多輸入多輸出正交分頻多工系統中基於編碼可靠度混合重傳機制及適應性調變編碼之聯合設計

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(1)國立交通大學電信工程學系碩士班碩士論文. 多輸入多輸出正交分頻多工系統中基於編碼可靠度混合重傳機制及適應性調變編碼之聯合設計 Joint Design of Reliability-Based Hybrid ARQ and Adaptive Modulation / Coding in MIMO-OFDM Systems. 研究生：王俊傑. Student : Chun-Chieh Wang. 指導教授：李大嵩博士. Advisor : Dr. Ta-Sung Lee. 中華民國九十五年六月.

(2) 多輸入多輸出正交分頻多工系統中基於編碼可靠度混合重傳機制及適應性調變編碼之聯合設計 Joint Design of Reliability-Based Hybrid ARQ and Adaptive Modulation / Coding in MIMO-OFDM Systems 研究生：王俊傑. Student : Chun-Chieh Wang. 指導教授：李大嵩博士. Advisor : Dr. Ta-Sung Lee. 國立交通大學電信工程學系碩士班碩士論文. A Thesis Submitted to Institute of Communication Engineering College of Electrical Engineering and Computer Science National Chiao Tung University in Partial Fulfillment of the Requirements for the Degree of Master of Science in Communication Engineering June 2006 Hsinchu, Taiwan, Republic of China. 中華民國九十五年六月.

(3) 多輸入多輸出正交分頻多工系統中基於編碼可靠度混合重傳機制及適應性調變編碼之聯合設計. 學生：王俊傑. 指導教授：李大嵩博士. 國立交通大學電信工程學系碩士班摘要編碼混合重傳機制(Hybrid Automatic Repeat Request, HARQ)為一種結合順向錯誤更正(Forward Error Correction, FEC)與自動重送機制(Automatic Repeat Request, ARQ)的錯誤更正技術；並被認為是第四代高速通訊在無線通道雜訊干擾下，解決錯誤更正問題之可行技術，而編碼可靠度混合重傳 (reliability-based HARQ, RB-HARQ)機制為一新式編碼混合重傳機制，僅需重傳信賴度較低的位元，較傳統機制提供更優異效能表現且更具適應性；本論文研究主題之ㄧ，即為根據不同服務品質要求，針對編碼可靠度混合重傳機制提出一套適應性選擇重傳封包長度的演算法。另一方面，多輸入多輸出正交分頻多工(Multiple-Input Multiple-Output Orthogonal Frequency Division Multiplexing, MIMO-OFDM)系統被認為是符合第四代高速通訊需求的最佳解決方案之ㄧ；MIMO 為使用多天線於傳送和接收端的可靠通訊技術，OFDM 為一種具高頻譜效益，並能有效克服多路徑衰落效應的調變技術；本論文中研究主題之二，即為針對 MIMO-OFDM 系統提出一種結合編碼可靠度混合重傳機制與調變編碼的跨層適應性收發架構，使其能夠隨時間動態地在頻率與空間通道上調整傳輸參數。吾人根據媒體存取層不同的服務品質要求，包含容許最大延遲時間及封包錯誤率，適應性的調整重傳次數、重傳封包長度、傳輸功率、傳輸速率、調變型態等系統參數，達到最佳的性能。最後，吾人藉由電腦模擬驗證上述架構在寬頻無線接取通道環境中具有優異的傳輸表現。 I.

(4) Joint Design of Reliability-Based Hybrid ARQ and Adaptive Modulation / Coding in MIMO-OFDM Systems Student: Chun-Chieh Wang. Advisor: Dr. Ta-Sung Lee. Institute of Communication Engineering National Chiao Tung University Abstract Hybrid automatic repeat request (HARQ) that combines ARQ and forward error correction (FEC) is a promising error-correcting technique for wireless communications. In reliability-based HARQ (RB-HARQ), the bits that are to be retransmitted are adaptively selected at the receiver based on the estimated bit reliabilities at the output of a soft decoder. This technique has the potential of improving system throughput. In this thesis, we propose an adaptive algorithm which can accordingly choose the sizes of retransmissions under the quality of service (QoS) constraints such as the maximum number of retransmissions allowed per packet and packet loss probability. Multiple-input. multiple-output. orthogonal. frequency-division. multiplexing. (MIMO-OFDM) is suitable for the increasing demand of the high-performance 4G broadband wireless communications with multiple antennas at both the transmitter and receiver sides. In this thesis, we then consider a new wireless communication system combining both MIMO-OFDM and RB-HARQ techniques and propose an adaptive MIMO-OFDM transceiver architecture along with a specifically designed loading procedure to dynamically adjust the transmission parameters such as retransmission size, number of retransmission, modulation order and transmit power over spatial and frequency channels, according to the instantaneous channel statistics, to meet the target QoS. Finally, we evaluate of the performance of the proposed systems, and confirm that it functions well in a typical broadband wireless access environment. II.

(5) Acknowledgement I would like to express my deepest gratitude towards my advisor, Dr. Ta-Sung Lee, for his enthusiastic guidance and great patience. His positive attitude has guided me in many areas and has propelled me in the direction of reaching my future goals. In addition, I would like to express many heartfelt thank you to all the members and staff of the Communication System Design and Signal Processing (CSDSP) Lab for their constant support and encouragement; I would not be where I am today without your help. Last by not least, I would like to show my most sincere appreciation and love for my family for their continual love and support of my pursuit of excellence. Thank you once again.. III.

(6) Contents Chinese Abstract. I. English Abstract. II. Acknowledgement. III. Contents. IV. List of Figures. VII. List of Tables. XI. Acronym Glossary. XII. Notations. XV. 1 Introduction. 1. 2 Overview of IEEE 802.16 System. 6. 2.1 Review of MIMO-OFDM System ..................................................6 2.1.1. OFDM : Concept and Technique .........................................................7. 2.1.2. MIMO : Concept and Technique .......................................................10. 2.1.3. V-BLAST Based OFDM....................................................................17. 2.2 WiMAX Overview ........................................................................19 2.2.1. Review of IEEE 802.16 PHY ............................................................20. 2.2.2. Review of IEEE 802.16 MAC ...........................................................21. IV.

(7) 2.2.3. Review of IEEE 802.16-2005............................................................23. 2.3 MIMO Channel Model..................................................................24 2.3.1. Correlation Channel Matrices............................................................25. 2.3.2. Generation of a MIMO Channel Using Correlation Matrix Approach............................................................................................27. 2.4 Computer Simulations...................................................................30. 3 Reliability-Based Incremental Redundancy Hybrid ARQ Scheme with LDPC Codes. 33. 3.1 Review of LDPC Codes ................................................................33 3.1.1. LDPC Codes ......................................................................................34. 3.1.2. Construction of LDPC Codes ............................................................35. 3.1.3. Generator matrix of LDPC Codes .....................................................39. 3.1.4. Decoding Algorithm of LDPC Codes ................................................39. 3.2 Review of ARQ Schemes..............................................................43 3.2.1. Conventional ARQ.............................................................................43. 3.2.2. Hybrid ARQ Type I............................................................................44. 3.2.3. Hybrid ARQ Type II ..........................................................................45. 3.2.4. Hybrid ARQ Type III .........................................................................46. 3.3 Reliability-Based HARQ ..............................................................47 3.3.1. Review of Reliability-Based HARQ..................................................48. 3.3.2. System Model for RB-HARQ scheme...............................................48. 3.4 Proposed Adaptive RB-HARQ Algorithm....................................51 3.5 Computer Simulations...................................................................55 3.6 Summary .......................................................................................61. V.

(8) 4. Combing RB-HARQ and Adaptive Modulation in IEEE 802.16-like MIMO-OFDM Systems. 62. 4.1 The Concept of Cross Layer Design .............................................63 4.2 Adaptive Modulation Assisted MIMO -OFDM System...............64 4.2.1. Adaptive Modulation .........................................................................65. 4.3 System Model for V-BLAST Based Apadtive MIMO-OFDM System ...........................................................................................67 4.4 V-BLAST Based Adapdtive MIMO-OFDM System ....................69 4.5 Combining HARQ with AMC Mechanism...................................75 4.5.1. System Performance Requirement at Physical Layer........................75. 4.5.2. AMC Design at the Physical Layer ...................................................77. 4.5.3. Error Performances of AMC Design .................................................78. 4.6 Adaptive RB-HARQ with AMC Mechanism ...............................79 4.7 Physical/MAC Cross-Layer AMC Design ....................................80 4.8 Computer Simulations...................................................................81 4.9 Summary .......................................................................................88. 5 Conclusion. 89. Bibliography. 91. VI.

(9) List of Figures Figure 2.1. Diagram of a MIMO wireless transmission system................................10. Figure 2.2. Illustration of a spatial multiplexing system...........................................11. Figure 2.3. Diagonal and vertical layered space-time encoding with N t = 3 ........13. Figure 2.4. Diagonal layered space-time decoding with N t = 3 ............................14. Figure 2.5. Vertical layered space-time decoding with N t = 3 ..............................15. Figure 2.6. V-BLAST based MIMO-OFDM transmitter architecture. .....................19. Figure 2.7. V-BLAST based MIMO-OFDM receiver architecture. .........................19. Figure 2.8. The flow chart for the generation of MIMO channel model coefficients..............................................................................................28. Figure 2.9. ZF V-BLAST performance with ideal detection and cancellation. QPSK modulation is used. (N t , N r ) = (4, 4) ........................................31. Figure 2.10. ZF V-BLAST performance with error propagation. QPSK modulation is used. (N t , N r ) = (4, 4) ...................................................31. Figure 2.11. Comparison of ZF V-BLAST (N t , N r ) = (4, 4) with QPSK modulation and (N t , N r ) = (2, 4) with 16-QAM modulation. ............32. Figure 3.1. Parity-check matrix of the (960, 640) LDPC code ..............................37. Figure 3.2. Generator matrix of the (960, 640) LDPC code...................................37. Figure 3.3. Bipartite graph of (7, 4) Hamming Code .............................................40. Figure 3.4. Constraint node of (7, 4) Hamming Code............................................40. VII.

(10) Figure 3.5. Block diagram of ARQ and HARQ Type I.............................................43. Figure 3.6. Block diagram of HARQ Type II............................................................46. Figure 3.7. Block diagram of RB-HARQ. ................................................................47. Figure 3.8. System model of RB-HARQ scheme .....................................................49. Figure 3.9. Packet reliability versus retransmission size (bits) in RB-HARQ scheme ....................................................................................................53. Figure 3.10. PER versus packet reliability in RB-HARQ scheme..............................54. Figure 3.11. PER versus average Eb / N 0 for (960,640) LDPC coded system in a Rayleigh channel with QPSK, 16-QAM, and 64-QAM. .................57. Figure 3.12. Throughput (bits/symbol) versus average Eb / N 0 for (960, 640) LDPC coded system in a Rayleigh fading channel with QPSK, 16-QAM, and 64-QAM ..........................................................................57. Figure 3.13. PER versus average effective Eb / N 0 for (960, 640) LDPC coded system in a Rayleigh fading channel with QPSK by the RB-HARQ scheme, no-ARQ scheme, and IR-HARQ scheme ..............58. Figure 3.14. PER versus average SNR for (960, 640) LDPC coded system in a Rayleigh fading channel with QPSK by HARQ scheme, RB-ARQ scheme, and proposed RB-HARQ scheme (required PER = 10−2 ) ....60. Figure 3.15. Throughput (bits/symbol) versus average SNR for (960,640) LDPC coded system in Rayleigh fading channel with QPSK by HARQ scheme, RB-ARQ scheme, and proposed RB-HARQ scheme (required PER = 10−2 ) ..........................................................................61. Figure 4.1. System architecture of proposed V-BLAST based adaptive MIMO-OFDM system ............................................................................66. Figure 4.2. Proposed V-BLAST based adaptive MIMO-OFDM system transmitter architecture ...........................................................................67. VIII.

(11) Figure 4.3. Proposed V-BLAST based adaptive MIMO-OFDM system receiver architecture..............................................................................................68. Figure 4.4. Throughput versus average SNR for the cross layer design AMC system (required Ploss = 10−2 ) in IEEE 802.20 Model-C channel.. (N t , N r ) = (2, 2) with RB-HARQ scheme, ARQ scheme, and AMC-only scheme. Other parameters are listed in Table 4.1.................83 Figure 4.5. Retransmission data rate versus average SNR for the cross layer design AMC system (required Ploss = 10−2 ) in IEEE 802.20 Model-C channel. (N t , N r ) = (2, 2) with RB-HARQ scheme, and ARQ scheme. Other parameters are listed in Table 4.1 ..........................84. Figure 4.6. PER versus average SNR for the cross layer design AMC system (required Ploss = 10−2 ) in. IEEE. 802.20. Model-C. channel.. (Nt , N r ) = (2, 2) with RB-HARQ scheme. Other parameters are listed in Table 4.1....................................................................................84 Figure 4.7. Throughput versus average SNR for the cross layer design AMC system (required Ploss = 10−2 ) in IEEE 802.20 Model-C channel.. (Nt , N r ) = (1,1) with RB-HARQ scheme, ARQ scheme, and AMC-only scheme. Other parameters are listed in Table 4.1.................85 Figure 4.8. Retransmission data rate versus average SNR for the cross layer design AMC system (required Ploss = 10−2 ) in IEEE 802.20 Model-C channel. (N t , N r ) = (1,1) with RB-HARQ scheme, and ARQ scheme. Other parameters are listed in Table 4.1. .........................85. Figure 4.9. PER versus average SNR for the cross layer design AMC system (required Ploss = 10−2 ) in. IEEE. 802.20. Model-C. channel.. (Nt , N r ) = (1,1) with RB-HARQ scheme. Other parameters are listed in Table 4.1....................................................................................86. IX.

(12) Figure 4.10. Throughput versus average SNR for the cross layer design AMC system (required Ploss = 10−2 ) in IEEE 802.20 Model-C channel in the presence of partial CSIT Σh = 0.01I . (N t , N r ) = (2, 2) f with RB-HARQ scheme, ARQ scheme, and AMC-only scheme. Other parameters are listed in Table 4.1 .................................................87. Figure 4.11. PER versus average SNR for the cross layer design AMC system (required Ploss = 10−2 ) in IEEE 802.20 Model-C channel in the presence of partial CSIT Σh = 0.01I . (N t , N r ) = (2, 2) with f RB-HARQ scheme, ARQ scheme, and AMC-only scheme. Other parameters are listed in Table 4.1 ...........................................................88. X.

(13) List of Tables Table 2.1. Summary of SISO link-level parameters for IEEE 802.20 channel models.................................................................................................... 25. Table 2.2. Summary of SISO environment parameters for IEEE 802.20 channel models ...................................................................................... 25. Table 2.3. Summary of MIMO link-level parameters for IEEE 802.20 channel models.................................................................................................... 29. Table 3.1. LDPC block sizes and code rates in IEEE 802.16-2005........................ 38. Table 3.2. Notations of sum-product algorithm...................................................... 63. Table 3.3. Simulation parameters of the adaptive RB-HARQ system ................... 56. Table 4.1. Simulation parameters of the ZF-BLAST based cross layer design AMC system .......................................................................................... 82. Table 4.2. SNR threshold table for various M-QAM at target PER = 10−2 ........ 82. XI.

(14) Acronym Glossary 4G. the fourth generation. AMC. adaptive modulation and coding. ARQ. automatic repeat request. AWGN. additive white Gaussian noise. BER. bit error rate. BPSK. binary phase shift keying. BLAST. Bell Lab Layered space time. BS. base station. CP. cyclic prefix. CRC. cyclic redundancy check. CSI. channel state information. CSIT. channel state information in the transmitter. DFT. discrete Fourier transform. FDD. frequency division duplex. FFT. fast Fourier transform. HARQ. hybrid automatic repeat request. ICI. intercarrier interference. IEEE. institute of electrical and electronics engineers. IFFT. inverse fast Fourier transforms. ISI. intersymbol interference. LDPC. low density parity-check. LOS. line of sight. MAC. medium access control layer. MIMO. multiple-input multiple-output. ML. maximum likelihood. XII.

(15) MMSE. minimum mean square error. MRC. maximal ratio combining. MS. mobile station. MUX. multiplex. OFDM. orthogonal frequency division multiplexing. OSIC. ordered successive interference cancellation. PHY. physical layer. PER. packet error rate. QAM. quadrature amplitude modulation. QoS. quality of service. QPSK. quaternary phase shift keying. RB-HARQ. reliability-based hybrid automatic repeat request. RF. radio frequency. RX. receiver. SD. spatial diversity. SM. spatial multiplexing. SNR. signal-to-noise ratio. SIC. successive interference cancellation. STC. space-time coding. TDD. time division duplex. TX. transmitter. V-BLAST. vertical Bell laboratory layered space-time. ZF. zero forcing. XIII.

(16) Notations bi. rate at the ith transmit antenna. C. transmission code words matrix. fd. Doppler frequency. Eb. bit energy. Es. symbol energy. hti , j. channel gain between the jth transmit and ith receive antenna at time t. H [k ]. channel frequency response on the kth subcarrier. M. modulation order. Nc. number of subcarriers (FFT/IFFT size). N cp. number of guard interval samples. Nt. number of transmit antenna. Nr. number of receive antenna. N0. noise power spectrum density. pn. path metric associated with the nth information bit. Pbudget. power budget. q. antenna state. rti. received data at the ith transmit at time t. S. set of signal constellation. st j. transmitted signal form the jth transmit at time t. T. set of switching levels. Ts. symbol duration. Tsample. sampling period. d [k ]. input symbol on the kth subcarrier. r[ k ]. received data on the kth subcarrier. η[k ]. additive white noise vector on the kth subcarrier. XIV.

(17) wj. weighting vector for the jth layer. ηti. additive white noise at the ith receive antenna at time t. σ n2. noise power. ε error. target BER. γ. instantaneous SNR. τ rms. root mean squared excess delay spread. ρ. average SNR at each receive antenna. λ. eigenvalue. XV.

(18) Chapter 1 Introduction Next generation broadband wireless communication systems are expected to provide users with multimedia services such as high-speed internet access, wireless television, mobile computing, and etc. The rapid growing demand for these services is driving the wireless communication technology towards higher data rates, higher mobility and higher carrier frequency. However, the physical limitation of the wireless channel, typically subject to both time-selective and frequency-selective fading that are induced by carrier phase/frequency drifts, Doppler shifts and multipath propagation, presents a fundamental challenge for reliable communications. On the other hand, the limited availability of bandwidth promotes an emerging issue of high spectral efficiency. Hence, recent research efforts are carried out to develop efficient coding and modulation schemes along with sophisticated signal processing algorithms to improve the quality and spectral efficiency of wireless communication links. Some popular examples include smart antenna, in particular multiple-input multiple-output (MIMO) technology [1]-[6], coded multicarrier modulation, adaptive modulation [7]-[10], and link-level retransmission techniques [11]. MIMO systems can be defined as follows: Given an arbitrary wireless system, we consider a link for which the transmitter side as well as the receiver side is equipped. 1.

(19) with multiple antennas. Such setup is illustrated in Figure 2.1. The signals on the transmit antennas at one end and the receive antennas at the other end are “co-processed” in such a way that the quality (packer error rate (PER)) or the data rate (bits/sec) of the communication link is improved. A core idea in MIM-OFDM systems is the space-time signal processing in which time is complemented with the spatial dimension inherent in the use of multiple spatially distributed antennas. A key feature of MIMO systems is to efficiently exploit the multipath, rather than mitigate it, to achieve the signal decorrelation necessary for separating the co-channel signals. Specifically, the multipath phenomenon presents itself as a source of diversity that takes advantage of random fading. Orthogonal frequency division multiplexing (OFDM) is a multipath-friendly mechanism that treats the whole transmission band as a set of adjacent narrow sub-bands. This property leads OFDM to be chosen over a single-carrier solution to avoid using a complicated equalizer, which is usually a heavy burden in a wideband communication receiver. Moreover, with proper coding and interleaving across frequencies, multipath turns into an OFDM system advantage by yielding frequency diversity. OFDM can be implemented efficiently by using the Fast Fourier Transforms (FFTs) at the transmitter and receiver. At the receiver, FFT reduces the channel response into a multiplicative constant on a tone-by-tone basis. In 1996, a new wireless communication scheme based on combination of the concepts of MIMO and OFDM was proposed [12]. Since then, MIMO-OFDM becomes an emerging research topic. The signaling scheme and receiver design are categorized into two categories: spatial multiplexing (SM) and spatial diversity (SD) schemes. In the former system, different data streams are transmitted from different antennas simultaneously and detected based on their unique spatial signature at the receiver. This. 2.

(20) implies the creation of parallel spatial channels to maximize the data rate. For the next communication, the requirement of Quality of Services (QoS) becomes more important. Two techniques are fundamental for reliability: forward error correction (FEC) and automatic repeat request (ARQ). Hybrid ARQ (HARQ) is a variation of the ARQ error control method, which gives better performance than ordinary ARQ, particularly over wireless channels, at the cost of increased implementation complexity. When the coded data block is received, the receiver first decodes the error-correction code. If the channel quality is good enough, all transmission errors should be correctable, and the receiver can obtain the correct data block. If the channel quality is bad and not all transmission errors can be corrected, the receiver will detect this situation using the error-detection code, then the received coded data block is discarded and a retransmission is requested by the receiver, similar to ARQ. WiMAX is defined as Worldwide Interoperability for Microwave Access by the WiMAX Forum [13], [14]. The Forum describes WiMAX as "a standards-based technology enabling the delivery of last mile wireless broadband access as an alternative to cable and DSL." WiMAX uses the advanced techniques such as multi-channel scalable OFDM, HARQ, FEC, MIMO and other complementary technologies as are part of WiMAX. WiMAX is designated as the metropolitan area network (MAN) technology that can connect IEEE 802.11 (Wi-Fi) hotspots with each other and to other parts of the Internet and provide a wireless alternative to cable and DSL for last mile broadband access. It is also anticipated that WiMAX will allow inter-penetration for broadband service provision of VoIP, video, and Internet access—simultaneously. In principle, the MIMO technologies can provide not only the antenna gain for. 3.

(21) interference suppression, but also various point-to-point link profits for covering wider service regions and improving various QoS. High-speed data service in WMANs through MIMO largely relies on rich-scattering and reliable background channel conditions. The radio environment inside a network, however, may be time-varying, and within which high-speed transmission may lead to high frame error rates. To sustain good link services, adaptive modulation techniques are proposed to dynamically adjust transmission parameters based on the near instantaneous channel state information (CSI) [9],[10] to ease channel impairments. Also, most wireless communication transceivers have built-in modules for supporting PHY layer data processing and MAC layer resource management. As a result, cross-layer processing that exploits the joint resource for more efficient PHY layer designs and more effective MAC protocol setups will become an important issue. In this thesis, we will attempt to develop an adaptive wireless transceiver that can take advantages of the existing system jointly to effectively exploit the available degrees of freedom in the wireless communication systems. Besides, an adaptive wireless transceiver which employs smart antenna and spatial multiplexing techniques is proposed to overcome the wireless channel impairments. This thesis is organized as follows. In Chapter 2, we describe the general data model and channel capacity of a MIMO communication link. Spatial multiplexing technique is also presented to provide a preliminary overview. In Chapter 3, we introduce the principle of algorithm of reliability-based HARQ (RB-HARQ) which is based on low density parity-check (LDPC) codes [15]-[20]; Moreover, we propose an adaptive algorithm which can accordingly choose the sizes of retransmissions under the QoS constraints such as the maximum number of retransmissions allowed per packet and packet loss probability. In Chapter 4, we develop the cross-layer design by. 4.

(22) combining AMC at PHY layer with several MAC protection strategies; We propose an adaptive MIMO-OFDM transceiver architecture along with a specifically designed loading procedure to dynamically adjust the transmission parameters such as retransmission size, number of retransmission, modulation order and transmit power over spatial and frequency channels, according to the instantaneous channel statistics, to meet the target QoS. Finally, Chapter 5 gives concluding remarks of this thesis and leads the way to some potential future works.. 5.

(23) Chapter 2 Overview of IEEE 802.16 System IEEE 802.16 is a wireless communication system that provides high-throughput broadband connections. IEEE 802.16 can be used for a number of applications, including "last mile" broadband connections, hotspots and cellular backhaul, and high-speed enterprise connectivity for business. IEEE 802.16 uses several advance techniques in PHY layer, such as OFDM, and MIMO. OFDM is one of the most promising PHY layer technologies for high data rate wireless communications due to its robustness to frequency selective fading, high spectral efficiency, and low computational complexity. OFDM can be used in conjunction with a MIMO transceiver to increase the diversity gain and/or the system capacity by exploiting spatial domain. Because the OFDM system effectively provides numerous parallel narrowband channels, MIMO-OFDM is considered a key technology in emerging high-data rate systems such as IEEE 802.16, IEEE 802.11n, and 4G. In this chapter, we introduce the basic ideas of the MIMO-OFDM systems and key features of IEEE 802.16.. 2.1 Review of MIMO-OFDM System MIMO-OFDM is considered a key technique in high-data rate systems. In this section, we introduce the basic ideas and key features of MIMO-OFDM systems.. 6.

(24) 2.1.1 OFDM : Concept and Technique OFDM can be regarded as either a modulation or a multiplexing technique. The basic concept of OFDM is to split a high rate data stream into a number of lower rate streams that are transmitted simultaneously over subcarriers. In order to eliminate the effect of inter-symbol interference (ISI), a guard time is appended to each OFDM symbol. The guard time is chosen to be larger than the maximum delay spread such that the current OFDM symbol never hears the interference from the previous one. However, this method will cause the inter-carrier interference (ICI) due to the loss of orthogonality between subcarriers. To solve this problem, OFDM symbols are cyclically extended in the guard time to introduce cyclic prefix (CP). This ensures that the delayed replicas of an OFDM symbol always have an integer number of cycles within the FFT interval. As a result, CP resolves both ISI and ICI problems caused by multipath, as long as the delay spread of channel is smaller than the length of CP. Besides, adding CP makes the transmitted OFDM symbol appear periodic, and the linear convolution process of the transmitted OFDM symbols (containing CP) with channel impulse response will be translated into a circular convolution one. According to discrete-time linear system theory, this circular convolution is equivalent to multiplying the frequency response of the OFDM symbol with the channel’s frequency response. This property can be demonstrated as follows: Assuming that the channel length is smaller than Ncp (number of samples in CP), we can express the received data vector y as. y = Hx + η. 7. (2.1).

(25) ⎡h0 h1 hNcp ⎡yN −1 ⎤ ⎢⎢ ⎢ c ⎥ ⎢ 0 h0 h1 ⎢ ⎥=⎢ ⎢ ⎥ ⎢0 0 ⎢ ⎥ y ⎢⎣ 0 ⎥⎦ ⎢⎢ 0 h0 ⎢⎣ 0 y. ⎡x N −1 ⎤ ⎢ c ⎥ 0 ⎤⎢ ⎥ ⎥⎢ ⎥ ⎥ ⎢ x ⎥ ⎡⎢ ηNc −1 ⎤⎥ 0 ⎥⎢ ⎥ ⎥ ⎥ ⎢ x ⎥ + ⎢⎢ ⎥ 0 ⎥ ⎢ −1 ⎥ ⎢ ⎥ ⎥⎢ ⎥ ⎢ η0 ⎥ ⎦ ⎥ ⎣ hNcp ⎥⎥ ⎢ η ⎥ ⎦⎢ ⎢x −Ncp ⎥ ⎣ ⎦. 0 hNcp. 0. h1. H. (2.2). x. When we use singular value decomposition (SVD), we have. H = FΛMH. (2.3). where FFH = I and MMH = I . If we let x = MX and Y = FH y , then we can get. Y = FH y = FH (Hx + η) = FH HMX + N = ΛX + N. (2.4). H. F η. It is interesting to note that when the guard period contains a CP, that is, x−i = x N −i for i = 1,..., Ncp , Equation (2.2) can be rewritten in a more compact matrix form. ⎡yN −1 ⎤ ⎢ c ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢⎣ y0 ⎥⎦. ⎡ h0 ⎢ ⎢ 0 ⎢ ⎢ ⎢ ⎢ = ⎢⎢ 0 ⎢ ⎢hNcp ⎢ ⎢ ⎢ ⎢ h ⎢⎣ 1. h1 h0. hNcp h1. ⎤ ⎥ 0 ⎥⎥ ⎥ ⎥ ⎡x N −1 ⎤ ⎡ ηN −1 ⎤ ⎥⎢ c ⎥ ⎢ c ⎥ ⎥ ⎢ ⎥ hNcp ⎥⎥ ⎢⎢ ⎥+⎢ ⎥, ⎥⎢ ⎥ ⎢ ⎥ hNcp −1 ⎥ ⎢ x 0 ⎥ ⎢ η0 ⎥ ⎣ ⎦ ⎣ ⎦ ⎥ ⎥ ⎥ h0 ⎥⎥ ⎦. 0. 0. hNcp. 0 0 hNcp. h0. h1. 0. h0. 0. 0. (2.5). and H becomes the so called “circulant matrix” and has the property that H = QH ΛQ , where Q is a discrete Fourier transform (DFT) matrix with klth entry as kl. Qkl =. 1 − j 2 π Nc e Nc. (2.6). and the transformed symbol is x = QH X (inverse DFT (IDFT) of x). Thus X can be interpreted as symbols in the frequency domain. At the receiver, we have the received data y being transformed to Y .. 8.

(26) Y = QH y = QH (Hx + η) = QH HQH X + QH η. (2.7). N. Λ. = ΛX + N Now, we can realize that by using CP, the OFDM modulation is equivalent to multiplying the frequency domain signals of the OFDM symbol (that is, X ) with the channel’s frequency response Λ . Broadband transmission over multipath channels usually exhibits frequency selective fading. Since data rate requirements can be expected to increase even further in the future, this effect is likely to amplify. In OFDM, frequency diversity can be realized through coding and interleaving across subcarriers. Because information bits are separated over many subcarriers, the impairment of fading occurring at particular frequency tones can be mitigated. As a consequence, in the coded OFDM systems the presence of frequency selective fading actually saves the frequency tones at fading. Depending on the coding rate and interleaving death, gains can be achieved at locations experiencing significant delay spread. It can be concluded that OFDM is a powerful modulation technique that increases bandwidth efficiency and simplifies the removal of distortion due to a multipath channel. Advances in FFT algorithm enable OFDM to be efficiently implemented in hardware, even for a large number of subcarriers. The key advantages of OFDM transmission are summarized as follows: 1.. OFDM deals with multipath delay channels in an efficient way. The implementation complexity is significantly lower than that of a single carrier system with an equalizer.. 2.. OFDM has a long symbol period (compared to an equal data-rate single-carrier system) that allows OFDM to be more robust against impulse noise. 9.

(27) 3.. OFDM supports dynamic bit loading that enable different subcarriers to use different modulation modes depending on the channel characteristic or the noise level. Therefore, improved performance can be achieved in this systematic way.. 2.1.2 MIMO : Concept and Technique MIMO contains two important techniques: SM and diversity. Figure 2.1 shows the diagram of a MIMO wireless transmission system. SM is a technique that yields an increased bit rate by using multiple antennas at both end of the wireless link [1]-[3]. This increase comes at no extra bandwidth and power consumption. However, such a technique calls for an efficient way to map the transmit signals to individual antenna elements. At the receiver, the individual data streams are separated and demultiplexed to yield the original transmitted signals, as illustrated in Figure 2.2. The separation is made possible by the fact that the rich multipath contributes to lower correlation between MIMO channel coefficients, and hence creates a desirable coefficient matrix condition (i.e., full rank and low condition number) to resolve N t unknowns from a linear system of N r equations. In the following, we will introduce two SM schemes. Transmitter. ht1,1. 1 t. s. Receiver. ht2,1. s. ⊕. ht1, Nt. s. ⊕. ηt2. 2 t. Nt t. ηt1. htNr , Nt. Rich Scattering Environment. ηt2. ⊕. rt1 rt 2. rt Nr. N R -antennas. NT -antennas. Figure 2.1: Diagram of a MIMO wireless transmission system 10.

(28) Transmitter. Receiver. Figure 2.2: Illustration of a spatial multiplexing system. 2.1.2.1 Diagonal Bell Labs’ Layered Space-Time The Layered Space-Time processing concept was first introduced by Foschini [1] at Bell Labs. The first version, Diagonal Bell Labs’ Layered Space-Time (D-BLAST), utilizes multiple antenna arrays at both the transmitter and receiver, and an elegant diagonally-layered coding structure in which code blocks are dispersed across diagonals in space-time. The encoding and decoding procedures are described as follows: • Encoding:. Considering a system equipped with N t transmit and N r receive antennas, the encoder applies the space-time codes to the input to generate a semi-infinite matrix C of N t rows to be transmitted. Figure 2.3 shows the encoding scheme, where cτk , representing an element in the kth row and τ th column of C, is transmitted by the kth transmit antenna at time τ . The data received at time τ by the lth receive antenna is rτl , which contains a superposition of cτk , k = 1, 2, …, N t , and an AWGN noise component. Each subsequence is encoded using a conventional 1-D constituent code with low decoding complexity. • Decoding:. At any instance τ , the received data vector is rτ = Hτ cτ + ητ . The decoding 11.

(29) T task is to determine cτ = ⎡⎢cτ1 , cτ2,..., cτNt ⎤⎥ with the only available information being ⎣ ⎦. rτ and Hτ . The D-BLAST uses a repeated process of interference suppression, symbol. detection. and. interference. cancellation. for. decoding. all. symbols,. cτNt , cτNt −1,..., cτ1 . Such decoding process could be expressed in a general form: Let the QR decomposition of Hτ be Qτ R τ , where Qτ is an N r × N r unitary matrix and R τ is an N r × N t upper triangular matrix. We modify the received data to get H H H H y τ = QH τ rτ = Q τ H τ c τ + Qτ ητ = Qτ Qτ R τ cτ + Qτ ητ INr. ητ. (2.8). = R τ cτ + ητ where ⎡r 1,1 r 1,2 τ ⎢τ ⎢ ⎢ 0 rτ2,2 ⎡ y1 ⎤ ⎢ ⎢ τ ⎥ ⎢ 0 0 ⎢ 2⎥ ⎢ ⎢ yτ ⎥ ⎢ ⎥ y τ = ⎢⎢ 0 ⎥ , R τ = ⎢⎢ ⎢ ⎥ ⎢ ⎢ N ⎥ ⎢ 0 ⎢y τ r ⎥ ⎢ ⎣⎢ ⎦⎥ ⎢ 0 0 ⎢ ⎢ 0 ⎢⎣ 0. rτ1,Nt ⎤⎥ ⎥ rτ2,Nt ⎥ ⎡ η1 ⎤ ⎥ ⎢ τ ⎥ ⎥ ⎢ 2⎥ ⎥ ⎢ ητ ⎥ ⎥ ⎥ Nt ,Nt ⎥ , η = ⎢ rτ ⎢ ⎥ ⎥ τ ⎢ ⎥ ⎥ ⎢ N ⎥ 0 ⎥ ⎢ ητ r ⎥ ⎥ ⎣⎢ ⎦⎥ ⎥ ⎥ ⎥ 0 ⎥ ⎦. (2.9). Since R τ is upper triangular, y τk = rτk ,kcτk + ηkτ + {contribution from cτk +1 , cτk + 2 ,..., cτNt }. (2.10). Now, we can figure out that the interference from cl , l < k ≤ N t , are first suppressed in y k and the residual interference terms in Equation (2.10) can be cancelled by the available decisions cˆτk +1 , cˆτk +2 ,…, cˆτNt . Assuming all these decisions are correct, the present decision variable is cτk = rτk ,kcτk + ητk , k = 1, 2, …, N t. (2.11). The relationship between ck and c k in Equation (2.11) can be interpreted as the input and output of a single-input and single output channel with the channel power 12.

(30) gain. r k ,k. 2. and AWGN. The channel power gain. r k ,k. 2. are independently. chi-squared distributed with 2 × (N r − k + 1) degrees of freedom. Moreover, if there are no decision feedback errors, we can treat the kth row of the C matrix as transmitted over a (N t , N r ) = (1, N r − k + 1) system without interference from the other rows and all fades are i.i.d. Figure 2.4 shows typical decoding steps (suppression, detection, decoding and cancellation) performed in a D-BLAST system. The receiver generates decisions for the first diagonal of C, cˆ11 , cˆ22 ,... , cˆNNtt . Based on these decisions, the diagonal is decoded and fed back to remove the contribution of this diagonal from the received data. The receiver continues to decode the next diagonal and so on. The encoded substreams share a balanced presence over all paths to the receiver, so none of the individual substreams is subject to the worst path.. Nt = 3 In fo rm at io n B its. 1 :3 DEM UX. E n co d e r 1 E n co d e r 2 E n co d e r 3. S p ac e D -B L A S T. ⎡ ⎢ C = ⎢⎢ ⎢ ⎣. c 11 c 12 c 31 c 14 2 0 c 22 c 3 c 42 3 3 0 0 c3 c4. c 52 c 53 c 63. ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ T im e. S p ac e V -B L A S T. ⎡ ⎢ C = ⎢⎢ ⎢ ⎣. ⎤ ⎥ ⎥ ⎥ ⎥ ⎦. c 11 c 12 c 31 c 12 c 22 c 32 c 13 c 23 c 33. T im e. Figure 2.3: Diagonal and vertical layered space-time encoding with N t = 3 .. 13.

(31) Figure 2.4: Diagonal layered space-time decoding with N t = 3. 2.1.2.2 Vertical Bell Labs’ Layered Space-Time The diagonal approach suffers from certain implementation complexities that make it inappropriate for initial implementation. Therefore, Foschini proposed another low-complexity version of detecting the symbols transmitted synchronously over antennas, that is, V-BLAST [3]. The “V” here stands for the vertical vector mapping process, which differs from the diagonal form in D-BLAST. In V-BLAST, no inter-substream coding, or coding of any kind, is required, though conventional coding of the individual substreams may certainly be applied. In [4], a vertical-and-horizontal coding structure along with iterative detection and decoding (IDD) was promoted and showed to significantly improve the performance with limited complexity. Figures 2.3 and 2.5 display the typical encoding and decoding steps in V-BLAST, respectively. The decoding process can also be interpreted via the general form (QR decomposition) as mentioned in decoding D-BLAST. In each step I, the signals from all but one transmit antenna are eliminated using interference suppression and 14.

(32) cancellation with already detected signals. Following the data model in D-BLAST, at a given time instant τ , let Hi =1 = Hτ and ri =1 = rτ at the first decoding step. In each step i, the nulling matrix Gi is calculated as the pseudo-inverse of Hi Gi = (Hi )+ −1. = ((Hi )H Hi ). (Hi )H. (2.12). Each row of Gi can be used to null all but the ith desired signal. Instead of choosing an arbitrary layer to be detected first, it was suggested to start with the layer showing the biggest post-detection signal-to-noise ratio (SNR) to efficiently reduce the error propagation effect [3]. This corresponds to choosing the row of Gi with the minimum norm and defining the corresponding row, wTki , as the nulling vector at this step: ki = arg min || (Gi )j ||2. (2.13). wki = (Gi )Tki. (2.14). j ∉{k1,...,ki −1 }. Multiplying w ki with the vector of received data r i suppresses all layers but the one transmitted from antenna ki and we get a soft decision value. cτ ki = wTki rτi. Figure 2.5: Vertical layered space-time decoding with N t = 3 15. (2.15).

(33) Now the ki th layer can be detected within the constellation set S that we use:. cˆτ ki = arg min || c − cτki ||2. (2.16). x ∈S. As soon as one layer is detected, we can improve the detection performance for the subsequent layers by subtracting the part of the detected signal from the received vector, ki. rτi +1 = rτi − cˆτ ki (Hi ). where. (H ) i. ki. (2.17). denotes the kith column of H i . After canceling out the signal from the. kith transmit antenna, the channel matrix is reduced to ki. Hi +1 = (Hi ). ( ). where the notation H i. ki. (2.18). denotes the matrix obtained by zeroing columns k1 , k2 ,..., ki. of H i . Since we decrease the number of layers to be nulled out in the next step by one, the diversity gain is increased by one at each step (from (N r − N t + i ) to. (N r − N t + i + 1) ). This can be proven by the Cauchy-Schwartz inequality [3]. The full Zero-Forcing V-BLAST detection algorithm can be summarized as follows: Initialization:. i ←1 +. G1 = (H1 ). k1 = arg min || (G1)j ||2 j. Recursion:. wki = (Gi )Tki c ki = wTki ri cˆki = Q(c ki ) , Q(⋅) denotes the slicing operation. 16.

(34) ri +1 = ri − cˆki (Hi )ki ki. Hi +1 = (Hi ). +. Gi+1 = (Hi +1 ) ki +1 = arg. min. j ∉{k1 , ki }. || (Gi +1 )j ||2. i ← i +1. The post-processing SNR for the kith detected component of c is ρki =. <| c ki |2 > σ 2 || wki ||2. (2.19). where the expectation value in the numerator is taken over the constellation set S. Another way to improve detection performance especially for mid-range SNR values is to replace the ZF nulling matrix by the more powerful MMSE one [3]:. ⎛ 1 ⎞⎟−1 i H Gi = ⎜⎜(Hi )H Hi + I ⎟ (H ) ⎝ SNR ⎠⎟. (2.20). In this case, in additional to nulling out the interference, the noise level on the channel is taken into account. Thus, the SNR has to be estimated at the receiver. Figure 2.5 shows the typical decoding procedure in V-BLAST. The D-BLAST code blocks are organized along diagonals in space-time. It is this coding that leads to D-BLAST’s higher spectral efficiencies for a given number of transmit and receive antennas.. 2.1.3 V-BLAST Based OFDM Due to the scarcity of radio spectrum, high spectral efficiency becomes a must-have requirement that encourages modern wireless modems toward this trend. An evolution of the V-BLAST supporting OFDM modulation seems to be a solution that. 17.

(35) can dramatically increase the capacity of wireless radio links with no additional power and bandwidth consumption. The core idea in such scheme is that with the aid of OFDM, the whole detection problem in MIMO-OFDM would be translated into Nc parallel sub-problems. In the transmitter, as shown in Figure 2.6, a traditional 1-D channel encoder is used to encode the information bits. These coded bits are then mapped on the symbols of constellation adopted for each subcarrier. At a given time slot n, Nc × N t bit streams {ci [n, k ] : k = 0,1, … Nc } for i = 1, 2 …, N t are fed to the IFFT at the ith transmit antenna on the kth subcarrier to generate the nth transmitted OFDM symbols from the ith transmit antenna. At the receiver side, as shown in Figure 2.7, receive antennas 1 − N r will receive the radiate signal from transmit antennas 1 − N t , where the V-BLAST requires N r ≥ N t to ensure its proper working. The received data at each receive antenna will then pass through a FFT with the removal of the CP. The FFT output, at the receive antenna j, is a set of Nc signals, one for each frequency subcarrier, expressed as rj [n, k ] =. Nt. ∑ H j ,i [n, k ]ci [n, k ] + η j [n, k ]. i =1. ∀k = 1, 2,..., Nc. (2.21). where H i , j [n, k ] is the flat fading coefficient representing the channel gain form the transmit antenna i to the receive antenna j at frequency k, and η j [n, k ] denotes the additive complex Gaussian noise at the receiver antenna j and frequency k with two sides power spectral density N 0 / 2 per dimension and uncorrelated for different n’s, k’s, and j’s.. 18.

(36) TX Antenna 1. c1[n, N c ]. M-QAM 1 Symbols. c1[ n, N c − 1] S/P. . .. IFFT. ADD CP. c1[n,1]. S/P Information bits. Channel Encoder. Bit Æ M-QAM. TX Antenna 2. c2 [ n, N c ] c2 [n, N c − 1]. M-QAM 2 Symbols. . .. IFFT. ADD CP. c2 [n,1]. DEMUX 1ÆNt . . .. . . .. TX Antenna N t. c N t [ n, N c ] cNt [n, Nc − 1]. M-QAM N t Symbols S/P. . .. IFFT. ADD CP. cNt [n,1]. Figure 2.6: V-BLAST based MIMO-OFDM transmitter architecture Nc. r1[n, N c ] Remove CP. RX Antenna 1. • •. . .. FFT. r1[ n, 2]. 1. 2. •. cˆ1[ n, N c ]. r1[n,1]. cˆ2 [.n, N c ]. r2 [ n, N c ] Remove CP. RX Antenna 2. . .. . .. FFT. cˆNt [n, Nc ]. r2 [ n, 2]. cˆ1[ n, 2] cˆ2 [.n, 2]. r2 [n,1] . . . . . . RX Antenna N r. Remove CP. . . . . .. . .. V-BLAST. M-QAMÆBits. Channel Decoder. cˆNt [n, 2]. cˆ1[n,1]. rNr [n, Nc ]. cˆ2.[ n,1]. . .. FFT. MUX. . .. rNr [n, 2] rNr [n,1]. cˆNt [n,1]. Figure 2.7: V-BLAST based MIMO-OFDM receiver architecture.. 2.2. WiMAX Overview. WiMAX is defined as Worldwide Interoperability for Microwave Access by the WiMAX Forum, formed in April 2001 to promote conformance and interoperability of the standard IEEE 802.16 [13]-[14]. The Forum describes WiMAX as "a standards-based technology enabling the delivery of last mile wireless broadband access as an alternative to cable and DSL." The WiMAX Forum is "the exclusive organization dedicated to certifying the interoperability of BWA products, the WiMAX 19.

(37) Forum defines and conducts conformance and interoperability testing to ensure that different vendor systems work seamlessly with one another.". 2.2.1 Review of IEEE 802.16 PHY A recent addition to the WiMAX standard is underway which will add full mesh networking capability by enabling WiMAX nodes to simultaneously operate in "subscriber station" and "base station" mode. This will blur that initial distinction and allow for widespread adoption of WiMAX based mesh networks and promises widespread WiMAX adoption. WiMAX/802.16's use of OFDMA and scheduled MAC allows wireless mesh networks to be much more robust and reliable. These differences between and evolution of Wi-Fi and WiMAX mesh networks could serve as a separate Wikipedia topic. The original WiMAX standard, IEEE 802.16, specifies WiMAX in the 10 to 66 GHz range. 802.16a, updated in 2004 to 802.16-2004, added support for the 2 to 11 GHz range, of which most parts are already unlicensed internationally and only very few still require domestic licenses. Most business interest will probably be in the 802.16-2004 standard, as opposed to licensed frequencies. The WiMAX specification improves upon many of the limitations of the Wi-Fi standard by providing increased bandwidth and stronger encryption. It also aims to provide connectivity between network endpoints without direct line of sight in some circumstances. The details of performance under non-line of sight (NLOS) circumstances are unclear as they have yet to be demonstrated. It is commonly considered that spectrum under 5−6 GHz is needed to provide reasonable NLOS performance and cost effectiveness for PtM (point to multi-point) deployments. WiMAX makes clever use of multi-path signals but does not defy the laws of physics. 20.

(38) A number of PHY considerations were taken into account for the target environment. At higher frequencies, line of sight is a must. This requirement eases the effect of multipath, allowing for wide channels, typically greater than 10 MHz in bandwidth. This gives IEEE 802.16 the ability to provide very high capacity links on both the uplink and the downlink. For sub 11 GHz non line of sight capability is a requirement. The original IEEE 802.16 MAC was enhanced to accommodate different PHYs and services, which address the needs of different environments. The standard is designed to accommodate either Time Division Duplexing (TDD) or Frequency Division Duplexing (FDD) deployments, allowing for both full and half-duplex terminals in the FDD case.. 2.2.2 Review of IEEE 802.16 MAC The IEEE 802.16 media access controller (MAC) [14] is significantly different from that of IEEE 802.11 Wi-Fi MAC. In Wi-Fi, the MAC uses contention access—all subscriber stations wishing to pass data through an access point are competing for the AP's attention on a random basis. This can cause distant nodes from the AP to be repeatedly interrupted by less sensitive, closer nodes, greatly reducing their throughput. And this makes services, such as VoIP or IPTV which depend on a determined level of QoS difficult to maintain for large numbers of users. By contrast, the IEEE 802.16 MAC is a scheduling MAC where the subscriber station only has to compete once (for initial entry into the network). After that it is allocated a time slot by the base station. The time slot can enlarge and constrict, but it remains assigned to the subscriber station meaning that other subscribers are not supposed to use it but take their turn. This scheduling algorithm is stable under overload and over-subscription (unlike IEEE 802.11). It is also much more bandwidth 21.

(39) efficient. The scheduling algorithm also allows the base station to control QoS by balancing the assignments among the needs of the subscriber stations. The MAC was designed specifically for the PMP wireless access environment. It supports higher layer or transport protocols such as ATM, Ethernet or Internet Protocol (IP), and is designed to easily accommodate future protocols that have not yet been developed. The MAC is designed for very high bit rates (up to 268 mbps each way) of the truly broadband PHY layer, while delivering ATM compatible QoS; UGS, rtPS, nrtPS, and Best Effort. The frame structure allows terminals to be dynamically assigned uplink and downlink burst profiles according to their link conditions. This allows a trade-off between capacity and robustness in real-time, and provides roughly a two times increase in capacity on average when compared to non-adaptive systems, while maintaining appropriate link availability. The IEEE 802.16 MAC uses a variable length Protocol Data Unit (PDU) along with a number of other concepts that greatly increase the efficiency of the standard. Multiple MAC PDUs may be concatenated into a single burst to save PHY overhead. Additionally, multiple Service Data Units (SDU) for the same service may be concatenated into a single MAC PDU, saving on MAC header overhead. Fragmentation allows very large SDUs to be sent across frame boundaries to guarantee the QoS of competing services. And, payload header suppression can be used to reduce the overhead caused by the redundant portions of SDU headers. The MAC uses a self-correcting bandwidth request/grant scheme that eliminates the overhead and delay of acknowledgements, while simultaneously allowing better QoS handling than traditional acknowledged schemes. Terminals have a variety of options available to them for requesting bandwidth depending upon the QoS and traffic. 22.

(40) parameters of their services. They can be polled individually or in groups. They can steal bandwidth already allocated to make requests for more. They can signal the need to be polled, and they can piggyback requests for bandwidth.. 2.2.3 Review of IEEE 802.16-2005 IEEE 802.16-2005, approved December, 2005 (formerly named but still best known as 802.16e or Mobile WiMAX) [13]. The WiMAX mobility standard is an improvement on the modulation schemes stipulated in the original (fixed) WiMAX standard. It allows for fixed wireless and mobile Non Line of Sight (NLOS) applications primarily by enhancing the OFDMA (Orthogonal Frequency Division Multiple Access). Many think that by stipulating a new modulation method called Scalable OFDMA (SOFDMA), 802.16-2005 will make the older 802.16-2004 which uses OFDM-256 obsolete. However, several manufacturers plan for a migration path from the older version of the standard to the more robust, mobile modulation scheme. In any case, manufacturers are working through the WiMAX Forum to achieve compatibility between similar system profiles. SOFDMA will improve upon OFDM-256 for NLOS applications by: •. Improving NLOS coverage by utilizing advanced antenna diversity schemes, and hybrid-Automatic Retransmission Request. •. Increasing system gain by use of denser sub-channelization, thereby improving indoor penetration. •. Introducing high-performance coding techniques such as Turbo coding and LDPC, enhancing security and NLOS performance. 23.

(41) •. Introducing downlink sub-channelization, allowing administrators to trade coverage for capacity or vice versa. •. Improving coverage by introducing Adaptive Antenna Systems (AAS) and MIMO technology. •. Eliminating channel bandwidth dependencies on sub-carrier spacing, allowing for equal performance under any RF channel spacing (1.25-14 MHz). •. Enhanced FFT algorithm can tolerate larger delay spreads, increasing resistance to multipath interference. SOFDMA and OFDMA-256 are not compatible so most equipment will have to be replaced. However, some manufacturers are attempting to provide a migration path for older equipment to SOFDMA compatibility which would ease the transition for those networks which have already made the OFDMA-256 investment.. 2.3. MIMO Channel Model. We use IEEE 802.20 channel models in simulations [21]. In single-in single-out systems shall use the ITU model in simulations. The parameters are list in Table 2.1. Table 2.2 shows the SISO Channel Environment Parameters. We will describe a MIMO channel model that captures the above characteristics and that can be collapsed to an underlying SISO ITU channel mode by using a correlation matrix approach in simulations. The correlation matrices are only antenna system dependent.. 24.

(42) Table 2.1:. Summary of SISO link-level parameters for IEEE 802.20 channel models Case-B. PDP. Pedestrian-A. Vehicular-A. Number of Paths. 4. 6. Delay (ns). Case-A. Relative Path power (dB). Models. Speed (km/h). Table 2.2:. Case-C. Case-D. Pedestrian-B. Vehicular-B. (Phase I). (Phase I). 6. 6. 0. 0. 0. 0. 0. 0. -2.5. 0. -9.7. 110. -1.0. 310. -0.9. 200. 0. 300. -19.2. 190. -9.0. 710. -4.9. 800. -12.8. 8900. -22.8. 410. -10.0. 1090. -8.0. 1200. -10.0. 12900. -15.0. 1730. -7.8. 2300. -25.2. 17100. -20.0. 2510. -23.9. 3700. -16.0. 20000. 3, 30, 120. 30, 120, 250. 3. 30, 120, 250. Summary of SISO environment parameters for IEEE 802.20 channel models. Channel Scenario. Suburban Macro. Urban Macro. Lognormal shadowing standard deviation. 10dB. 10dB. Urban Micro NLOS: 10dB LOS: 4dB NLOS:. Pathloss model (dB), d is in meters. 31.5 + 35log10(d). 34.5 + 35log10(d). 34.53+38log10(d) LOS: 30.18 + 26*log10(d). 2.3.1 Correlation Channel Matrices In the correlation matrix approach, the channel from any of the N transmit antennas to the M receive antenna elements is generated from M independent channels from that transmit antenna to the M receive antennas. That is, for any given 25.

(43) channel tap, we will have [21] 2 hi (τ ) = R1/ ⋅ gi (τ ) r. (2.22). where hi (τ ) is the channel vector from the i -th transmitting antenna to the M receive antennas, gi (τ ) is the underlying independent Gaussian channel vector (i.e. it is the channel vector from the i -th transmitting antenna to the M receive antennas if the 2 is the square root of the channel receive receive antennas were uncorrelated), and R1/ r 2 are correlation matrix. Please note that the dimensions of hi (τ ) , gi (τ ) , and R1/ r. M × 1 , M × 1 , and M × M , respectively.. In addition, we note that each ITU. channel profile defines a number of taps with a corresponding tap delay and average tap power.. The above description for the channel vector hi (τ ) is repeated for each. channel tap. Moreover, please note that the underlying independent Gaussian channel vector gi (τ ) is completely different (i.e. independent) for each tap. Note that, when 2 is simply 1 and the there is only one transmit antenna and one receive antenna, R1/ r. above reduces to the scalar ITU channel model. In a similar fashion, let us now consider the channel from the N transmit antennas to any of the. M. receive antennas.. The channel row-vector. h j (τ ) corresponding to the channels from all the N transmit antennas to the j -th receive antenna is related to the underlying independent Gaussian channel row-vector g j (τ ) (i.e the channel row-vector from all N -transmit antennas to the j -th receive. antenna if the transmit antennas were uncorrelated) by [21] 2 h j (τ ) = g j (τ ) ⋅ R1/ t. (2.23). 2 is the square root of the transmit array correlation matrix. We note that the where R1/ t 2 are 1 × N , 1 × N , and N × N respectively . dimensions of h j (τ ) , g j (τ ) , and R1/ t. 26.

(44) 2.3.2 Generation of a MIMO Channel Using Correlation Matrix Approach Some of the parameters that can be used in the correlation channel model are shown in Table 2.3. In order to generate a MIMO channel, we first need to have a pair of transmit and receive R t and R r correlation matrices. These are generated for each mobile station (MS) and base station (BS) based on the number of antennas, antenna spacing, number of clusters, power azimuth spectrum (PAS), azimuth spread (AS), and angle of arrival (AoA). In addition to the correlation matrices, we also need to specify an underlying ITU SISO model from Table 2.1 and choose the mobile speed. As an example, a MIMO link with N transmit and M receive antennas can be then generated as follows: [21] 1.. Generate N ⋅ M SISO links based on the chosen ITU profiles as follows a. Let A1, A2,. , AK. τ1, τ2,. and. , τK. represent the power-delay. profile for the specified ITU channel model b. Generate K independent Rayleigh fading processes each having a Doppler spread fd (function of the chosen mobile speed). The number of samples in each of the fading processes is given by the required number of symbols at the specified sampling rate c. Scale the k -th Rayleigh process by Pk where Pk2 =. Ak. K. (2.24). ∑ Ak. k =1. d. Generate the pulse shaping matrix G( τ) e. Compute the channels taps. This will result in L + 1 Rayleigh fading processes where L + 1 is the number of taps in the digital channel corresponding to the specified ITU channel model. 27.

(45) 2.. Given the N ⋅ M SISO links generated in step 1 above, each is described by L + 1 processes, we define the following M × N i -th tap gain matrix for. every channel sample (i.e. for every t ) [21] ⎛ (i ) ⎞ ⎜⎜ h11 (t ) … h1(nN)(t ) ⎟⎟ ⎟⎟ ⎜⎜ ⎟⎟ Hi (t ) = ⎜⎜ ⎟⎟ ⎜⎜ ⎟⎟ (i ) ⎜⎜h (i ) (t ) (t )⎠⎟⎟ hMN ⎝ M1. 3.. (2.25). Color the tap gain matrix by the receive and transmit correlation matrices as follows [21] ˆ (t ) = R1/ 2 ⋅ H (t ) ⋅ R1/ 2 H i r i t. The overall procedure for generating the channel matrices consists of three basic steps: 1.. Specify an environment, i.e., suburban macro, urban macro, or urban micro.. 2.. Obtain the parameters to be used in simulations, associated with that environment.. 3.. Generate the channel coefficients based on the parameters.. The following sections describe the details of overall procedure. Figure 2.8 provides a flow chart for generating channel coefficients. Choose Environment Scenario: Suburban Macro-cell Urban Macro-Cell Urban Micro-Cell Indoor Pico-Cell. Determine Link-Level Model Parameters: Angle Spread (PAS) Lognormal Shadowing Fading Delay Spread (path delays, path powers, AoA) Pathloss Orientation Speed Antenna Gains. Generate MIMO Channel Model Coefficients. Figure 2.8: Flow chart for the generation of MIMO IEEE 802.20 Channel Models coefficients 28.

(46) Table 2.3:. Summary of MIMO link-level parameters for IEEE 802.20 Channel Models Case-B. Case-C. Case-D. PDP. Pedestrian-A. Vehicular-A. Pedestrian-B. Vehicular-B. Number of Paths. 4. 6. 6. 6. Delay (ns). Case-A. Relative Path power (dB). Models. Speed (km/h) Topology. 0. 0. 0. 0. 0. 0. -2.5. 0. -9.7. 110. -1.0. 310. -0.9. 200. 0. 300. -19.2. 190. -9.0. 710. -4.9. 800. -12.8. 8900. -22.8. 410. -10.0. 1090. -8.0. 1200. -10.0. 12900. -15.0. 1730. -7.8. 2300. -25.2. 17100. -20.0. 2510. -23.9. 3700. -16.0. 20000. 3, 30, 120. 30, 120, 250. 3. 30, 120, 250. 0.5λ. 0.5λ. 0.5λ. 0.5λ. RMS angle spread. RMS angle. of 35 degrees per. spread of 35. path with a. degrees per path. Laplacian. with a Laplacian. distribution. distribution. Mobile Station. Fixed AoA for LOS component, PAS. has 360 degree. PAS. uniform PAS. DoT (°). 0. 22.5. -22.5. 22.5. AoA (°). 22.5 / 67.5. 67.5 (all paths). 67.5 (all paths). 67.5 (all paths). Topology. Base Station. remaining power. 360 degree uniform. PAS. AoD/AoA(°). Reference: ULA with 0.5λ-spacing or 4λ-spacing or 10λ-spacing. Laplacian distribution with RMS angle spread of 2 degrees or 5 degrees, per path depending on AoA/AoD. 50ο for 2ο RMS angle spread per path or 20ο for 5ο RMS angle spread per path. 29.

(47) 2.4 Computer Simulations In this section, we simulate the V-BLAST performance both for the ideal and realistic case. We define the relation between SNR and Eb N 0 at each receive antenna as follows: Es Eb ⋅ N t ⋅ M signal power E T Ts SNR = = s = = b ⋅ (N t ⋅ M ) 1 noise power N 0B N0 N0 Ts. (2.28). where Es is the symbol energy, Ts is the symbol duration, B is the system bandwidth and M is the modulation order. Throughout the following simulations, the system transmit power is normalized to 1, and hence the noise power corresponding to a specific Eb N 0 is generated by. noise power =. N0 Eb ⋅ N t ⋅ M. (2.29). Figure 2.9 shows the BER performance of the (N t , N r ) = (4, 4) ZF V-BLAST system with ideal detection and cancellation. It is obvious that in the ideal case, the diversity gain increases as the number of effective transmit antennas decreases. However, as shown in Figure 2.10, the realistic V-BLAST system suffers from error propagation and hence the diversity gain degrades. In Figure 2.11, we compare two equal rate V-BLAST systems. It is interesting to see that the system with fewer transmit antennas will outperform the one with more transmit antennas in the BER performance. This phenomenon hints that given a MIMO channel and some transmit power budget, we can improve the MIMO system performance by simply adjusting transmission parameters at no cost of transmission rate. So, it strongly motivates us to incorporate the concept of adaptive modulation in MIMO, which will be described in Chapter 4.. 30.

(48) 0. 10. -1. 10. -2. BER. 10. -3. 10. -4. 10. -5. 10. 1st detected layer 2nd detected layer 3th detected layer 4th detected layer. -6. 10. -5. 0. 5 E b/No (dB). 10. 15. Figure 2.9: ZF V-BLAST performance with ideal detection and cancellation. QPSK modulation is used. (N t , N r ) = (4, 4). 0. 10. 1st detected layer 2nd detected layer 3th detected layer 4th detected layer. -1. BER. 10. -2. 10. -3. 10. -4. 10. -5. 0. 5. 10. 15. 20. Eb/No (dB). Figure 2.10: ZF V-BLAST performance with error propagation. QPSK modulation is used. (N t , N r ) = (4, 4). 31.

(49) 0. 10. (4Tx, 4Rx) QPSK (2Tx, 4Rx) 16-QAM -1. 10. -2. BER. 10. -3. 10. -4. 10. -5. 10. -5. 0. 5. 10 Eb/No (dB). 15. 20. 25. Figure 2.11: Comparison of ZF V-BLAST (N t , N r ) = (4, 4) with QPSK modulation and (N t , N r ) = (2, 4) with 16-QAM modulation.. 32.

(50) Chapter 3 Reliability-Based Hybrid Scheme with LDPC Codes. ARQ. For wireless communications on fading channel, two techniques are fundamental for reliability: FEC and ARQ. HARQ scheme that combines ARQ and FEC can offer a performance superior to either scheme. RB-HARQ, a new attractive ARQ scheme, could bring significant performance gain while only a few bits need to be retransmitted. RB-HARQ consists a soft-input, soft-output (SISO) decoder, so we will introduce the SISO decoder which is based on LDPC codes first, then introduce the basis and key fractures of the HARQ schemes and propose an adaptive algorithm of RB-HARQ scheme.. 3.1. Review of LDPC Codes. LDPC codes were introduced along with an iterative probability-based decoding algorithm by Gallager in the early 1960's [22]. These codes were constructed using sparse random parity check matrices and showed promising distance properties. However, they went largely unnoticed until the advent of turbo codes, where they were “rediscovered” by MacKay, who showed that they perform almost as close to capacity. 33.

(51) as turbo codes. More recently, Richardson and Urbanke have developed irregular LDPC codes that perform even better than turbo codes for very large block lengths. (n > 105 ). and can come within 0.1 dB of the Shannon capacity.. 3.1.1 LDPC Codes LDPC codes were originally invented by Gallager [22], However, these codes were larger ignored until the introduction of turbo codes, which rekindled some of the same ideas. LDPC codes were rediscovered by Mackay and Neal. Shortly thereafter it was recognized that these new code designs were actually reinventions of Gallager’s original ideas, and much work has been devoted to finding the capacity limits, encoder and decoder designs, and practical implementation of LDPC codes for different channels. LDPC codes are linear block codes with particular structure for the parity check matrix H, which will define in next section. Since the fraction of non-zeros entries in H is small, the parity-check matrix for the code has a low-density – hence the name low-density parity-check codes. Provided that the codeword length is long, LDPC codes achieve performance close to the Shannon limit and in some cases surpass the performance of parallel or serially concatenated codes [23]. The fundamental practical difference between turbo codes and LDPC codes is that turbo codes tend to have low encoding complexity (linear in block-length) but high decoding complexity (due to their iterative nature and message passing). In contrast, LDPC codes tend to have relatively high encoding complexity but low decoding complexity. The decoding algorithm of LDPC codes will present in section 3.1.3.. 34.

(52) 3.1.2 Construction of LDPC Codes In this section, we will generate the LDPC codes based on the standard of IEEE 802.16-2005 [13]. The LDPC codes are based on a set of one or more fundamental LDPC codes. Each of the fundamental codes is a systematic linear block code. How to adjust the various code rates and block sizes based on fundamental codes will present in the below. Each LDPC code in the set of LDPC codes is defined by a matrix H of size m-by-n, where n is the length of the code and m is the number of parity check bits in. the code. The number of systematic bits is k = n − m . The matrix H is defined as: [13] ⎡ P0,0 ⎢ ⎢ P ⎢ 1,0 ⎢ H = ⎢ P2,0 ⎢ ⎢ ⎢ ⎢ Pm −1,0 ⎢⎣ b. P0,1. P0,2. P0,nb −2. P1,1. P1,2. P1,nb −2. P2,1. P2,2. P2,nb −2. Pmb −1,1 Pmb −1,2. Pmb −1,nb −2. P0,nb −1 ⎤ ⎥ P1,nb −1 ⎥⎥ ⎥ P2,nb −1 ⎥ = PHb ⎥ ⎥ ⎥ Pmb −1,nb −1 ⎥⎥ ⎦. (3.1). where Pi,j is one of a set of z-by-z permutation matrices or a z-by-z matrix. The matrix H is expanded from a binary Hb of size mb-by-nb, where n = z×nb, and m = z×mb, with z is a positive integer. The base matrix is expanded by replacing each 1 in the base matrix with a z-by-z permutation matrix, and each 0 with a z-by-z zero matrix. The base matrix size nb is an integer equal to 24. The permutations used are circular right shifts, and the set of permutation matrices contains the z×z identity matrix and circular right shifted versions of the identity matrix. Because each permutation matrix is specified by a single circular right shift, the binary base matrix information and permutation replacement information can be combined into a single model Hbm. The model matrix Hbm is the same size as the binary matrix Hb, with each binary entry (i, j ) of the base matrix Hb replaced to create the 35.

(53) model matrix Hbm. Each 0 in the Hb is replaced by a blank or negative (e.g., by -1) to denote a z × z all zero matrix, and each 1 in Hb is replaced by a circular shift size p (i, j ) ≥ 0 . The model matrix can then be directly expanded to H. Figure 3.1 and. Figure 3.2 shows of parity check matrix and generator matrix for the (960,640) LDPC code, respectively. The points show the non-zero terms in the parity check matrix. We can see the non-zeros terms is about 0.355 percentage of the parity check matrix. ⎡1 ⎢ ⎢0 ⎢ ⎢ ⎢0 ⎢ ⎢0 ⎢ ⎢0 ⎢ S0 = ⎢ ⎢0 ⎢ ⎢0 ⎢ ⎢0 ⎢ ⎢ ⎢0 ⎢ ⎢0 ⎢⎣. ⎡0 ⎢ ⎢0 ⎢ ⎢ ⎢0 ⎢ ⎢1 ⎢ ⎢0 ⎢ S7 = ⎢ ⎢0 ⎢ ⎢0 ⎢ ⎢0 ⎢ ⎢ ⎢0 ⎢ ⎢0 ⎣⎢. 0 0 0 0 0 0 0 0 0⎤ ⎥ 1 0 0 0 0 0 0 0 0⎥⎥ ⎥ 0 1 0 0 0 0 0 0 0⎥ ⎥ 0 0 1 0 0 0 0 0 0⎥ ⎥ 0 0 0 1 0 0 0 0 0⎥⎥ ⎥, 0 0 0 0 1 0 0 0 0⎥ ⎥ 0 0 0 0 0 1 0 0 0⎥ ⎥ 0 0 0 0 0 0 1 0 0⎥⎥ ⎥ 0 0 0 0 0 0 0 1 0⎥ ⎥ 0 0 0 0 0 0 0 0 1 ⎥⎥ ⎦. ⎡0 ⎢ ⎢0 ⎢ ⎢ ⎢0 ⎢ ⎢0 ⎢ ⎢0 ⎢ S3 = ⎢ ⎢0 ⎢ ⎢0 ⎢ ⎢1 ⎢ ⎢ ⎢0 ⎢ ⎢0 ⎢⎣. 0 0 0 0 0 0 1 0 0⎤ ⎥ 0 0 0 0 0 0 0 1 0⎥⎥ ⎥ 0 0 0 0 0 0 0 0 1⎥ ⎥ 0 0 0 0 0 0 0 0 0⎥ ⎥ 1 0 0 0 0 0 0 0 0⎥⎥ ⎥, 0 1 0 0 0 0 0 0 0⎥ ⎥ 0 0 1 0 0 0 0 0 0⎥ ⎥ 0 0 0 1 0 0 0 0 0⎥⎥ ⎥ 0 0 0 0 1 0 0 0 0⎥ ⎥ 0 0 0 0 0 1 0 0 0⎥ ⎦⎥. ⎡0 ⎢ ⎢0 ⎢ ⎢ ⎢0 ⎢ ⎢0 ⎢ ⎢0 ⎢ =⎢ ⎢0 ⎢ ⎢0 ⎢ ⎢0 ⎢ ⎢ ⎢0 ⎢ ⎢0 ⎣⎢. S−1. 0 0 1 0 0 0 0 0 0⎤ ⎥ 0 0 0 1 0 0 0 0 0⎥⎥ ⎥ 0 0 0 0 1 0 0 0 0⎥ ⎥ 0 0 0 0 0 1 0 0 0⎥ ⎥ 0 0 0 0 0 0 1 0 0⎥⎥ ⎥ 0 0 0 0 0 0 0 1 0⎥ ⎥ 0 0 0 0 0 0 0 0 1⎥ ⎥ 0 0 0 0 0 0 0 0 0⎥⎥ ⎥ 1 0 0 0 0 0 0 0 0⎥ ⎥ 0 1 0 0 0 0 0 0 0⎥⎥ ⎦. 0 0 0 0 0 0 0 0 0⎤ ⎥ 0 0 0 0 0 0 0 0 0⎥⎥ ⎥ 0 0 0 0 0 0 0 0 0⎥ ⎥ 0 0 0 0 0 0 0 0 0⎥ ⎥ 0 0 0 0 0 0 0 0 0⎥⎥ ⎥ 0 0 0 0 0 0 0 0 0⎥ ⎥ 0 0 0 0 0 0 0 0 0⎥ ⎥ 0 0 0 0 0 0 0 0 0⎥⎥ ⎥ 0 0 0 0 0 0 0 0 0⎥ ⎥ 0 0 0 0 0 0 0 0 0⎥ ⎦⎥. Hb is partitioned in two sections, where Hb1 correspond to the systematic bits and Hb2 corresponds to the parity-check bits, such that Hb = ⎡⎢(Hb1 )m ×k | (Hb 2 )m ×m ⎤⎥ . b b b b⎦ ⎣ Hb1 is partitioned into two sections, where vector hb has odd weight, and H’b2 has a dual-diagonal structure with matrix elements at row i, column j equal to 1 for i = j, for i = j + 1 , and 0 elsewhere. 36.

(54) 0 50. nz = 3200. 100 150 200 250 300 0. 100. 200. 300. 400. 500. 600. 700. 800. 900. Figure 3.1: Parity-check matrix of the (960,640) LDPC code.. 0. 100 nz = 23600. 200. 300. 400. 500. 600 0. 100. 200. 300. 400. 500. 600. 700. 800. 900. Figure 3.2: Generator matrix of the (960,640) LDPC code.. Hb2 = ⎡⎢ hb | Hb′2 ⎤⎥ ⎣ ⎦ ⎡ hb (0) ⎢ ⎢ h (1) b ⎢ ⎢ ⎢ ⋅ = ⎢⎢ ⋅ ⎢ ⎢ ⎢ ⋅ ⎢ ⎢h m − 1 ) ⎢⎣ b ( b. | 1 | 1 1 |. 1. | |. 0. |. ⎤ ⎥ 0 ⎥⎥ ⎥ ⎥. ⎥ 1 ⎥⎥ ⎥ 1 1⎥ ⎥ 1⎥⎥ ⎦. (3.2). A based model matrix is defined for the largest code length (n = 2304) of each code rate. The set of shifts. {p (i, j )} in the base model matrix are used to determine. the shift sizes for all other code lengths of the same code rate. Each base model matrix has nb = 24 columns, and the expansion factor z f is equal to n / 24 for code. 37.

(55) length n, Here f. is the index of the code lengths for a given code rate,. f = 0,1, 2, …,18 . For code length n = 2304 the expansion factor is designated z 0 = 96 . The shift size z f are derived from. {p (i, j )} for a code size corresponding to expansion factor. {p (i, j )} by scaling {p (i, j )} proportionally, [13] ⎪⎪⎧ p (i, j ) , p (i, j ) ≤ 0 ⎪ p ( f , i, j ) = ⎪⎨⎢ p (i, j ) z f ⎥ ⎪⎪⎢ ⎥ , p (i, j ) > 0 ⎥ ⎪⎪⎣⎢ z 0 ⎦ ⎪⎩. (3.3). where ⎣x ⎦ denotes the flooring function that gives the nearest integer towards −∞ . Table 3.1 shows the LDPC block sizes and code rates which are used by IEEE 802.16-2005.. Table 3.1: LDPC block sizes and code rates in IEEE 802.16-2005. 38.