressing using route C[END_REF].

Another aspect for evaluating the microstructural change is the orientation or randomness of the processed grains. For this purpose, the analysis of the macrotexture evolution was performed in all samples, using the normal plane (NP), as illustrated in Fig. 1. The pole figures are shown in Fig. 7. At the initial condition (Fig. 7-0P) two partial fibers were observed. They were designated as 〈110〉 θ and {111} θ , respectively. An orientation along the 〈110〉 θ -fiber has a 〈110〉 θ -direction, which is counterclockwise rotated by θ = 90°from the ED, and orientation along the {111} θ -fiber has a {111}-plane counterclockwise rotated by θ from the ND-plane [START_REF] Li | Texture formation during equal channel angular extrusion of fcc and bcc materials: comparison with simple shear[END_REF]. The 1P sample (Fig. 6-1P) showed five different texture components, identified as A 2θ * , A 1θ * , C θ , A θ and Ā θ . These components are considered as the ideal ones for a simple shear process [START_REF] Li | Texture evolution during multi-pass equal channel angular extrusion of copper: neutron diffraction characterization and polycrystal modeling[END_REF]. The pole figures for the 2P sample (Fig. 7-2P), showed the components A θ , A 2θ * , B θ and B θ . The pole figures for the samples from 3P to 6P (Fig. 7-3P-6P) showed the disappearance of A θ , whilst the A 2θ * , B θ and B θ components displayed a decrement in in- tensity. The initial texture was strongly modified from the first to the third ECAP passes; however, it remained rather constant from the fourth to the sixth passes. Some shear components were found as expected, according to the literature [START_REF] Li | Texture evolution during multi-pass equal channel angular extrusion of copper: neutron diffraction characterization and polycrystal modeling[END_REF]. Not all texture maxima on the PFs are described within the A, B, and C components of the simple shear texture. Kocks et al. mentioned that highly deformed metals might release some of the lattice strain through recovery, without changing the texture [START_REF] Kocks | Preferred Orientations in Polycrystals and Their Effect on Materials Properties[END_REF]. On the contrary, recrystallization might produce different texture in the new grains. Nevertheless, in this case, such recrystallization tended to be rather limited, as the process temperature was carried out at 200 °C. Fig. 8 shows the total volume fraction as function of ECAP passes. It was observed that the total volume fraction decrease monotonously as a function of ECAP passes. These results suggest that the new grains are, mainly, randomly orientated.

The orientation distribution functions (ODFs) were calculated for a complete study of the sample texture and are presented in Fig. 9. This figure confirms the presence of the aforementioned deformation components. From the same image, the presence of the following fibers was observed, being labeled as:

f1 = A 1θ * -A θ /Ā θ -A 2θ * {111} θ , f2 = C θ
passes through B θ / B θ and Ā θ / A θ ending at A 1θ * and f3 = C θ -B θ / B θ -A θ / Ā θ 〈110〉 θ and A θ / Ā θ -A 2θ * {111} θ (symmetrical to the f2) [START_REF] Beyerlein | Texture evolution in equal-channel angular extrusion[END_REF]. The fibers intensity diminished after 3P sample for all fibers, showing a loss of symmetry intensity. These results indicated the strong effect of the deformation mechanism of the ECAP process over the sample texture. However, it is also important to evaluate the effects of the mechanical process on the generated residual stresses. This has been attributed to the accumulative dislocation density, stored energy in the sample and heterogeneity of deformation process. The macro residual stress distribution profiles were obtained from the inner surface of the ECAPed samples, as shown in Fig. 10. For 0P, a linear profile almost horizontal or neutral in terms of stresses was observed, this was expected as all the starting samples were annealed and therefore any stress tends to be released. Sample 1P showed a linear profile with a positive slope that indicated a tensile stress behavior. A linear profile also denotes an alignment of main stresses with the sample axes (absence of σ 13 o σ 23 ). In the case of the last ECAP passes (after 3P), a compressive stress slope profile was obtained. The compressive stress slopes are strongly related to the size of the highly deformed layer was produced due to friction effect between the die and the sample, during the ECAP process, as the size of this layer was proportional to the extrusion passes.

Fig. 11a displays the surface hardness for 0P and for 1P, 3P and 6P. Fig. 11b shows the residual stresses at the surface of the processed samples. Although there is no a correlation between the hardness and residuals stresses, in this particular case, the change in microhardness and the residual stresses showed, somehow, an asymmetric tendency, where both increased (in absolute values) as a function of the ECAP passes. The observed hardness drop, for samples 3P and 6P, was attributed to the dynamic recovery that was originated for the temperature (200 °C) used in the ECAP process.

The evolution of the micro-strain was obtained by means of the Williamson-Hall plots (Fig. 12). From this figure, the slopes, which correspond to 2Ɛ, increased as a function of ECAP passes. From the microstructural point of view, the ECAP process introduces a large number of dislocations. Therefore, it is anticipated an increment in the residual stress magnitude as a function of the number ECAP passes, however, such magnitude changed slightly for the last ECAP passes (3P-6P). This indicates that the process does influence a dislocation rearrangement. It is thought that this condition is due to the inherent nature of the recovery that is taking place at the present ECAP processing temperature.

Fig. 13a shows the Vickers microhardness measurements for 0P, 1P, 3P and 6P samples. In this figure, it was possible to evaluate the local hardness distribution from the internal to the external faces of the tested samples. The maximum hardness value was obtained for 1P sample (1176 ± 2 MPa), and then it dropped down to a rather constant value of 1081 ± 2 MPa, for the subsequent passes. This tendency can be clearly observed in Fig. 13b, where the bulk microhardness values are plotted, exhibiting the same behavior.

From the hardness evolution, the maxima and subsequent drop after 2 passes, could be explained in terms of partial dynamic recovery, as already stated. A similar phenomenon in an alloy of Al-1.7 at.% Cu processed by ECAP has been reported [START_REF] Murayama | Microstructure of two-phase Al-1.7 at% Cu alloy deformed by equal-channel angular pressing[END_REF], being attributed to this phenomenon. Here, the organization of the dislocation tangles gives way to new ordered borders with few dislocations inside the grain.

The lack of softening in the first ECAP pass can be explained regarding the limited occurrence of diffusional processes [START_REF] Rekik | Recovery of industrial and recycled Al-Cu alloys subjected to severe plastic deformation[END_REF]. It is well known that the diffusion is accelerated in SPD-processed metals due to the highly non-equilibrium grain boundaries [START_REF] Valiev | Principles of equal-channel angular pressing as a processing tool for grain refinement[END_REF] and internal stresses [START_REF] Bachmaier | Rate independent and rate dependent structural Fig. 13. Microhardness measurements a) line profile and b) bulk microhardness as a function of ECAP passes. evolution during severe plastic deformation[END_REF], therefore, it is necessary to increase the dislocation density, by work hardening, being generated after the first ECAP pass. Then, the sample extrusion temperature used in this study was high enough to accelerate the diffusive processes during the applied deformation in subsequent ECAP passes, as demonstrated in previous reports [START_REF] Liu | Influence of stacking fault energy and temperature on microstructures and mechanical properties of fcc pure metals processed by equal-channel angular pressing[END_REF][START_REF] Chinh | Experimental evidence for grainboundary sliding in ultrafine-grained aluminum processed by severe plastic deformation[END_REF]. Such phenomenon is more frequent in materials with a high stacking fault energy (SFE), as is the case for highly pure Al with an SFE reported in the literature of ~160 mJ/m 2 [START_REF] Liu | Influence of stacking fault energy and temperature on microstructures and mechanical properties of fcc pure metals processed by equal-channel angular pressing[END_REF][START_REF] Xue | Texture-directed twin formation propensity in Al with high stacking fault energy[END_REF]. In addition to the drop in hardness for sample 2P, the hardness values for the alloys with higher deformation passes are also congruent with the dynamic recovery process. These samples (2P to 6P) showed lower hardness values than those reported for similar compositions, after being subjected to the ECAP process [START_REF] El Aal | Wear properties of ECAP-processed ultrafine grained Al-cu alloys[END_REF][START_REF] Kaibyshev | Effect of ECAP on mechanical properties of an AA2014 alloy[END_REF]. The dynamic recovery effect of this system is not enough to avoid the formation of new grains in the last ECAP passes, as shown in Fig. 5. Here, the increment of grain misorientation angles indicates the possible dislocations re-arrangement, generated during the ECAP process.

Conclusions

From the results obtained in this study, the following conclusions can be considered as the most important:

1) The grain refinement was evident from the first ECAP pass, where at least 20% of grains showed a size smaller than 100 μm 2 . For 1P sample, 72% of low angle grain boundaries (LAGB) were observed, being the result of sub-grains formation due to the ECAP process.

2) The Al 2 Cu and Mg 2 Si precipitates did not change the morphology or size after the deformation process.

3) The formation of fibers f1, f2 and f3 were observed for all deformed samples. 4) The residual macro-stresses profile showed a neutral tendency for the initial condition, tensile behavior for 1P sample and compressive values from 3P to 6P samples. The maximum absolute value was obtained for the sample with 3 ECAP passes. This tendency is also congruent with the resultant surface hardness. 5) The hardness profile from the internal to external faces showed an augmentation of hardness after the first ECAP pass. Subsequently, a drop from 1P to 2P was observed. For the subsequent passes, the hardness values exhibited a rather constant trend. 6) For the last ECAP passes, the resultant low grain refinement, the drop of macro-residual stresses and surface hardness are congruent with a dynamic recovery phenomenon. Similarly, the low percentage of HAGBs and the almost constant values hardness profile can also be associated with this phenomenon.

Fig. 2 .

 2 Fig. 2. a) SEM images of the ECAPed samples, indicating the presence of Al 2 Cu phase and Mg 2 Si precipitates for the initial condition (0P) and 6P sample, b) EDS mapping of Al 2 Cu and Mg 2 Si phases, c) X-ray diffractogram for the alloy studied.

Fig. 3 .

 3 Fig. 3. XRD patterns for 0P, 1P and 6P samples.

Fig. 4 .

 4 Fig. 4.Representative FIB images showing the microstructures for initial condition (0P), first, fifth and sixth ECAP passes (1P, 5P, and 6P respectively). For a better grain size statistics, the image for 0P has been taken with less magnification. TD is transversal direction and ED extrusion direction.

Fig. 5 .

 5 Fig. 5. EBSD results showing the misorientation histograms and micrographs for samples a-b) 0P, c-d) 1P, and e-f) 6P, respectively.

Fig. 6 .

 6 Fig. 6. Grain size distribution 0P, 1P and 6P samples.

Fig. 7 .

 7 Fig. 7. Pole figures for samples 0P, 1P, 2P, 3P, 4P, 5P and 6P and key positions of ideal shear texture components for (111), (200) and (220) poles.

Fig. 8 .

 8 Fig. 8. Total volume fraction of texture components as function of ECAP passes.

Fig. 9 .

 9 Fig. 9. Orientation distribution functions (ODFs) for 1P, 3P, and 6P samples. The evolution of fibers f1, f2 and f3 are shown as dotted lines.

Fig. 9 .Fig. 9 .Fig. 10 .Fig. 11 .

 991011 Fig. 9. (continued)

Fig. 12 .

 12 Fig. 12. Microstrain values for 0P, 1P and 6P samples.

Acknowledgments

The authors would like to thank the funding support for this project by UNAM-DGAPA-PAPIIT [IN101917]. LR gratefully acknowledges the funding from scholarship CONACyT [592722]. Valuable technical support provided by A. Dutt, G. Lara, E. Hernández M., A. López-V., A. Tejeda, O. Novelo-Peralta, A. Amaro, J. Romero and C. Flores is also acknowledged.

Data availability statement

The raw data related to this manuscript would be made available on request.