exploiting cloze questions for few shot text classification and natural language inference

时间: 2023-04-30 20:05:28 浏览: 39
题目翻译:利用填空题进行少样本文本分类和自然语言推理。 这篇论文使用填空题来辅助进行少样本文本分类和自然语言推理任务。作者利用已有的模型预测填空题的答案,并将预测结果作为样本的特征。结果表明,这种方法可以提高任务的准确率和泛化能力。
相关问题

exploiting bert for end-to-end aspect-based sentiment analysis

Bert是一种在自然语言处理中被广泛使用的模型,其在各种任务中表现出了出色的性能。然而,对于方面级情感分析,Bert并不直接适用。因此,需要对Bert进行利用,并通过修改和扩展来适应这一任务。 端到端(end-to-end)的方面级情感分析是指通过一个模型直接从文本中提取方面和情感信息。为了利用Bert进行端到端的方面级情感分析,首先需要对数据进行预处理,并将其转换成Bert模型所接受的输入格式。这包括将文本分段、添加特殊标记以及填充序列等操作。 在Bert模型的基础上,需要添加相关的层来实现方面级情感分析。一种常见的方法是利用注意力机制来捕获方面词与其他词之间的关系。通过计算不同词之间的注意力权重,可以将方面词的相关信息传递给其他词,从而更好地理解整个文本。另外,也可以添加一些分类层来预测每个方面的情感。 为了更好地利用Bert,还可以使用领域特定的语料库来进行预训练。通过在大规模的语料库上进行预训练,模型可以更好地理解特定领域的文本,并提升方面级情感分析的性能。 此外,还可以通过调整Bert模型的超参数来进一步改善性能。例如,可以调整学习率、批大小和训练周期等超参数,以获得更好的结果。 总之,“exploiting bert for end-to-end aspect-based sentiment analysis”意味着通过对Bert进行修改和扩展,将其应用于端到端的方面级情感分析任务中,以提升模型的性能和效果。

麻雀算法中的麻雀飞行机制

In the sparrow algorithm, the sparrow flight mechanism refers to the way in which the sparrow swarm searches for optimal solutions. This mechanism involves the sparrow swarm moving through the solution space, exploring different regions, and exploiting promising areas to improve the overall fitness of the swarm. The flight patterns of real sparrows, such as coordinated movements and flocking behavior when foraging for food or migrating, inspired this mechanism.

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作者: Yong Soo Cho 目录 Preface. Limits of Liability and Disclaimer of Warranty of Software. 1 The Wireless Channel: Propagation and Fading. 1.1 Large-Scale Fading. 1.1.1 General Path Loss Model. 1.1.2 Okumura/Hata Model. 1.1.3 IEEE 802.16d Model. 1.2 Small-Scale Fading. 1.2.1 Parameters for Small-Scale Fading. 1.2.2 Time-Dispersive vs. Frequency-Dispersive Fading. 1.2.3 Statistical Characterization and Generation of Fading Channel. 2 SISO Channel Models. 2.1 Indoor Channel Models. 2.1.1 General Indoor Channel Models. 2.1.2 IEEE 802.11 Channel Model. 2.1.3 Saleh-Valenzuela (S-V) Channel Model. 2.1.4 UWB Channel Model. 2.2 Outdoor Channel Models. 2.2.1 FWGN Model. 2.2.2 Jakes Model. 2.2.3 Ray-Based Channel Model. 2.2.4 Frequency-Selective Fading Channel Model. 2.2.5 SUI Channel Model. 3 MIMO Channel Models. 3.1 Statistical MIMO Model. 3.1.1 Spatial Correlation. 3.1.2 PAS Model. 3.2 I-METRA MIMO Channel Model. 3.2.1 Statistical Model of Correlated MIMO Fading Channel. 3.2.2 Generation of Correlated MIMO Channel Coefficients. 3.2.3 I-METRA MIMO Channel Model. 3.2.4 3GPP MIMO Channel Model. 3.3 SCM MIMO Channel Model. 3.3.1 SCM Link-Level Channel Parameters. 3.3.2 SCM Link-Level Channel Modeling. 3.3.3 Spatial Correlation of Ray-Based Channel Model. 4 Introduction to OFDM. 4.1 Single-Carrier vs. Multi-Carrier Transmission. 4.1.1 Single-Carrier Transmission. 4.1.2 Multi-Carrier Transmission. 4.1.3 Single-Carrier vs. Multi-Carrier Transmission. 4.2 Basic Principle of OFDM. 4.2.1 OFDM Modulation and Demodulation. 4.2.2 OFDM Guard Interval. 4.2.3 OFDM Guard Band. 4.2.4 BER of OFDM Scheme. 4.2.5 Water-Filling Algorithm for Frequency-Domain Link Adaptation. 4.3 Coded OFDM. 4.4 OFDMA: Multiple Access Extensions of OFDM. 4.4.1 Resource Allocation – Subchannel Allocation Types. 4.4.2 Resource Allocation – Subchannelization. 4.5 Duplexing. 5 Synchronization for OFDM. 5.1 Effect of STO. 5.2 Effect of CFO. 5.2.1 Effect of Integer Carrier Frequency Offset (IFO). 5.2.2 Effect of Fractional Carrier Frequency Offset (FFO). 5.3 Estimation Techniques for STO. 5.3.1 Time-Domain Estimation Techniques for STO. 5.3.2 Frequency-Domain Estimation Techniques for STO. 5.4 Estimation Techniques for CFO. 5.4.1 Time-Domain Estimation Techniques for CFO. 5.4.2 Frequency-Domain Estimation Techniques for CFO. 5.5 Effect of Sampling Clock Offset. 5.5.1 Effect of Phase Offset in Sampling Clocks. 5.5.2 Effect of Frequency Offset in Sampling Clocks. 5.6 Compensation for Sampling Clock Offset. 5.7 Synchronization in Cellular Systems. 5.7.1 Downlink Synchronization. 5.7.2 Uplink Synchronization. 6 Channel Estimation. 6.1 Pilot Structure. 6.1.1 Block Type. 6.1.2 Comb Type. 6.1.3 Lattice Type. 6.2 Training Symbol-Based Channel Estimation. 6.2.1 LS Channel Estimation. 6.2.2 MMSE Channel Estimation. 6.3 DFT-Based Channel Estimation. 6.4 Decision-Directed Channel Estimation. 6.5 Advanced Channel Estimation Techniques. 6.5.1 Channel Estimation Using a Superimposed Signal. 6.5.2 Channel Estimation in Fast Time-Varying Channels. 6.5.3 EM Algorithm-Based Channel Estimation. 6.5.4 Blind Channel Estimation. 7 PAPR Reduction. 7.1 Introduction to PAPR. 7.1.1 Definition of PAPR. 7.1.2 Distribution of OFDM Signal. 7.1.3 PAPR and Oversampling. 7.1.4 Clipping and SQNR. 7.2 PAPR Reduction Techniques. 7.2.1 Clipping and Filtering. 7.2.2 PAPR Reduction Code. 7.2.3 Selective Mapping. 7.2.4 Partial Transmit Sequence. 7.2.5 Tone Reservation. 7.2.6 Tone Injection. 7.2.7 DFT Spreading. 8 Inter-Cell Interference Mitigation Techniques. 8.1 Inter-Cell Interference Coordination Technique. 8.1.1 Fractional Frequency Reuse. 8.1.2 Soft Frequency Reuse. 8.1.3 Flexible Fractional Frequency Reuse. 8.1.4 Dynamic Channel Allocation. 8.2 Inter-Cell Interference Randomization Technique. 8.2.1 Cell-Specific Scrambling. 8.2.2 Cell-Specific Interleaving. 8.2.3 Frequency-Hopping OFDMA. 8.2.4 Random Subcarrier Allocation. 8.3 Inter-Cell Interference Cancellation Technique. 8.3.1 Interference Rejection Combining Technique. 8.3.2 IDMA Multiuser Detection. 9 MIMO: Channel Capacity. 9.1 Useful Matrix Theory. 9.2 Deterministic MIMO Channel Capacity. 9.2.1 Channel Capacity when CSI is Known to the Transmitter Side. 9.2.2 Channel Capacity when CSI is Not Available at the Transmitter Side. 9.2.3 Channel Capacity of SIMO and MISO Channels. 9.3 Channel Capacity of Random MIMO Channels. 10 Antenna Diversity and Space-Time Coding Techniques. 10.1 Antenna Diversity. 10.1.1 Receive Diversity. 10.1.2 Transmit Diversity. 10.2 Space-Time Coding (STC): Overview. 10.2.1 System Model. 10.2.2 Pairwise Error Probability. 10.2.3 Space-Time Code Design. 10.3 Space-Time Block Code (STBC). 10.3.1 Alamouti Space-Time Code. 10.3.2 Generalization of Space-Time Block Coding. 10.3.3 Decoding for Space-Time Block Codes. 10.3.4 Space-Time Trellis Code. 11 Signal Detection for Spatially Multiplexed MIMO Systems. 11.1 Linear Signal Detection. 11.1.1 ZF Signal Detection. 11.1.2 MMSE Signal Detection. 11.2 OSIC Signal Detection. 11.3 ML Signal Detection. 11.4 Sphere Decoding Method. 11.5 QRM-MLD Method. 11.6 Lattice Reduction-Aided Detection. 11.6.1 Lenstra-Lenstra-Lovasz (LLL) Algorithm. 11.6.2 Application of Lattice Reduction. 11.7 Soft Decision for MIMO Systems. 11.7.1 Log-Likelihood-Ratio (LLR) for SISO Systems. 11.7.2 LLR for Linear Detector-Based MIMO System. 11.7.3 LLR for MIMO System with a Candidate Vector Set. 11.7.4 LLR for MIMO System Using a Limited Candidate Vector Set. Appendix 11.A Derivation of Equation (11.23). 12 Exploiting Channel State Information at the Transmitter Side. 12.1 Channel Estimation on the Transmitter Side. 12.1.1 Using Channel Reciprocity. 12.1.2 CSI Feedback. 12.2 Precoded OSTBC. 12.3 Precoded Spatial-Multiplexing System. 12.4 Antenna Selection Techniques. 12.4.1 Optimum Antenna Selection Technique. 12.4.2 Complexity-Reduced Antenna Selection. 12.4.3 Antenna Selection for OSTBC. 13 Multi-User MIMO. 13.1 Mathematical Model for Multi-User MIMO System. 13.2 Channel Capacity of Multi-User MIMO System. 13.2.1 Capacity of MAC. 13.2.2 Capacity of BC. 13.3 Transmission Methods for Broadcast Channel. 13.3.1 Channel Inversion. 13.3.2 Block Diagonalization. 13.3.3 Dirty Paper Coding (DPC). 13.3.4 Tomlinson-Harashima Precoding. References. Index.
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DES对称分组密码系统 import java.security.spec.*; import javax.crypto.*; import javax.crypto.spec.*; class DES01 { private String strkey; private SecretKey skey=null; private String[] algo= {"DES/ECB/PKCS5Padding","DES/ECB/NoPadding","DES"}; public DES01(String key) { strkey=key; } public void keyGenerating() throws Exception { byte[] bkey=strkey.getBytes(); KeySpec ks = new DESKeySpec(bkey); SecretKeyFactory kf = SecretKeyFactory.getInstance("DES"); skey = kf.generateSecret(ks); } public static void main(String[] a) { DES01 des = new DES01("IAMASTUDENT"); des.test02("STUDENTWANGFENGLIMING"); } public byte[] Encripting(String plaintext,int i) throws Exception { byte[] bpt=plaintext.getBytes(); Cipher cf = Cipher.getInstance(algo[i]); if(skey==null)this.keyGenerating(); cf.init(Cipher.ENCRYPT_MODE,skey); byte[] bct = cf.doFinal(bpt); return bct; } public byte[] decripting(byte[] bct,int i) throws Exception { Cipher cf = Cipher.getInstance(algo[i]); if(skey==null)this.keyGenerating(); cf.init(Cipher.DECRYPT_MODE,skey); byte[] bpt = cf.doFinal(bct); return bpt; } public void test01(String mess) { try{ byte[] ct=this.Encripting(mess,0); byte[] pt=this.Decripting(ct,0); String ptt=new String(pt); System.out.println(ptt); }catch(Exception ex) { return; } } public void test02(String mess) { try{ //Encripting print("Plaintext to be encripted:"); print(mess); byte[] ct=this.Encripting(mess,0); //Exploiting the results print("Byte array of cipher:"); for(int i=0;i<ct.length;i++) System.out.print(ct[i]+" "); print(""); for(int i=0;i<ct.length;i++) ct[i]=(byte)(ct[i]&0xFF); String ciphertxt=new String(ct); print("Cipher Text :"+ciphertxt); byte[] ctcode = ciphertxt.getBytes(); //Decripting byte[] pt=this.decripting(ctcode,0); String ptt=new String(pt); print("Plaintext after decripting:"); print(ptt); }catch(Exception ex) { return; } } public static byte[] hex2Bytes(String str) { if (str==null) { return null; } else if (str.length() < 2) { return null; } else { int len = str.length() / 2; byte[] buffer = new byte[len]; for (int i=0; i<len; i++) { buffer[i] = (byte) Integer.parseInt( str.substring(i*2,i*2+2),16); } return buffer; } } public static String bytes2Hex(byte[] data) { if (data==null) { return null; } else { int len = data.length; String str = ""; for (int i=0; i<len; i++) { if ((data[i]&0xFF)<16) str = str + "0" + java.lang.Integer.toHexString(data[i]&0xFF); else str = str + java.lang.Integer.toHexString(data[i]&0xFF); } return str.toUpperCase(); } } }
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书名: 无线通信基础 原书名: Fundamentals of Wireless Communication 原出版社: Cambridge University Press 分类: 电子电气 >> 通信 作者: David Tse, Pramod Viswanath Contents 1 Introduction 12 1.1 Book Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2 Wireless Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3 Book Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2 The Wireless Channel 21 2.1 Physical Modeling for Wireless Channels . . . . . . . . . . . . . . . . . 21 2.1.1 Free space, fixed transmitting and receive antennas . . . . . . . 23 2.1.2 Free space, moving antenna . . . . . . . . . . . . . . . . . . . . 24 2.1.3 Reflecting wall, fixed antenna . . . . . . . . . . . . . . . . . . . 25 2.1.4 Reflecting wall, moving antenna . . . . . . . . . . . . . . . . . . 27 2.1.5 Reflection from a Ground Plane . . . . . . . . . . . . . . . . . . 29 2.1.6 Power Decay with Distance and Shadowing . . . . . . . . . . . . 30 2.1.7 Moving Antenna, Multiple Reflectors . . . . . . . . . . . . . . . 31 2.2 Input/Output Model of the Wireless Channel . . . . . . . . . . . . . . 32 2.2.1 The Wireless Channel as a Linear Time-Varying System . . . . 32 2.2.2 Baseband Equivalent Model . . . . . . . . . . . . . . . . . . . . 34 2.2.3 A Discrete Time Baseband Model . . . . . . . . . . . . . . . . . 37 Discussion 2.1 Degrees of Freedom . . . . . . . . . . . . . . . 40 2.2.4 Additive White Noise . . . . . . . . . . . . . . . . . . . . . . . . 41 2.3 Time and Frequency Coherence . . . . . . . . . . . . . . . . . . . . . . 42 2.3.1 Doppler Spread and Coherence Time . . . . . . . . . . . . . . . 42 2.3.2 Delay Spread and Coherence Bandwidth . . . . . . . . . . . . . 44 2.4 Statistical Channel Models . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.4.1 Modeling Philosophy . . . . . . . . . . . . . . . . . . . . . . . . 47 2.4.2 Rayleigh and Rician Fading . . . . . . . . . . . . . . . . . . . . 48 2.4.3 Tap Gain Autocorrelation Function . . . . . . . . . . . . . . . . 50 Example 2.2 Clarke’s Model . . . . . . . . . . . . . . . . . . . 51 2.5 Bibliographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3 Point-to-Point Communication: Detection, Diversity and Channel Uncertainty 64 3.1 Detection in a Rayleigh Fading Channel . . . . . . . . . . . . . . . . . 65 3.1.1 Noncoherent Detection . . . . . . . . . . . . . . . . . . . . . . . 65 3.1.2 Coherent Detection . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.1.3 From BPSK to QPSK: Exploiting the Degrees of Freedom . . . 72 3.1.4 Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.2 Time Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.2.1 Repetition Coding . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.2.2 Beyond Repetition Coding . . . . . . . . . . . . . . . . . . . . . 80 Example 3.1 Time Diversity in GSM . . . . . . . . . . . . . . 86 3.3 Antenna Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.3.1 Receive Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . 89 3.3.2 Transmit Diversity: Space-Time Codes . . . . . . . . . . . . . . 90 3.3.3 MIMO: A 2 × 2 Example . . . . . . . . . . . . . . . . . . . . . . 94 3.4 Frequency Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 3.4.1 Basic Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 3.4.2 Single-Carrier with ISI Equalization . . . . . . . . . . . . . . . . 102 3.4.3 Direct Sequence Spread Spectrum . . . . . . . . . . . . . . . . . 109 3.4.4 Orthogonal Frequency Division Multiplexing . . . . . . . . . . . 114 3.5 Impact of Channel Uncertainty . . . . . . . . . . . . . . . . . . . . . . 122 3.5.1 Noncoherent Detection for DS Spread Spectrum . . . . . . . . . 122 3.5.2 Channel Estimation . . . . . . . . . . . . . . . . . . . . . . . . . 125 3.5.3 Other Diversity Scenarios . . . . . . . . . . . . . . . . . . . . . 127 3.6 Bibliographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 3.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 4 Cellular Systems: Multiple Access and Interference Management 143 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 4.2 Narrowband Cellular Systems . . . . . . . . . . . . . . . . . . . . . . . 146 4.2.1 Narrowband allocations: GSM system . . . . . . . . . . . . . . 147 4.2.2 Impact on Network and System Design . . . . . . . . . . . . . . 150 4.2.3 Impact on Frequency Reuse . . . . . . . . . . . . . . . . . . . . 151 4.3 Wideband Systems: CDMA . . . . . . . . . . . . . . . . . . . . . . . . 152 4.3.1 CDMA Uplink . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 4.3.2 CDMA Downlink . . . . . . . . . . . . . . . . . . . . . . . . . . 170 4.3.3 System Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 4.4 Wideband Systems: OFDM . . . . . . . . . . . . . . . . . . . . . . . . 174 4.4.1 Allocation Design Principles . . . . . . . . . . . . . . . . . . . . 174 4.4.2 Hopping Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . 175 4.4.3 Signal Characteristics and Receiver Design . . . . . . . . . . . . 177 4.4.4 Sectorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 Example 4.1 Flash-OFDM . . . . . . . . . . . . . . . . . . . . 179 4.5 Bibliographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 4.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 5 Capacity of Wireless Channels 195 5.1 AWGN Channel Capacity . . . . . . . . . . . . . . . . . . . . . . . . . 196 5.1.1 Repetition Coding . . . . . . . . . . . . . . . . . . . . . . . . . 196 5.1.2 Packing Spheres . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 Discussion 5.1 Capacity-Achieving AWGN Channel Codes . . 199 5.2 Resources of the AWGN Channel . . . . . . . . . . . . . . . . . . . . . 201 5.2.1 Continuous-Time AWGN Channel . . . . . . . . . . . . . . . . . 202 5.2.2 Power and Bandwidth . . . . . . . . . . . . . . . . . . . . . . . 202 Example 5.2 Bandwidth Reuse in Cellular Systems . . . . . . 205 5.3 Linear Time-Invariant Gaussian Channels . . . . . . . . . . . . . . . . 209 5.3.1 Single Input Multiple Output (SIMO) Channel . . . . . . . . . 209 5.3.2 Multiple Input Single Output (MISO) Channel . . . . . . . . . 210 5.3.3 Frequency-Selective Channel . . . . . . . . . . . . . . . . . . . . 211 5.4 Capacity of Fading Channels . . . . . . . . . . . . . . . . . . . . . . . . 217 5.4.1 Slow Fading Channel . . . . . . . . . . . . . . . . . . . . . . . . 218 5.4.2 Receive Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . 221 5.4.3 Transmit Diversity . . . . . . . . . . . . . . . . . . . . . . . . . 222 5.4.4 Time and Frequency Diversity . . . . . . . . . . . . . . . . . . . 227 5.4.5 Fast Fading Channel . . . . . . . . . . . . . . . . . . . . . . . . 231 5.4.6 Transmitter Side Information . . . . . . . . . . . . . . . . . . . 236 Example 5.3 Rate Adaptation in IS-856 . . . . . . . . . . . . . 244 5.4.7 Frequency-Selective Fading Channels . . . . . . . . . . . . . . . 247 5.4.8 Summary: A Shift in Point of View . . . . . . . . . . . . . . . . 248 5.5 Bibliographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 5.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 6 Multiuser Capacity and Opportunistic Communication 266 6.1 Uplink AWGN Channel . . . . . . . . . . . . . . . . . . . . . . . . . . 267 6.1.1 Capacity via Successive Interference Cancellation . . . . . . . . 267 6.1.2 Comparison with Conventional CDMA . . . . . . . . . . . . . . 271 6.1.3 Comparison with Orthogonal Multiple Access . . . . . . . . . . 271 6.1.4 General K-user Uplink Capacity . . . . . . . . . . . . . . . . . . 273 6.2 Downlink AWGN Channel . . . . . . . . . . . . . . . . . . . . . . . . . 275 6.2.1 Symmetric Case: Two Capacity-Achieving Schemes . . . . . . . 276 6.2.2 General Case: Superposition Coding Achieves Capacity . . . . . 279 Discussion 6.1 SIC: Implementation Issues . . . . . . . . . . . 283 6.3 Uplink Fading Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 6.3.1 Slow Fading Channel . . . . . . . . . . . . . . . . . . . . . . . . 285 6.3.2 Fast Fading Channel . . . . . . . . . . . . . . . . . . . . . . . . 287 6.3.3 Full Channel Side Information . . . . . . . . . . . . . . . . . . . 289 6.4 Downlink Fading Channel . . . . . . . . . . . . . . . . . . . . . . . . . 292 6.4.1 Channel Side Information at Receiver Only . . . . . . . . . . . . 293 6.4.2 Full Channel Side Information . . . . . . . . . . . . . . . . . . . 294 6.5 Frequency-Selective Fading Channels . . . . . . . . . . . . . . . . . . . 294 6.6 Multiuser Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 6.6.1 Multiuser Diversity Gain . . . . . . . . . . . . . . . . . . . . . . 295 6.6.2 Multiuser versus Classical Diversity . . . . . . . . . . . . . . . . 298 6.7 Multiuser Diversity: System Aspects . . . . . . . . . . . . . . . . . . . 300 6.7.1 Fair Scheduling and Multiuser Diversity . . . . . . . . . . . . . 301 6.7.2 Channel Prediction and Feedback . . . . . . . . . . . . . . . . . 308 6.7.3 Opportunistic Beamforming using Dumb Antennas . . . . . . . 309 6.7.4 Multiuser Diversity in Multi-cell Systems . . . . . . . . . . . . . 318 6.7.5 A System View . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 6.8 Bibliographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 6.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 7 MIMO I: Spatial Multiplexing and Channel Modeling 342 7.1 Multiplexing Capability of Deterministic MIMO Channels . . . . . . . 343 7.1.1 Capacity via Singular Value Decomposition . . . . . . . . . . . 343 7.1.2 Rank and Condition Number . . . . . . . . . . . . . . . . . . . 346 7.2 Physical Modeling of MIMO Channels . . . . . . . . . . . . . . . . . . 347 7.2.1 Line-of-Sight SIMO channel . . . . . . . . . . . . . . . . . . . . 348 7.2.2 Line-of-Sight MISO Channel . . . . . . . . . . . . . . . . . . . . 350 7.2.3 Antenna arrays with only a line-of-sight path . . . . . . . . . . 351 7.2.4 Geographically separated antennas . . . . . . . . . . . . . . . . 352 7.2.5 Line-of-sight plus one reflected path . . . . . . . . . . . . . . . . 359 7.3 Modeling of MIMO Fading Channels . . . . . . . . . . . . . . . . . . . 364 7.3.1 Basic Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 364 7.3.2 MIMO Multipath Channel . . . . . . . . . . . . . . . . . . . . . 365 7.3.3 Angular Domain Representation of Signals . . . . . . . . . . . . 367 7.3.4 Angular Domain Representation of MIMO Channels . . . . . . . 370 7.3.5 Statistical Modeling in the Angular Domain . . . . . . . . . . . 372 7.3.6 Degrees of Freedom and Diversity . . . . . . . . . . . . . . . . . 372 Example 7.1 Degrees of Freedom in Clustered Response Models 375 7.3.7 Dependency on Antenna Spacing . . . . . . . . . . . . . . . . . 380 7.3.8 I.I.D. Rayleigh Fading Model . . . . . . . . . . . . . . . . . . . 387 7.4 Bibliographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 7.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 8 MIMO II: Capacity and Multiplexing Architectures 393 8.1 The V-BLAST Architecture . . . . . . . . . . . . . . . . . . . . . . . . 394 8.2 Fast Fading MIMO Channel . . . . . . . . . . . . . . . . . . . . . . . . 396 8.2.1 Capacity with CSI at Receiver . . . . . . . . . . . . . . . . . . . 396 8.2.2 Performance Gains . . . . . . . . . . . . . . . . . . . . . . . . . 399 8.2.3 Full CSI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408 8.3 Receiver Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 8.3.1 Linear Decorrelator . . . . . . . . . . . . . . . . . . . . . . . . . 411 8.3.2 Successive Cancellation . . . . . . . . . . . . . . . . . . . . . . . 417 8.3.3 Linear MMSE Receiver . . . . . . . . . . . . . . . . . . . . . . . 419 8.3.4 Information Theoretic Optimality* . . . . . . . . . . . . . . . . 427 Discussion 8.1 Connections with CDMA Multiuser Detection and ISI Equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 8.4 Slow Fading MIMO Channel . . . . . . . . . . . . . . . . . . . . . . . . 431 8.5 D-BLAST: An Outage-Optimal Architecture . . . . . . . . . . . . . . . 433 8.5.1 Sub-optimality of V-BLAST . . . . . . . . . . . . . . . . . . . . 433 8.5.2 Coding Across Transmit Antennas: D-BLAST . . . . . . . . . . 435 8.5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 8.6 Bibliographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440 8.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440 9 MIMO III: Diversity-Multiplexing Tradeoff and Universal Space-Time Codes 451 9.1 Diversity-Multiplexing Tradeoff . . . . . . . . . . . . . . . . . . . . . . 452 9.1.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452 9.1.2 Scalar Rayleigh Channel . . . . . . . . . . . . . . . . . . . . . . 454 9.1.3 Parallel Rayleigh Channel . . . . . . . . . . . . . . . . . . . . . 458 9.1.4 MISO Rayleigh Channel . . . . . . . . . . . . . . . . . . . . . . 459 9.1.5 2 × 2 MIMO Rayleigh Channel . . . . . . . . . . . . . . . . . . 460 9.1.6 nt × nr MIMO i.i.d. Rayleigh Channel . . . . . . . . . . . . . . 463 9.2 Universal Code Design for Optimal Diversity-Multiplexing Tradeoff . . 467 9.2.1 QAM is Approximately Universal for Scalar Channels . . . . . . 468 9.2.2 Universal Code Design for Parallel Channels . . . . . . . . . . . 470 9.2.3 Universal Code Design for MISO Channels . . . . . . . . . . . . 477 9.2.4 Universal Code Design for MIMO Channels . . . . . . . . . . . 481 Discussion 9.1 Universal Codes in the Downlink . . . . . . . . 485 9.3 Bibliographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487 9.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488 10 MIMO IV: Multiuser Communication 497 10.1 Uplink with Multiple Receive Antennas . . . . . . . . . . . . . . . . . . 498 10.1.1 Space-Division Multiple Access . . . . . . . . . . . . . . . . . . 498 10.1.2 SDMA Capacity Region . . . . . . . . . . . . . . . . . . . . . . 500 10.1.3 System Implications . . . . . . . . . . . . . . . . . . . . . . . . 503 10.1.4 Slow Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 10.1.5 Fast Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509 10.1.6 Multiuser Diversity Revisited . . . . . . . . . . . . . . . . . . . 512 10.2 MIMO Uplink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516 10.2.1 SDMA with Multiple Transmit Antennas . . . . . . . . . . . . . 517 10.2.2 System Implications . . . . . . . . . . . . . . . . . . . . . . . . 521 10.2.3 Fast Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521 10.3 Downlink with Multiple Transmit Antennas . . . . . . . . . . . . . . . 523 10.3.1 Degrees of Freedom in the Downlink . . . . . . . . . . . . . . . 523 10.3.2 Uplink-Downlink Duality and Transmit Beamforming . . . . . . 525 10.3.3 Precoding for Interference Known at Transmitter . . . . . . . . 530 10.3.4 Precoding for the downlink . . . . . . . . . . . . . . . . . . . . . 543 10.3.5 Fast Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546 10.4 MIMO Downlink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549 10.5 Multiple Antennas in Cellular Networks: A System View . . . . . . . . 552 10.5.1 Inter-cell Interference Management . . . . . . . . . . . . . . . . 554 10.5.2 Uplink with Multiple Receive Antennas . . . . . . . . . . . . . . 555 10.5.3 MIMO Uplink . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557 10.5.4 Downlink with Multiple Receive Antennas . . . . . . . . . . . . 558 10.5.5 Downlink with Multiple Transmit Antennas . . . . . . . . . . . 559 Example 10.1 SDMA in ArrayComm Systems . . . . . . . . . 559 10.6 Bibliographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562 10.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563 A Detection and Estimation in Additive Gaussian Noise 579 A.1 Gaussian Random Variables . . . . . . . . . . . . . . . . . . . . . . . . 579 A.1.1 Scalar Real Gaussian Random Variable . . . . . . . . . . . . . . 579 A.1.2 Real Gaussian Random Vectors . . . . . . . . . . . . . . . . . . 580 A.1.3 Complex Gaussian Random Vectors . . . . . . . . . . . . . . . . 583 A.2 Detection in Gaussian Noise . . . . . . . . . . . . . . . . . . . . . . . . 586 A.2.1 Scalar Detection . . . . . . . . . . . . . . . . . . . . . . . . . . 586 A.2.2 Detection in a Vector Space . . . . . . . . . . . . . . . . . . . . 587 A.2.3 Detection in a Complex Vector Space . . . . . . . . . . . . . . . 591 A.3 Estimation in Gaussian Noise . . . . . . . . . . . . . . . . . . . . . . . 593 A.3.1 Scalar Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 593 A.3.2 Estimation in a Vector Space . . . . . . . . . . . . . . . . . . . 594 A.3.3 Estimation in a Complex Vector Space . . . . . . . . . . . . . . 595 A.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597 B Information Theory Background 599 B.1 Discrete Memoryless Channels . . . . . . . . . . . . . . . . . . . . . . . 599 Example B.1 Binary Symmetric Channel . . . . . . . . . . . . 601 Example B.2 Binary Erasure Channel . . . . . . . . . . . . . . 601 B.2 Entropy, Conditional Entropy and Mutual Information . . . . . . . . . 602 Example B.3 Binary Entropy . . . . . . . . . . . . . . . . . . 603 B.3 Noisy Channel Coding Theorem . . . . . . . . . . . . . . . . . . . . . . 605 B.3.1 Reliable Communication and Conditional Entropy . . . . . . . . 606 B.3.2 A Simple Upper Bound . . . . . . . . . . . . . . . . . . . . . . . 606 B.3.3 Achieving the Upper Bound . . . . . . . . . . . . . . . . . . . . 607 Example B.4 Binary Symmetric Channel . . . . . . . . . . . . 609 Example B.5 Binary Erasure Channel . . . . . . . . . . . . . . 609

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