Two of the most prominent techniques to meet the next generation wireless communication system's demands are cognitive radio and massive MIMO systems. Cognitive radio systems improve radio spectrum utilization either by spectrum sharing or by opportunistically utilizing the spectrum of the licensed users. Employing multiple antennas at the transmitter and/or the receiver of the radio can further improve the overall performance of the wireless systems. Massive MIMO systems, on the other hand, improve the spectral and energy efficiencies of currently deployed systems by reaping all the benefits of the multi-antenna systems at a very large scale. The price paid for employing a large number of antennas either at the transmitter or receiver is the high hardware cost. Judicious transmit or receive antenna selection can reduce this cost, while retaining most of the benefits offered by multiple antennas. In my doctoral research, we have presented both upper and lower bounds on the capacity of a general selection diversity system. These novel bounds are simple to compute and can be used in a variety of different fading environments. We have also proposed and analyzed the performance of different antenna selection schemes for both an underlay cognitive radio and a massive MIMO system. Specifically, we have considered both receive and transmit antenna selection in an underlay cognitive radio based on the maximization of secondary link signal-to-interference plus noise ratio. Exact and asymptotic performance analyses of the secondary system with such selections are carried out, and numerical examples are presented to verify the correctness of the analytical results. Several sub-optimal antenna subset selection schemes for both a single-cell and a multi-cell multi-user massive MIMO system are also proposed. Numerical results on the sum rate of the system in different scenarios are presented to verify the superior performance of the proposed schemes over the existing sub-optimal antenna subset selection schemes. Lastly, we have also presented three novel hybrid analog/digital precoding schemes to reduce the hardware and software complexities of a sub-connected massive MIMO system. / Graduate / 0544

The past decade has seen an enormous increase in the number of connected wireless devices, and currently there are billions of devices that are connected and managed by wireless networks. At the same time, the applications that are running on these devices have also developed significantly and became more data rate insatiable. As the number of wireless devices and the demand for a high data rate will always increase, in addition to the growing concern about the energy consumption of wireless communication systems, the future wireless communication systems will have to meet three main requirements. These three requirements are: i) being able to achieve high throughput; ii) serving a large number of users simultaneously; and iii) being energy efficient (less energy consumption). Massive multiple-input multiple-output (MIMO) technology can satisfy the aforementioned requirements; and thus, it is a promising candidate technology for the next generations of wireless communication systems. Massive MIMO technology simply refers to the idea of utilizing a large number of antennas at the base station (BS) to serve a large number of users simultaneously using the same time-frequency resources. The hypothesis behind using a massive number of antennas at the BS is that as the number of antennas increases, the channels become favourable. In other words, the channel vectors between the users and their serving BS become (nearly) pairwisely orthogonal as the number of BS antennas increases. This in turn enables the use of linear processing at the BS to achieve near optimal performance. Moreover, a huge throughput and energy efficiency can be attained due to users multiplexing and array gain. In this thesis, we investigate the performance of massive MIMO systems under different scenarios. Firstly, we investigate the performance of a single-cell multi-user massive MIMO system, in which the channel vectors for the different users are assumed to be correlated. In this aspect, we propose two algorithms for users grouping that aim to improve the system performance. Afterwards, the problem of pilot contamination in multi-cell massive MIMO systems is discussed. Based on this discussion, we propose a pilot allocation algorithm that maximizes the minimum achievable rate in a target cell. Following that, we consider two different scenarios for pilot sequences allocation in multi-cell massive MIMO systems. Lower bounds on the achievable rates are derived for two linear detectors, and the performance under different system settings is analysed and discussed for both scenarios. Finally, two algorithms for pilot sequences allocation are proposed. The first algorithm takes advantage of the multiplicity of pilot sequences over the number of users to improve the achievable rate of edge cell users. While the second algorithm aims to mitigate the negative impact of pilot contamination by utilizing more system resources for the channel estimation process to reduce the inter-cell interference.

The architecture of cellular networks has been undergoing an extraordinarily fast evolution in the last years to keep up with the ever increasing user demands for wireless data and services. Motivated by a search for a breakthrough in network capacity, the paradigm of heterogeneous networks (HetNets) has become prominent in modern cellular systems, where carefully deployed macrocells coexist with layers of irregularly deployed cells of reduced coverage sizes. Users can thus be offloaded from the macrocell and the capacity of the network increases. However, universal frequency reuse is usually employed to maximize capacity gains, thereby introducing the fundamental problem of inter-cell interference (ICI) in the network caused by the sharing of the spectrum among the different tiers of the HetNet. The objective of this PhD thesis is to provide analysis and mitigation techniques for the fundamental problem of interference in heterogeneous cellular networks. First, the interference of a two-tier network is modeled and analyzed by making use of spatial statistics tools that allow the reconstruction of complete coverage maps. A correlation analysis is then performed by deriving a spatial coverage cross-tier correlation function. Second, a novel architecture design is proposed to minimize interference in HetNets whose base stations may be equipped with very large antenna arrays, another key technology of future wireless systems. Then, we present interference mitigation techniques for different types of small cells, namely picocells and femtocells. In the third contribution of this thesis, we analyze the case of clustered deployments by proposing and comparing techniques suitable for this scenario. Fourth, we tackle the case of femtocell deployments by analyzing the degrading effect of interference and proposing new mitigation methods. Fifth, we introduce femtorelays, a novel small cell access technology that combats interference in femtocell networks and provides higher backhaul capacity.

Next generation wireless systems will support higher data rates, improved spectral efficiency, and less latency. Massive multiple-input multiple-output (MIMO) is proposed to satisfy these demands. In massive MIMO, many benefits come from employing hundreds of antennas at the base station (BS) and serving dozens of user terminals (UTs) per cell. As the number of antennas increases at the BS, the channel becomes sparse. By exploiting sparse channel in massive MIMO, compressive sensing (CS) methods can be implemented to estimate the channel. In CS methods, the length of pilot sequences can be shortened compared to pilot-based methods. In this paper, a novel channel estimation algorithm based on a CS method called elastic net is proposed. Channel estimation accuracy of pilot-based, lasso, and elastic-net based methods in massive MIMO are compared. It is shown that the elastic-net based method gives the best performance in terms of error for the less pilot symbols and SNR values.

Communications over millimeter wave (mmWave) frequencies is a key component of the fifth generation (5G) cellular networks due to the large bandwidth available at mmWave bands. Thanks to the short wavelength of mmWave bands, large antenna arrays (32 to 256 elements are common) can be mounted at the transceivers. The array sizes are typical of a massive MIMO communication system, which makes fully digital beamforming difficult to implement due to high power consumption and hardware cost. This motivates the development of hybrid beamforming due to its versatile tradeoff between implementation cost (including hardware cost and power consumption) and system performance. However, due to the non-convex constraints on hardware (phase shifters), finding the global optima for hybrid beamforming design is often intractable. In this thesis, we focus on hybrid beamforming design for mmWave cellular communications both narrowband and wideband scenarios are considered. Starting from narrowband SU-MIMO mmWave communications, we propose a Gram-Schmidt orthogonalization (GSO) aided hybrid precoding algorithm to reduce computation complexity. GSO is a recursive process that depends on the order in which the matrix columns are selected. A heuristic solution to the order of column selection is suggested according to the array response vector along which the full digital precoder has the maximum projection. The proposed algorithm, not only constrained to uniform linear arrays (ULAs), can avoid the matrix inversion in designing the digital precoder compared to the orthogonal matching pursuit (OMP) algorithm. For the narrowband MU-MIMO mmWave communications, we propose an interference cancellation (IC) framework on hybrid beamforming design for downlink mmWave multi-user massive MIMO system. Based on the proposed framework, three successive interference cancellation (SIC) aided hybrid beamforming algorithms are proposed to deal with inter-user and intra-user interference. Furthermore, the optimal detection order of data streams is derived according to the post-detection signal-to-interference- plus-noise ratio (SINR). When considering wideband MU-MIMO mmWave communications, how to design a common RF beamformer across all subcarriers becomes the main challenge. Furthermore, the common RF beamformer in wideband channels leads to the need of more effective baseband schemes. By adopting a relaxation of the original mutual information and spectral efficiency maximization problems at the transceiver, we design the radio frequency (RF) precoder and combiner by leveraging the average of the covariance matrices of frequency domain channels, then a SIC aided baseband precoder and combiner are proposed to eliminate inter-user and intra-user interference / Graduate

By endowing the base station with hundreds of antennas and relying on spatial multiplexing, massive multiple-input-multiple-output (MIMO) allows impressive advantages in many fronts. To reduce this promising technology to reality, thorough performance analysis has to be conducted. Along this line, this work is focused on the convenient high-dimensionality of massive MIMO’s corresponding model. Indeed, the large number of antennas allows us to harness asymptotic results from Random Matrix Theory to provide accurate approximations of the main performance metrics. The derivations yield simple closed-form expressions that can be easily interpreted and manipulated in contrast to their alternative random equivalents. Accordingly, in this dissertation, we investigate and optimize the performance of massive MIMO in different contexts. First, we explore the spectral efficiency of massive MIMO in large-scale multi-tier heterogeneous networks that aim at network densification. This latter is epitomized by the joint implementation of massive MIMO and small cells to reap their benefits. Our interest is on the design of coordinated beamforming that mitigates cross-tier interference. Thus, we propose a regularized SLNR-based precoding in which the regularization factor is used to allow better resilience to channel estimation errors. Second, we move to studying massive MIMO under Line-of-Sight (LoS) propagation conditions. To this end, we carry out an analysis of the uplink (UL) of a massive MIMO system with per-user channel correlation and Rician factor. We start by analyzing conventional processing schemes such as LMMSE and MRC under training-based imperfect-channel-estimates, and then, propose a statistical combining technique that is more suitable in LoS-prevailing environments. Finally, we look into the interplay between LoS and the fundamental limitation of massive MIMO systems, namely, pilot contamination. We propose to analyze and compare the performance using single-cell and multi-cell detection methods. In this regard, the single-cell schemes are shown to produce higher SEs as the LoS strengthens, yet remain hindered by LoS-induced interference and pilot contamination. In contrast, for multi-cell combining, we analytically demonstrate that M-MMSE outperforms both single-cell detectors by generating a capacity that scales linearly with the number of antennas, and is further enhanced with LoS.

3-dimensional (3D) massive multiple-input-multiple-output (MIMO)/full dimensional (FD) MIMO and application of artificial intelligence are two main driving forces for next generation wireless systems. This dissertation focuses on aspects of channel estimation and precoding for 3D massive MIMO systems and application of deep reinforcement learning (DRL) for MIMO broadcast beam synthesis. To be specific, downlink (DL) precoding and power allocation strategies are identified for a time-division-duplex (TDD) multi-cell multi-user massive FD-MIMO network. Utilizing channel reciprocity, DL channel state information (CSI) feedback is eliminated and the DL multi-user MIMO precoding is linked to the uplink (UL) direction of arrival (DoA) estimation through estimation of signal parameters via rotational invariance technique (ESPRIT). Assuming non-orthogonal/non-ideal spreading sequences of the UL pilots, the performance of the UL DoA estimation is analytically characterized and the characterized DoA estimation error is incorporated into the corresponding DL precoding and power allocation strategy. Simulation results verify the accuracy of our analytical characterization of the DoA estimation and demonstrate that the introduced multi-user MIMO precoding and power allocation strategy outperforms existing zero-forcing based massive MIMO strategies. In 3D massive MIMO systems, especially in TDD mode, a base station (BS) relies on the uplink sounding signals from mobile stations to obtain the spatial information for downlink MIMO processing. Accordingly, multi-dimensional parameter estimation of MIMO channel becomes crucial for such systems to realize the predicted capacity gains. In this work, we also study the joint estimation of elevation and azimuth angles as well as the delay parameters for 3D massive MIMO orthogonal frequency division multiplexing (OFDM) systems under a parametric channel modeling. We introduce a matrix-based joint parameter estimation method, and analytically characterize its performance for massive MIMO OFDM systems. Results show that antenna array configuration at the BS plays a critical role in determining the underlying channel estimation performance, and the characterized MSEs match well with the simulated ones. Also, the joint parametric channel estimation outperforms the MMSEbased channel estimation in terms of the correlation between the estimated channel and the real channel. Beamforming in MIMO systems is one of the key technologies for modern wireless communication. Creating wide common beams are essential for enhancing the coverage of cellular network and for improving the broadcast operation for control signals. However, in order to maximize the coverage, patterns for broadcast beams need to be adapted based on the users' movement over time. In this dissertation, we present a MIMO broadcast beam optimization framework using deep reinforcement learning. Our proposed solution can autonomously and dynamically adapt the MIMO broadcast beam parameters based on user' distribution in the network. Extensive simulation results show that the introduced algorithm can achieve the optimal coverage, and converge to the oracle solution for both single cell and multiple cell environment and for both periodic and Markov mobility patterns. / Doctor of Philosophy / Multiple-input-multiple-output (MIMO) is a technology where a transmitter with multiple antennas communicates with one or multipe receivers having multiple antennas. 3- dimensional (3D) massive MIMO is a recently developed technology where a base station (BS) or cell tower with a large number of antennas placed in a two dimensional array communicates with hundreds of user terminals simultaneously. 3D massive MIMO/full dimensional (FD) MIMO and application of artificial intelligence are two main driving forces for next generation wireless systems. This dissertation focuses on aspects of channel estimation and precoding for 3D massive MIMO systems and application of deep reinforcement learning (DRL) for MIMO broadcast beam synthesis. To be specific, downlink (DL) precoding and power allocation strategies are identified for a time-division-duplex (TDD) multi-cell multi-user massive FD-MIMO network. Utilizing channel reciprocity, DL channel state information (CSI) feedback is eliminated and the DL multi-user MIMO precoding is linked to the uplink (UL) direction of arrival (DoA) estimation through estimation of signal parameters via rotational invariance technique (ESPRIT). Assuming non-orthogonal/non-ideal spreading sequences of the UL pilots, the performance of the UL DoA estimation is analytically characterized and the characterized DoA estimation error is incorporated into the corresponding DL precoding and power allocation strategy. Simulation results verify the accuracy of our analytical characterization of the DoA estimation and demonstrate that the introduced multi-user MIMO precoding and power allocation strategy outperforms existing zero-forcing based massive MIMO strategies. In 3D massive MIMO systems, especially in TDD mode, a BS relies on the uplink sounding signals from mobile stations to obtain the spatial information for downlink MIMO processing. Accordingly, multi-dimensional parameter estimation of MIMO channel becomes crucial for such systems to realize the predicted capacity gains. In this work, we also study the joint estimation of elevation and azimuth angles as well as the delay parameters for 3D massive MIMO orthogonal frequency division multiplexing (OFDM) systems under a parametric channel modeling. We introduce a matrix-based joint parameter estimation method, and analytically characterize its performance for massive MIMO OFDM systems. Results show that antenna array configuration at the BS plays a critical role in determining the underlying channel estimation performance, and the characterized MSEs match well with the simulated ones. Also, the joint parametric channel estimation outperforms the MMSE-based channel estimation in terms of the correlation between the estimated channel and the real channel. Beamforming in MIMO systems is one of the key technologies for modern wireless communication. Creating wide common beams are essential for enhancing the coverage of cellular network and for improving the broadcast operation for control signals. However, in order to maximize the coverage, patterns for broadcast beams need to be adapted based on the users' movement over time. In this dissertation, we present a MIMO broadcast beam optimization framework using deep reinforcement learning. Our proposed solution can autonomously and dynamically adapt the MIMO broadcast beam parameters based on user' distribution in the network. Extensive simulation results show that the introduced algorithm can achieve the optimal coverage, and converge to the oracle solution for both single cell and multiple cell environment and for both periodic and Markov mobility patterns.

Par la révolution du Cloud Computing et des Smartphones, une quantité énorme de données devrait traverser le réseau chaque seconde où la plupart de ces données sont fournies par des mobiles utilisant des services Internet. La croissance rapide de la bande passante et des demandes de QoS rend les réseaux mobiles du 4ème G insuffisants. Le système de prochaine génération doit avoir un taux de sommation de 100Mbps à 1Gbps par terminal utilisateur (UT), avec une densité de connexion supérieure à 1M connexion / Km2, la mobilité des véhicules à grande vitesse jusqu'à 500 km / h et une fin à la fin (E2E) retardent moins de 10 ms. Un candidat prometteur qui peut répondre à ces demandes est le système sans fil à multiples sorties multiples (MIMO) Multi-Cell Multi-Cell. Cependant, la capacité Massive MIMO est délimitée par l'Inter-cell Interference (ICI) en raison de la réutilisation du pilote et, par conséquent, de la contamination du pilote. Dans cette thèse, nous étudions la contamination du pilote de liaison montante dans le système de formation à la division temporelle (TDD) des réseaux sans fil MIMO massifs. En supposant un canal de décoloration, l'intervalle de cohérence sera temporairement limité, où l'estimation du canal, la réception des symboles et le précodage des symboles doivent être effectués dans le même intervalle. Cela dit, la longueur du pilote de formation est limitée. De même, le nombre de terminaux de l'utilisateur (UT) par zone d'interférence est également limité. Inspiré par la variation de la taille de l'intervalle de cohérence parmi les UT, cette recherche présente deux nouvelles contributions indépendantes pour faire face à la contamination pilote de liaison montante dans le MIMO massif. La première contribution répertorie la région de couverture de la cellule de base (BS) dans une carte d'information d'état de chaîne (CSI). Cette carte est créée et mise à jour à l'aide d'un algorithme spécial d'apprentissage machine, et elle est exploitée pour prédire UT CSI au lieu d'estimer ses canaux. Compte tenu de cela, la formation des pilotes aériens et de liaison montante est considérablement réduite. La deuxième contribution classe les UT en fonction de la taille de leur intervalle de cohérence de canal. En outre, nous appliquons une technique de changement de pilote pour déplacer des pilotes similaires vers différentes positions temporelles (qui sont considérées comme vides en raison de trames TDD pilotes vides). Les résultats de la simulation montrent une augmentation à l'échelle de la performance du MIMO massif, en particulier dans la performance de l'efficacité énergétique et spectrale, UT par cellule et taux d'addition. En particulier, la troisième contribution évolue le MIMO massif multi-cellulaire à une performance de cellule unique et même surmonté un simple énorme conventionnel dans l'efficacité énergétique et UT par cellule. / By the revolution of Cloud Computing and Smartphones, an enormous amount of data should traverse the network every second where most of this data are delivered by mobiles using internet services. The fast growth in bandwidth and QoS demands makes the 4th G mobile networks insufficient. The next generation system must afford a sum rate from 100Mbps up to 1Gbps per User Terminal (UT), with a connection density that exceeds 1M connection/Km2, the mobility of high-speed vehicles up to 500 km/hr and an End to End (E2E) delay less than 10ms. A promising candidate that can offer those demands is the Multi-User Multi-Cell Massive Multiple-Input Multiple-Output (MIMO) wireless system. However, Massive MIMO capacity is upper bounded by the Inter-cell Interference (ICI) due to pilot reuse and thus, pilot contamination. In this thesis, we investigate the uplink pilot contamination in Time Division Duplexing (TDD) training scheme of massive MIMO wireless networks. Assuming block-fading channel, the coherence interval will lag for a limited duration, where channel estimation, symbol reception, and symbol precoding must be done within the same interval. Having said that, the training pilot length is limited. Likewise, the number of User Terminal’s (UT’s) per interference region is also limited. Inspired by the variation of coherence interval size among UT’s, this research introduces two independent novel contributions to deal with uplink pilot contamination in massive MIMO. The first contribution maps the Base Station (BS) cell coverage region into a Channel State Information (CSI) Map. This map is created and updated using a special machine-learning algorithm, and it is exploited to predict UT CSI instead of estimating their channels. In view of this, training overhead and uplink pilots are reduced significantly. The second contribution classifies UT’s based on the size of their channel coherence interval. Furthermore, we apply a pilot shifting technique to shift similar pilots to different time position (that considered empty due to empty pilot TDD frames). Simulation results show a scaled increase in the performance of massive MIMO especially in the performance of energy and spectral efficiency, UT per cell and sum-rate. In particular, the third contribution evolves multi-cell massive MIMO to a single cell performance and even overcome single conventional huge in the energy efficiency and UT per cell.

As the world becomes more globalised, user equipment such as smartphones and Internet of Things devices require increasingly more data, which increases the demand for wireless data traffic. Hence, the acceleration of next-generational networks (5G and beyond) focuses mainly on increasing the bitrate and decreasing the latency. A crucial technology for 5G and beyond is the massive MIMO. In a massive MIMO system, a detector processes the received signals from multiple antennas to decode the transmitted data and extract useful information. This has been implemented in many ways, and one of the most used algorithms is the Zero Forcing (ZF) algorithm. This thesis presents a novel parallel design to accelerate the ZF algorithm using the Cholesky decomposition. This is implemented on a GPU, written in the CUDA programming language, and compared to the existing state-of-the-art implementations regarding latency and throughput. The implementation is also validated from a MATLAB implementation. This research demonstrates promising performance using GPUs for massive MIMO detection algorithms. Our approach achieves a significant speedup factor of 350 in comparison to a serial version of the implementation. The throughput achieved is 160 times greater than a comparable GPU-based approach. Despite this, our approach reaches a 2.4 times lower throughput than a solution that employed application-specific hardware. Given the promising results, we advocate for continued research in this area to further optimise detection algorithms and enhance their performance on GPUs, to potentially achieve even higher throughput and lower latency. / <p>Our examiner Mahdi wants to wait six months before the thesis is published. </p>

[pt] As comunicações de ondas milimétricas (mmWave) são consideradas uma tecnologia essencial para os sistemas celulares de próxima geração, dado que a enorme largura de banda disponível pode potencialmente fornecer as taxas de vários gigabits por segundo. As técnicas convencionais de pré-codificação e combinação são impraticáveis nos cenários da mmWave devido ao custo de fabricação e ao consumo de energia. As alternativas híbridas foram consideradas uma tecnologia promissora para fornecer um compromisso entre a complexidade do hardware e o desempenho do sistema. Um grande número de projetos de pré-codificadores híbridos têm sido proposto com diferentes abordagens. Uma abordagem possível é procurar minimizar a distância euclidiana entre o pré-decodificador híbrido e o pré-decodificador totalmente digital. No entanto, essa abordagem torna o projeto do pré-codificador híbrido um problema de fatoração da matrices difícil de lidar devido às restrições de hardware dos componentes analógicos. Esta tese de doutorado propõe alguns projetos de pré-codificadores e combinadores híbridos por meio de uma estratégia hierárquica. O problema híbrido de pré-codificação / combinação é dividido em partes analógicas e digitais. Primeiro, o pré-codificador / combinador analógico é projetado. Em seguida, com o pré-codificador / combinador analógico fixo, o précodificador / combinador digital é calculado para melhorar o desempenho do sistema. Além disso, métodos de otimização linear e não linear são empregados para projetar a parte analógica do pré-codificador / combinador. A viabilidade dessas propostas é avaliada usando diferentes técnicas de detecção de dados e analisando o desempenho do sistema em termos de taxa de erros de bits (BER), sum–rate e outras métricas, em cenários internos do mmWave, considerando enlace diretos massivo do MU–MIMO. Além disso, este trabalho propõe um método para encontrar aproximações analíticas bastante restritas ao desempenho obtido no BER. A metodologia proposta exigiria o conhecimento da função densidade de probabilidade (fdp) das variáveis relacionadas que são desconhecidas para os cenários mmWave. Para resolver este problema, são utilizadas as aproximações fdp Gamma. As aproximações analíticas do BER resultaram em diferenças não superiores a 0,5 dB em relação aos resultados da simulação em alto SNR. / [en] Millimeter–wave (mmWave) communications have been regarded as a key technology for the next–generation cellular systems since the huge available bandwidth can potentially provide the rates of multiple gigabits per second. Conventional precoding and combining techniques are impractical at mmWave scenarios due to manufacturing cost and power consumption. Hybrid alternatives have been considered as a promising technology to provide a compromise between hardware complexity and system performance. A large number of hybrid precoder designs have been proposed with different approaches. One possible approach is to search for minimizing the Euclidean distance between hybrid precoder and the full-digital precoder. However, this approach makes the hybrid precoder design becomes a matrix factorization problem difficult to deal due to the hardware constraints of analog components. This doctoral thesis proposes some hybrid precoder and combiners designs through a hierarchical strategy. The hybrid precoding/combining problem is divided into analog and digital parts. First, the analog precoder/combiner is designed. Then, with the analog precoder/combiner fixed, the digital precoder/ combiner is computed to improve the system performance. Furthermore, linear and no-linear optimization methods are employed to design the analog part of the precoder/combiner. The viability of these proposals is evaluated using different data detection techniques and analyzing the system performance in terms of bit error rate (BER), sum rate, and other metrics, in indoor mmWave scenarios considering massive MU-MIMO downlink. Also, this work proposes a method to find fairly tight analytic approximations to the obtained BER performance. The methodology proposed would require the knowledge of the probability density function (pdf) of the variables involved, which are unknown for mmWave scenarios. In order to solve this problem, Gamma pdf approximations are used. The analytic BER approximations resulted in differences no larger than 0.5 dB with respect to the simulation results in high SNR.