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Notice that the greater the sequence length the quicker the SESS system converges to

BPSK in an Additive White Gaussian Noise (AWGN) channel. Conversely, for lower N values

the BER stays closer to 0.5 longer.

This makes sense when you consider that if there is an error for a small N of 1 or 2, the

next bit will be demodulated with the wrong spreading code leaving with either 100 or 50

percent of the wrong bits in the demodulating spreading sequence. This leads to the 50 percent

error rate that can been seen in these two values on Figure 5. The chip errors in the receiver

registers attenuate the de-spreaded signal strength. This can be regarded as a form of self

interference introduced by self encoding. Let X be the random variable denoting the number of

chip errors within the receiver register of length N. For l chip errors, the amplitude attenuation

can be expressed as:

(7)

  • |=

= 1

2

Then the conditional probability of error becomes:

(8)

  • |

=

1

2

2

The probability of error will be greater than 0.5 if the argument of the Q-function is

negative; this corresponds to the situation that X > N/2 [24]. This suggests that there exists an

undesirable situation caused by error propagation: a sufficient number of chip errors may

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