Spread-Spectrum Code-Division Multiple Access
Don J. Torrieri · 2002
This report is intended to provide a concise but lucid explanation and derivation of the fundamentals of spread-spectrum code-division multiple access (CDMA).The level of presentation is suitable for those with a solid background in the theory of digital communications.Throughout the report, there are many streamlined derivations, new derivations, and simplifications of the classical theory.Comprehensive mathematical details, some of them difficult to find elsewhere, are assembled in the appendices.Sections 1 and 2 contain brief overviews of fading and diversity that provide the basic theory accessed by the remainder of the report.Maximal-ratio combining, equal-gain combining, and selection diversity are distinguished and compared.The rake receiver and the impact of errorcorrecting codes on fading communications are examined.Direct-sequence CDMA is considered in Section 3. Bit error probabilities for a number of direct-sequence systems are derived.Power-control issues in cellular networks are emphasized and new results are presented.Diversity aspects of multiearrier and single-carrier systems are compared.Section 4 treats frequency-hopping CDMA for both peer-to-peer and cellular systems.The advantages of frequency hopping in network applications and the effects of spatial diversity, spectral splatter, and the number of equivalent frequency channels are explained. 7Branch A; of a maximal-ratio combiner with a phase stripper . .8 Maximal-ratio combiner for PSK with predetection combining and postdetection combining 9 Bit error probability of PSK for no fading, completely correlated fading, and independent fading 10 Bit error probability of PSK for Nakagami fading with m -4 . .11 Ratio of the maximum SINR to the maximal-ratio-combiner SINR 12 Postdetection combining with frequency cUsaiminator 13 Equal-gain combiner for DPSK with postdetection combining .14 Equal-gain combiner for noncoherent MFSK with postdetection combining 15 Bit error probability for MRC with PSK and coherent FSK and for EGC with DPSK and noncoherent FSK 16 Bit error probability for MRC with PSK and for EGC with DPSK and noncoherent FSK 17 Bit error probability for selection diversity with PSK, DPSK, and noncoherent FSK 18 Response of matched filter to input with three resolvable multipath components 19 Rake receiver for M orthogonal pulses 20 Rake receiver: basic configuration for generating a decision variable and a single finger 21 Rake receiver that uses equal-gain combiner to avoid channelparameter estimation 22 Information-bit error probability for extended Golay (24,12) code with soft and hard decisions, coherent PSK modulation, and Rayleigh fading, and for maximal-ratio combining with L = 1, 4,5, and 6 23 Information-bit error probability for Rayleigh fading, coherent PSK, and binary convolutional codes with various values of (K, r) and n r 24 Information-bit error probability for Rayleigh fading, coherent PSK, soft decisions, and concatenated codes comprising an inner binary convolurional code with K = 7 and n = 1/2, and various Reed-Solomon (n, A;) outer codes 59 25 Basic elements of receiver for direct-sequence signal with coherent PSK 61 26 Gold sequence generator 64 27 Symbol error probability of direct-sequence system with PSK in presence of single multiple-access interference signal and E s /No = 15 dB 72 28 Symbol error probability of direct-sequence system with PSK in presence of multiple-access interference signal and E S /NQ = 15 dB 72 29 Symbol error probability of direct-sequence system with PSK in presence of single multiple-access interference signal and E S /NQ = 15 dB 74 30 Receiver for direct-sequence signal with classical quaternary modulation 75 31 Receiver for direct-sequence signal with balanced quaternary modulation 77 32 Geometry of cellular network with base station at center of each hexagon 7933 Probability of no outage for instantaneous power control, G/Z = 40,7o/G = 0.5, and a e = 0,1,2,3 dB 88 34 Probability of no outage for perfect local-mean power control, G/Z = 40, and 7o /G = 0.5, oo 90 35 Local-mean outage probability for Z\-7 dB, q = 3/8, g = 0.558, G = 156.5, and 7o = 20.94dB with a e = 0,1,2,3 dB 92 36 Information-bit error probability for instantaneous power control and perfect local-mean power control, 70 = 13 dB, G = 128, and the BCH (63,30) code with various values of cr e in decibels .95 37 Information-bit error probability for slow fading and fast fading with different Doppler factors D 99 38 Upper bound on uplink capacity per megahertz for a = 0.1, a m = 1.5 dB, g = 0.634, iV 0 /po = 5 ^s, and T x = 100 /xs 100 39 Multicarrier direct-sequence CDMA system: transmitter and receiver 103 40 Bit error probability for multicarrier systems with M = 4 and 8 and for single-carrier systems with (727374) = (11 0)7 and Q \ |) 7, where 7 is the average bit SNR for both the multicarrier system and the largest multipath component of the single-carrier system 103 VI Tables 41 Time durations of a frequency-hopping pulse after the dehopping in the receiver 105 42 Geometry of a peer-to-peer communication network 110 43 Spatial reliability for ML = 250 and minimum area-mean SNR = 20 dB 112 44 Spatial reliability for ML = 500 and minimum area-mean SNR = 20 dB 113 45 Spatial reliability for Mi = 250 and minimum area-mean SNR = 25 dB 113 46 Hexagonal grid of cells.Communicators are in sector A. Sector B is an interfering sector 115 47 Spatial reliability for uplinks, separated orthogonal hopping, M = 100, and minimum area-mean SNR = 30 dB 119 48 Spatial reliability for uplinks, orthogonal hopping, M -100, and minimum area-mean SNR = 30 dB 119 49 Spatial reliability for uplinks, separated orthogonal hopping, M = 200, and minimum area-mean SNR = 30 dB 120 50 Spatial reliability for uplinks, separated orthogonal hopping, M = 100, and minimum area-mean SNR = 20 dB 121 51 Spatial reliability for downlinks, separated orthogonal hopping, M = 100, and minimum area-mean SNR = 30 dB 121 B-l Envelope extraction: direct-conversion receiver, associated spectra, and implementation with real-valued signals 136 1 Interference factor and variance factor as functions of a v when var[K] =0 84 vu Pi = P«10* /10 (1-2)Gaussian random variable.Thus, r(t) at a specific time is a complex Gaussian random variable with a nonzero mean equal to the deterministic first term, and (1-13) implies that E[r c (t)] = a 0 (t) cos[(f>o(t)} , E[r s (t)} = a 0 (t) sin[^>(t)](1-24)