28ghz多接收器mimo系统低复杂度混合波束形成

摘要
目前的无线服务已经饱和，几乎所有6GHz以下的频谱以及对高速无线通信的广泛增长的需求，特别是与沉浸式多媒体应用程序正在进入智能设备（例如智能手机，平板电脑，笔记本电脑等）。

空间视频流量占移动流量的61％，预计未来几年将会快速增长。

全高清视频的丰富性通过社交媒体分享，超高清和3D视频内容将会在未来发生，这促使研究人员深入研究了毫米波（mm波）频带作为经典乐队的替代品，并将广泛使用的带宽特权作为第五代无线通信系统及其以外即将到来的需求的有效解决方案。

毫米波频段特别是28GHz，我们的研究兴趣仍然处于研究阶段。

作为下一代无线通信的解决方案，毫米波频带中的一个显著的通道传播特性是通过频带的巨大传输信号路径损耗。

以前的研究已经显示了毫米波的通道测量结果，其中与波段频谱差比传统的蜂窝系统频带更差的传播损耗特性。

而且，它们也已经显示出基于波束形成技术的无线通信的可能性，其通过小波长的毫米波，对于视径（LoS）和非视径（NLoS）发射机和接收机传播而变得更容易实现。

已经证实，当我们从1.8GHz 跳到28GHz再到60GHz频带时，产生超过20dB的附加路径损耗，并且随着我们的差距正在迅速增加。

此外，由于频带变化情况，NLoS路径损耗大于LoS 损耗。

因此，为了利用毫米波频带中较小的波长，28GHz频段是更好的选择。

但是全数字28GHz系统的功耗和高成本的局限性使得它不太可能利用现有的半导体技术来实现，所以应该采用具有可控波束的混合数字模拟波束成形来使复杂度小型化。

因此，由于社交网络的革命性爆炸和用户对高速无线通信的巨大需求，更高数据速率的需求正在迅速增加，毫米波频段可成为下一代的解决方案的无线通信的超越。

选择28 GHz频段的基本目标是宽带无用和信道散布性。

在较高频率的无线通信环境如毫米波，天线阵列成为重要的组成部分。

因此，天线阵列的正常应用是多个接收机的同时传输。

但是，毫米波系统中的主要问题是硬件限制，从而使经典低频带上的多接收机MIMO波束成形技术的实现变得困难。

将各种数据流复用到各种接收机需要应用一些波束形成形式来产生发射的信号，并且对波束形成矩阵的条目具有优选的控制。

但是，这种波束成形通常
处于传统低频系统的基带阶段。

不幸的是，组合信号组件的系统成本，复杂性和功率耗尽使得全数字基带波束形成器不利于当前的制造技术。

此外，波束形成矩阵的设计通常基于几乎完美的信道状态信息，这在较小的波长系统中难以获得，这是因为当在系统中使用大量天线时需要巨大的训练开销，波束形成后的小信噪比（SNR）。

因此，多接收机波束成形的新颖算法考虑了毫米波系统的硬件约束。

并且需要开发低复杂度的毫米波系统。

为了改善28 GHz频段的链路预算，我们开发了一种用于下行链路多接收机28GHz系统的双相低复杂度混合模数数字波束成形，而我们假定在接收机侧进行模拟信号合并。

建议的算法可以归纳如下：
波束形成器和组合器之间的一般耦合已经被使用，但是额外的挑战是使用不同约束的波束形成操作的决斗不同的域。

因此，我们引用所提出的算法，我们必须参考将波束成形计算分为两个阶段的主要思想，在第一阶段，发射机的RF 波束形成器和接收机的RF组合器被联合设计最大化每个接收机的所需信号功率，忽略接收机之间的干扰。

在第二阶段，发射机的数字波束形成器被设计成处理多接收机干扰。

因此，在第一阶段，发射机和每个单个接收机设计RF波束成形和组合向量，以最大化所引用接收机的期望信号功率，并忽略其他接收机的干扰。

由于这是典型的单接收机RF波束成形设计问题，所以对于不需要显式信道估计并且具有较低训练开销的单接收机系统，改进的有效波束训练算法可用于设计射频波束形成组合向量。

在第二阶段，有效信道将由发射机和接收机的系统号进行训练。

每个有效信道向量的维数小于原始信道矩阵。

这不是有效信道具有较大发射机阵列的算法的情况，因此每个接收机使用码本对其有效信道进行量化，量化信道向量的索引将以已知位数反馈给发射机。

最后，发射机设计了基于量化信道的零强制数字波束形成器。

由于窄波束形成和28GHz信道的稀疏性，有效的MIMO信道有望进行有条件的调整，这使得采用简单的多接收机数字波束成形策略，如能够实现接近最佳性能的零强制。

在单接收器毫米波系统之前，对模拟和数字波束形成器的单独和联合设计进行了调查。

他们考虑了单个接收机单流MIMO-OFDM系统，其中模拟和数字波束形成器被依次设计为对不同频率子载波之间的所需接收信号强度或频谱效率应用最大化。

或者，模拟和数字波束形成器被联合设计以最大化单接收机系统的速率。

在本论文中，已经考虑了不同的设置，也就是多接收机下行链路传输。

因此，我们工作中混合模拟数字波束成形的目标与以前的工作不同，因为我们
还需要管理多接收机干扰。

这个解决方案使我们完全不同的分析。

所提出的算法将发射机混合波束形成器和接收机的模拟组合器设计成具有反馈开销和小的训练。

所提出的算法的性能分析已经采用两种情况，在单路径信道和具有大量发射机和接收机天线的多路径信道和具有两种类型的均匀阵列，均匀线性阵列（ULA）和均匀矩阵（URA）。

波束形成向量模拟和数字已经从量化的码本中选择，因此与混合波束形成的性能相比，与仅模拟波束形成和所有数字块对角化算法相比，由于联合量化和视觉的速率损失的表征系统。

为了能够分析混合波束形成，我们必须考虑到模拟和数字波束形成器之间的耦合，因此性能分析将会非常显着。

因此，我们对提出的算法的性能进行了两个案例研究，即单路径信道的情况和假设大量天线的多路径信道的情况。

这些情况是特别感兴趣的，因为28GHz信道可能是稀疏的，即仅存在少数路径，并且发射机和接收机都需要应用大的天线阵列以具有有效的接收功率。

此外，这些特殊情况的分析将对本文中已经展示的更一般的设置中的所提出的算法的性能给出有用的见解。

我们假设完全了解有效信道并假定RF射束向导的角度可以取连续值，分析所提出的算法的总和。

本论文改进了低复杂度功能的双相混合模数数字波束成形算法，用于下行链路多接收机毫米波系统。

所提出的算法在具有可用于发射机的阵列的已知尺寸和具有有限反馈的接收机信道之间的假设下更为通用。

我们可以简要列出本论文的主要贡献如下：
改进用于多接收机28GHz系统的混合发射机波束成形和接收机组合的算法。

我们假设接收机仅使用模拟组合器，而在发射机处实现混合模拟数字波束形成器，其中在所提出的系统中已经使用RF链的数量等于接收机的数量或更少的接收机数量。

所提出的算法的设计旨在减少反馈开销和训练，以获得更接近的结果给无约束的解决方案。

在单路径信道的假设下分析混合波束成形算法性能，然后假设在发射机和接收机侧都具有大尺寸阵列几何形状的多路径信道，这被称为28 GHz系统的有利设计。

混合量化码本的特征在于平均速率损失，与所有数字无约束算法和模拟波束成形解决方案相比，可以区分混合波束形成的大增益。

在本论文中，混合波束成形包括模拟和数字组合处理，受组合信号硬件和全射频功率消耗的启发。

所以安排如下：
系统架构和渠道模型的描述在第2章。

在第3章中，多接收机混合波束成形组合的总和速率计算问题已经通过训练和反馈开销的关联来形成。

然后描述了所提出的低复杂度双相混合波束形成组合算法。

第4章包括所提出的算法的
性能分析，在具有非常大数量的天线的单路径信道和多路径信道中，假设连续移相器角度。

第5章演示了两种不同分析案例研究中所提出的算法与模拟波束成形和块对角化算法全数字（无约束）的比较。

并通过使用两种类型的天线阵列ULA和URA。

所提出的混合波束成形算法表明，即使具有相对较小的训练和反馈开销也表现出良好的性能，我们确信我们感谢28 GHz信道的备用性质，并且已经在发射机和接收机中部署了大量的天线。

在本论文中，已经提出了用于下行链路多接收机28GHz系统的双相低复杂度混合模数数字波束成形算法，其利用大量天线和28GHz频带的稀疏信道特性。

对于两个案例研究，性能分析首先被考虑，当信道是单路径时，第二个是当通道是具有非常大数量的天线的多路径时被部署的。

对于上述情况，我们演示了所提出的双相混合波束成形算法的渐近最优性，以及仅针对模拟波束成形和全数字无约束波束成形的增益。

仿真结果表明，即使已经部署了大尺寸阵列，也需要多接收机28 GHz系统中的干扰管理。

利用小信道的反馈，对联合模拟数字码本量化的速率损失平均值进行了数值模拟分析。

这些结果表明混合波束形成的增益对于RF角度量化不是很敏感。

对于数字波束形成层来说，为了在仅模拟波束成形上保持合理的波束成形增益，具有很好的量化是重要的。

性能分析和仿真结果表明，所提出的模型对于仅模拟波束成形提供了更高的总和速率，并且通过相对小的码本几乎实现了所有数字系统的块对角化的相同方法。

关键词：毫米波；混合波束形成；5G；MIMO；阵列处理
Abstract
The demands of higher data rates is rapidly increasing due to the revolutionary explode in the social media world and the user’s enormous need for the high speed wireless communication, the current wireless services has been saturated almost all the spectrum below 6GHz so the millimeter wave (mm-wave) frequency band can be a brilliant solution for the for the next generation of wireless communication and beyond. The essential target of choosing the 28 GHz frequency band is wide unused bandwidth and the scattered nature of the channel. In the higher frequencies wireless communication environment such as mm-wave the antenna arrays become a significant ingredient. Therefor the normal application for the antenna arrays is the simultaneous transmission for the multiple receivers. But the major problem in mm-wave systems is the hardware constraints which makes the implementation of the multi receiver MIMO beamforming techniques at the classic lower frequency bands difficult.
In order to improve the links budget in the 28 GHz frequency band, we developed a dual phase Low-complexity hybrid analog-digital beamforming for the downlink multi-receiver 28 GHz systems, while we presume an analog only combining at the receivers’ side.
In this thesis the hybrid beamforming included analog and digital combined processing which is inspired by the combined signal hardware and full radio frequency power consumption.
The proposed algorithm designs the transmitter hybrid beamformer and the receiver’s analog combiners with feedback overhead and by a small training. The performance analysis of the proposed algorithm has been taken for two cases, in the single path channels and with multi path channels with large number of transmitter and receivers antennas and with two types of uniform arrays uniform linear array (ULA) and uniform rectangular array (URA). Both the beamforming vectors the analog and the digital has been chosen from quantized coodbooks, so the rate loss characterization due to joint quantization and the visions are given among the performance of the hybrid beamforming compared with analog only beamforming and all digital (block diagonalization algorithm) beamforming.
The performance Analysis and the simulation results demonstrates that the
proposed model offers a higher sum rates against the analog only beamforming and almost achieves the same approach of the block diagonalization all digital system by relatively small codebooks.
Keywords: Millimeter Wave, Hybrid Beamforming, 5G, MIMO, Array Processing.
L ist of F igures
Figure 1 Millimeter Wave Spectrum (13)
Figure 2 Path-loss of 1.8GHz, 28GHz and 60GHz frequency bands (14)
Figure 3 Uniform Linear Array Architecture (20)
Figure 4 Uniform Rectangular Array Architecture (21)
Figure 5 Impact of Changing d on ULA Beam Pattern (22)
Figure 6 Impact of Changing d on URA Beam Pattern (23)
Figure 7 Impact of changing N on ULA Beam Pattern (24)
Figure 8 Impact of changing N on ULA Beam Pattern (24)
Figure 9 Impact of changing N on URA Beam Pattern (25)
Figure 10 Impact of changing N on URA Beam Pattern (26)
Figure 11 K receivers 28 GHz downlink system model, in which Transmitter communicating with the receivers which has a limited feedback channels. (27)
Figure 12 Transmitter with hybrid analog/digital architecture communicating with the K Receivers that employs analog-only combining. (27)
Figure 13 Dual Phase Multi-Receiver Hybrid Beamforming Algorithm (37)
Figure 14 Dual Phase Multi-Receiver Hybrid Beamforming Algorithm (38)
Figure 15 Predefined RF beams ULA (39)
Figure 16 Predefined RF beams URA (40)
Figure 17 Achievable rates of the single receiver and analog only beamforming with perfect channel knowledge, with Single-path channels, ULA. (56)
Figure 18 Achievable rate of the Unconstrained (all digital) against the rates of single receiver and analog beamforming with perfect channel knowledge, with Single-path channels, ULA. (56)
Figure 19 Achievable rate of the proposed Hybrid Beamforming against the rates of Unconstrained (all digital) single receiver and analog beamforming with
perfect channel knowledge, with Single-path channels, ULA. (57)
Figure 20 Achievable rate of the proposed Hybrid Beamforming against the rates of Unconstrained (all digital) single receiver and analog beamforming with
presence of the Lower Bound Theorem perfect channel knowledge, with
Single-path channels, ULA. (57)
Figure 21 Achievable rates of the single receiver and analog only beamforming with perfect channel knowledge, with Single-path channels, URA (58)
Figure 22 Achievable rate of the Unconstrained (all digital) against the rates of single receiver and analog beamforming with perfect channel knowledge, with Single-path channels, URA. (58)
Figure 23 Achievable rate of the proposed Hybrid Beamforming against the rates of Unconstrained (all digital) single receiver and analog beamforming with
perfect channel knowledge, with Single-path channels, URA (59)
Figure 24 Achievable rate of the proposed Hybrid Beamforming against the rates of Unconstrained (all digital) single receiver and analog beamforming with
presence of the Lower Bound Theorem perfect channel knowledge, with
Single-path channels, URA. (59)
Figure 25 Achievable rates of the single receiver and analog only beamforming with perfect channel knowledge, and Multi-path channels, ULA. (61)
Figure 26 Achievable rate of the proposed Hybrid Beamforming against the rates of single receiver and analog beamforming with presence of the Lower Bound
Theorem with perfect channel knowledge, and Multi-path channels, ULA (61)
Figure 27 Achievable rates of the single receiver and analog only beamforming with perfect channel knowledge, and Multi-path channels, URA. (62)
Figure 28 Achievable rate of the proposed Hybrid Beamforming against the rates of single receiver and analog beamforming with presence of the Lower Bound
Theorem with perfect channel knowledge, and Multi-path channels, URA. (62)
Mathematical Notations
PL LoS Line of site Path loss
PL NLoS Non-Line of site Path loss
δDistance in meter
f c Carrier Frequency
a(θ)Antenna Response Vector
θAngle of arrival and/or departure
ΦAngle of arrival and/or departure
N Number of antennas
λFrequency wavelength
d Inter array elements spacing
,.-T Channel Matrix transpose
,.-−1Invers
,.-∗Hermitian
K Number of receivers
N S Streams Number
N RF Number of RF Chains
N Tx Number of Transmitter antennas
N Rx Number of Receiver antennas
F BB Baseband precoder
F RF RF Beamformer
X Transmitted signal
S Transmitted stream
E(.)Expectation
P Transmitted power
L Number of paths
αComplex gain
W k RF combiner
n Gaussian noise
y Received Signal
R k Achievable rate
eff Effective Channel
fb Feedback Channel
‖H‖Frobenius norm max Maximum
min Minimum
SNR Signal to Noise Ratio 1(.)Indicator Function
I Identity Matrix
σCovariance
Contents
摘要 (I)
Abstract (V)
List of Figures ............................................................................................ V II Mathematical Notations (IX)
Contents ............................................................................................................... X I Chapter 1 Introduction. (13)
1.1 Millimeter Wave Wireless Communication (13)
1.2 Why 28 GHz (13)
1.3 Analysis Of Literature Review (15)
1.4 Problem Statement (17)
1.5 Research Outlines (18)
Chapter 2 System Architecture (19)
2.1 Antenna Arrays (19)
2.1.1 Uniform Linear Arrays (19)
2.1.2 Uniform Rectangular Arrays (20)
2.2 Impact of Physical Parameters on Arrays (21)
2.2.1 Impact of Changing d on ULA (21)
2.2.2 Impact of Changing d on URA (22)
2.2.3 Impact of changing N on ULA (23)
2.2.4 Impact of changing N on URA (25)
2.3 System Model (26)
2.4 Channel Models (28)
2.4.1 Narrowband Geometric Channel Model (28)
2.4.2 Virtual Channel Model (30)
Chapter 3 Problem Formulation (32)
3.1 Sum Rate Calculation (32)
3.1.1 General Quantized Beamforming Codebooks (32)
3.1.2 Analog Beamforming Codebooks (32)
3.2 Beamformers-Combiners Designing (34)
3.2.1 Iterative Coordinated Beamforming Designs (34)
3.2.2 Non-Iterative Designs with Channel State Information at the Transmitter .
(34)
3.2.3 Non-Iterative Designs with Channel State Information at the Receiver . 35 3.3 Duel-Phase Low-Complexity Multi-Receiver Hybrid Beamforming (35)
Chapter 4 Performance Analysis (41)
4.1 Single Path Channel (41)
4.4.1 Lower Bound Theorem (41)
4.4.2 Single Receiver Rate (45)
4.4.3 Analog Beamforming (46)
4.4.4 Digital Beamforming (47)
4.2 Multi Path Channel (49)
Chapter 5 Simulation Results (54)
5.1 Simulation Results (54)
5.1.1 Single Path Channels (54)
5.1.2 Multi Path channel (60)
Conclusions (63)
References (64)
Papers and Patents (68)
(69)
Acknowledgement (70)
Chapter 1 Introduction
1.1 Millimeter Wave Wireless Communication
The current wireless services has been saturated almost all the spectrum below 6GHz as well as the vast growing demand for high-speed wireless communications, in particular with immersive multimedia applications are now making a foray into smart devices (e.g., smart phone, tablet, laptops, etc.). Spatially Video traffic constitutes a considerable 61 percent of the mobile traffic volume and is expected to increase rapidly in upcoming years.
Figure 1 Millimeter Wave Spectrum
The abundance of Full high definition (Full HD) video is been shared through social media and ultra HD and 3D video content will take place in the soon future, this has urged the researchers to dig into the millimeter wave (mm-wave) frequency bands as an alternative to the classic bands and to take the privilege of the wide unused bandwidth as a promising solution for the upcoming demands of the fifth generation of wireless communication systems and beyond [1, 2], see Figure 1.
1.2 Why 28 GHz
The mm-waves frequency bands in particular the 28GHz, our research interest
are still in the phase of research as a solution for the next generation of wireless communication.One of the conspicuous channel propagation characteristics in mm-wave frequency band is the huge transmitted signal path loss through the bands [3].
Figure 2 Path-loss of 1.8GHz, 28GHz and 60GHz frequency bands Previous studies have shown the channel measurement results for mm-wave [3-5], where the worse propagation loss characteristic of mm-wave frequency bands compared against the classic cellular system frequency bands has been verified. While, they also has been showed the possibility of wireless communication based on beamforming techniques, which become easier by the small wavelength of mm-wave, for the line of sight (LoS) and non-line of sight (NLoS) transmitter and receiver propagation path [5]. Figure 1 shows that more than 20dB additional path loss occurs when we jump from 1.8GHz to 28GHz to 60GHz frequency band and as we going up the gap is rapidly increasing. Further, the NLoS path loss is greater than LoS loss due to the frequency band changing circumstance. Note that the model of the path loss used for Figure 2 is based on the Urban Micro scenario:
PL LoS=22log10(δ)+28+20log10(f c)(1-1)
PL NLoS=36.7log10(δ)+22.7+26log10(f c)(1-2) where δis the distance in meter and f c is the carrier frequency in GHz. Thus,
the 28GHz frequency band is much better choice in order to exploiting the smaller wavelength in mm-wave frequency bands. but the limitations of the power consumption and high cost of fully digital 28GHz system make it unlikely to implement with existing technologies of semiconductors so a hybrid (Digital- Analog) Beamforming with steerable beams should accommodated to miniaturized the complexity.
1.3 Analysis of Literature Review
The need to employ the mm-wave communication in wireless local area networking because of the large spectrum bandwidths in it, which makes it also a favorable candidate for the cellular systems in soon future [1-7]. Large antenna arrays employment at the both ends, transmitter and the receiver of the cellular system are required to achieve high quality links in mm-wave communication systems [6, 8, 9]. Each transmitter necessarily needs to simultaneously serve a number of receivers to increase the performance and the system efficiency.
Multiplexing various data streams to various receivers needs to apply some beamforming form to generate the transmitted signal, and to have a preferable control over the entries of the beamforming matrix. But this beamforming was generally at the baseband stage in conventional lower frequency systems. Unfortunately, the system cost, complexity and power exhaustion of combined signal components make fully digital baseband beamformer undesired with current manufacturing techniques [6]. Moreover, the beamforming matrices design commonly is based on the almost perfect channel state information, which is hard to get in the smaller wavelength systems due to, a huge training overhead, is required when the massive number of antennas had been used in the system and beamforming after the small signal-to-noise ratio (SNR). Thus, the novel algorithms of multi-receiver beamforming are:
1-Take the hardware constraints of the mm-wave system in considerations.
2-Developing much low complexity mm-wave systems is required.
In the single receiver mm-wave systems, instead of the baseband solutions [10-14] proposed a controlled phase of the transmitted signal in each antenna by the analog beamformer through a network of the system phase shifters and all of that in
the radio frequency domain (RF). That model was adopted in the IEEE standards (IEEE 802.11ad [13] and IEEE 802.15.3c [14]), for the commercial indoor usage of the mm-wave communication. Developing a codebooks with multiple resolution design and an adaptive beamforming algorithms which jointly design the analog beamforming vectors of the transmitter and the receiver in [10, 11].
Making the training overhead as minimum as possible is smart proposal in [12], by assigning a unique signatures for different training beamforming vectors. In beamspace Multi Input Multi Output (MIMO) Discrete Fourier transforms (DFT) has been applied as beamforming vectors which is introduced in [13, 14], to steer the transmitted signals to the subspaces that can maximize the power of received signal asymptotically with large dimensional antenna regime.
In [10-16], more constraints has been added to the analog beamformers design, for example, digital controlling to the phase shifters which have values of quantized phase with neglecting any adaptation for the gain control. The solution of Analog beamforming can be limited by those constraints proportional to the baseband stage of beamforming, accordingly them ability will be limited to reach advanced processing deal with inter receiver interference.
In [6, 17, 18], a hybrid beamforming with two processing domains of analog and digital was introduced for several data streams multiplexing which is lead to more accurate performance. Under the proposition of the presence of the channel knowledge the basis pursuit algorithmic concept has been used to improve low complexity hybrid beamforming in [6]by that the mm-wave channel can be demonstrate it sparse temper. Single user for the system of MIMO-OFDM aims to maximizing the achievable rate over various sub-carriers or the received signal, also by proposing low complexity algorithms of hybrid beamforming. Devise an iterative algorithm of hybrid analog digital beamforming in [18], with assumption of partial mm-wave channel knowledge.
In [6, 17, 18], hybrid beamformers was introduced for single receiver channels to achieve the diversity or the spatial multiplexing but those models can support data streams with confided boundary of number [5]. The digital precoding stage of the hybrid beamforming can provide more reliability with the beamformers design, when the analog beamforming can be used for minimize the inter receiver interference in the multi receiver systems. Therefore, improving low complexity
hybrid beamforming algorithms for multi receiver mm-wave systems is of our special concern.
In [19-21]an initial beamforming system models were studied. Spatial multiplexing and diversity has been investigated in [19] when the system model was a joint analog and digital beamformer. The algorithms of hybrid beamforming in [20], has been improved to decrease the mean squared error of the received signals with interference existence and the shifters with only availability of quantized phases. Massive MIMO two layer beamforming system was devised in [21]in which the channel feedback overhead has been minimized by a set of receivers. The design of the systems which proposed in [19-21] was not meant to be exactly for the mm-wave as they didn’t discuss the constraints of mm-wave hardware.
1.4 Problem Statement
This Thesis has improved a Low-complexity yet functional dual-phase hybrid analog-digital beamforming algorithm for downlink multi receiver mm-wave systems.
The proposed algorithm is more generic under the assumption of the known dimensions of arrays which available with the transmitter and the receivers channel with limited feedback lying in between. We can briefly list the essential contributions of this thesis as follows:
1-Improving an algorithm for hybrid transmitter beamforming and receiver combining for multi receiver 28 GHz systems. We presume that the receivers use only analog combiners whereas a hybrid analog-digital beamformers to be implemented at the transmitter where the number of RF chains has been used in the proposed system is equal to the number of receivers or less of it.
The design of the proposed algorithm aims to decrease the feedback overhead and the training to get closer result to the unconstrained solution.
2-Analyze the hybrid beamforming algorithm performance, under the assumption of single path channel, and then we assume multi path channel with large dimensional array geometries at both the transmitter and receivers side which referred as a favorable design for the 28 GHz systems.
3-The average rate loss will be characterized for the hybrid quantized codebook, and then distinguishing the large gain of the hybrid beamforming
compared with all digital unconstrained algorithm and analog beamforming solutions.
1.5 Research Outlines
The performance of the upper and lower bounds of the introduced algorithm has been analyzed in chapter 4 where the simulation part in chapter 5 demonstrate the comparison with analog beamforming and block diagonalization algorithm all digital (unconstrained) in two different analysis case studies when there is only single path channels and when the number of the array antennas is very large with multi path channels. The proposed hybrid beamforming algorithm indicate that even with relatively small training and feedback overhead has showed a good performance, sure we are grateful to the spares nature of the mm-wave channel and the large number of antennas has been deployed in the transmitter and receivers.
The rest of this thesis has been arranged as follows:
1-The descriptions of the system architecture and channels model were in chapter 2.
2-In chapter 3, the sum rate calculation problem for multi receiver hybrid beamforming combining has been formulated with the association of
training and feedback overhead. Then the proposed low complexity dual
phase hybrid beamforming-combining algorithm has been described.
3-Chapter 4 included the performance analyzing of the proposed algorithm, in single path channel and multi path channel with very large number of
antennas with assumption of continuous phase shifters angles.
4-The simulation results and the conclusion of the thesis were presented in chapter 5.
Chapter 2 System Architecture
2.1 Antenna Arrays
Antenna array is a group of antenna elements which has a definite geometries, every single element has a special spatial position and a particular distance between its elements. The antenna array can take any geometric design. The uniform linear arrays (ULA’s) and the uniform rectangular arrays (URA’s) are the array geometries of our interest.
Actually the topic of arrays has been extensively covered by many textbooks, e.g. [22-24], much useful information can be found regarding the topic of arrays. Regarding to the literature had been studied about this topic the preferred structures to our system model are the uniform linear array (ULA) and the uniform rectangular array (URA).
2.1.1 Uniform Linear Arrays
We can describe the uniform linear array as the basic array geometry. Therefor all the elements are organized along one straight line and usually have a uniform spacing between its elements. Basically you can simply analyze the ULA and many valuable perceptions can be gained by comprehending its behavior. Two elements is the minimum length ULA which is called 2-element array. We are interesting to study the more general ULA case which is the N-element array, thus, the ULA antenna steering vector for N-number of antenna can be written us [23]:
a(θ)=
N e j
2π
λd sin (θ),…,e j(N−1)
2π
λd sin
(θ)]
T
(2-1)
where θrepresent the angle of arrival and/or departure (AoAs/AoDs) respectively, N is the number of array elements, λis the frequency band wavelength, and d represent the antenna elements spacing distance. Schematic demonstration of the ULA is shown in the Figure 3.
Figure 3 Uniform Linear Array Architecture
2.1.2 Uniform Rectangular Arrays
The more slightly complex geometry than the ULA is the Uniform Rectangular arrays URA’s, we can describe it as a uniform expansion of the ULA’s with more complex geometries, a URA with a uniform rectangular boundary grid can be showed in the Figure 4, the structure is similar to that found in [22, 23].
There are N elements in the x-direction and M elements in the y-direction creating an N×M array of elements. The elements in the x-direction dx spacing separately from the elements in the y-direction which spaced by dy. The URA can be observed as M linear arrays for N elements or we can describe it as N linear arrays of M elements reciprocally. Where the array response vector regarding to the above mentioned can be given by [23]:
a(Φ,θ)=
N
1,e j
2π
λd
(m sinΦsinθ+n cosθ),……
……,e j
2π
λd
((M−1)sinΦsinθ+(N−1)cosθ)
]+
T
(2-2)
Figure 4 Uniform Rectangular Array Architecture
2.2 Impact of Physical Parameters on Arrays
The inter-element spacing between the antenna array elements of the ULA is an important part in designing the ULA [22]. It is therefore, necessary to see the effects of varying the physical parameters such as array elements N and inter-element spacing d of the ULA and URA. The simulation for various values of inter-element spacing and fixed number of array elements of the ULA and URA and also for various numbers of N and fix will be performed in the following subsections.
2.2.1 Impact of Changing d on ULA
The impact of different inter-element spacing in the ULA can be seen by the Figure 5, which demonstrates different beam pattern response of the ULA. The beam pattern of the ULA for three different values of element spacing d and four elements N=4of ULA array and the wavelength of the 28GHz frequency band has been shown. It is seen from the beam pattern that when the d between the antenna array elements is greater than 0.5λ, we can see that a grating lobes appear in the radiation pattern of ULA [22] as can be seen from the Figure 5.
Figure 5 Impact of Changing d on ULA Beam Pattern
We can prove that by the equation of the array steering vector of the ULA in (2-1). As we know that the sin(θ)∈,1,−1-and from the equation (2-1), the
exponent term can be 2π
λd sin(θ)∈0−2π
λ
d,2π
λ
d1. And so, if d>0.5λ, the
exponent term extends beyond ,−π,π-and we can get the peak for several values of θfor the same argument of exponent which causes grating lobes in the array response.
2.2.2 Impact of Changing d on URA
Figure 6 illustrates the impact of changing the inter-element spacing d in four elements N=4of URA array for and the wavelength of the 28GHz frequency band. Different beam patterns for different d values can be substitute in the array steering vector in (2-2) without changing the number of array elements. The case here is not very different from the case of the ULA but with more stability and less grating lobes in the radiation pattern [23], and that has been demonstrated in the Figure 6.。