Welcome to the World of CDMA 

Direct Sequence Spread Spectrum In this page we show how direct sequence spectrum spreading
alters the detection statistics of a communication system. The major
result is the interference averaging property that we assume when doing
estimates of system capacity. The intent here is to do the math correctly,
or at least to outline the steps of the analysis. PseudoRandom Spreading Sequences In this section we approximate the actual binary PN spreading sequences by an ideal Bernoulli (cointossing) sequence with equiprobable outcomes. That is Pr[0] = Pr[1] = 1/2, with all trials independent. Mapping the (0, 1) sequence to a (+1, 1) discrete modulation sequence {a_{n}}, the autocorrelation of the latter is a Kronecker delta function, that isThe actual sequences have offtime correlations of the order of 1/N, where N is the length of the sequence. This approximation is well justified in practice because the random relative RF phases of the interferers tend to remove the small bias that the approximation might otherwise introduce. Alternative representations In transmitters the most convenient way to impose spreading on data is usually modulotwo addition (exclusive OR) in conventional binaryvalued logic. In the analog world those binary values are represented by bipolar signals. The modulotwo binary addition is equivalent to analog multiplication by ±1, provided binary 1 maps to bipolar 1 and binary 0 maps to +1.We also will refer to impulse modulators.
The impulse modulator accepts a binaryvalued input, but produces a
bipolar impulse output. Synchronization For the purposes of this analysis we assume that time
and frequency synchronization have been achieved by means we don't worry
about for now. A Note on the Differences between the models analyzed here and the real thing ... Forward CDMA Channel The QPSK model that we
consider here is similar to the Forward CDMA Channel except we neglect
the orthogonal channelization. We assume here that the spreading sequences
are completely uncorrelated between users. There are two consequences
of this assumption. First, it means that the users active in the various
channels of one base station interfere with one another just as though
they would if they came from different stations. Second, it means that
the expectations of the chip detection amplitudes depend only on the
user being addressed, and have no contributions from the other users. Reverse CDMA Channel The QPSK model that we consider here is very similar
to the Reverse CDMA Channel except for the offset modulation. This does
not affect the primary conclusion about interference averaging in any
significant way. Statistics The calculations we're doing here pertain only to the secondorder (i.e., mean and variance) of a single chip from the DSSS demodulator. The overall system performance depends on the coding that takes place outside the domain of the spreadingdespreading operations. The forward link, for purposes of calculating symbol energytonoise ratios, is essentially repetition coded. That is, each FEC code symbol is repeated 64 times. The SNR of its detection statistic is approximately 64 times (18 dB greater than) the perchip SNR because the 64 chips sum coherently, while the variances sum rms fashion. Subsequent to the soft decision detection statistic, one must consider the performance of the Viterbi decoder to ascertain the overall SNR (E_{b}/N_{0} performance. See, for example, Viterbi's CDMA book.The reverse link is somewhat more difficult because the receiver must form 64 decision metrics from 256 chips, and the noise contributions to those 64 metrics are correlated. An analysis of this situation can be found (until we get around to writing it here) in Proakis, pp. 807810. Our purpose here is to show how the effects of multiple access interference and possible jamming and interference can be accounted for in our capacity calculations and link budgets by a simple calculation of an effective noise power spectral density. The unwanted signals can be modeled, as far as the communication link is concerned, like thermal noise. within the spreading bandwidth.If you want to see all the details ... . . . Continue to BPSK Receiver Statistics ... or if you just want the main point, it's the interference averaging property.The primary result of all the mathematical gore is that the effect of mutual interference and jamming is, for most purposes, the same as an effective total noise level of This interference averaging property is the primary direct benefit of the use of CDMA.
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