Fundamentals of Wireless Communication1
David Tse, University of California, Berkeley
Pramod Viswanath, University of Illinois, Urbana-Champaign
December 9, 2004
1 Draft, to be published by Cambridge University Press, which owns the copyright. Online
version is available with their permission. Comments will be much appreciated; please send
them to or .
,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
1
,Tse and Viswanath: Fundamentals of Wireless Communications 2
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
, Tse and Viswanath: Fundamentals of Wireless Communications 3
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
David Tse, University of California, Berkeley
Pramod Viswanath, University of Illinois, Urbana-Champaign
December 9, 2004
1 Draft, to be published by Cambridge University Press, which owns the copyright. Online
version is available with their permission. Comments will be much appreciated; please send
them to or .
,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
1
,Tse and Viswanath: Fundamentals of Wireless Communications 2
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
, Tse and Viswanath: Fundamentals of Wireless Communications 3
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
