Interference cancellation using the Gibbs sampler

Soft-decision multistage multiuser interference cancellation

“…For example, if the soft bit estimate is , the Gibbs sampler draws a sample that will be 1 with probability 88%. With perfect power control and perfect amplitude information, the SIC using a Gibbs sampler achieves BER performance within 0.5 dB of the single-user bound [13]. While our SIC uses deterministic soft decisions, it may reach a fixed point faster than [13], although [13] may convergence to a lower steady-state error.…”

“…With perfect power control and perfect amplitude information, the SIC using a Gibbs sampler achieves BER performance within 0.5 dB of the single-user bound [13]. While our SIC uses deterministic soft decisions, it may reach a fixed point faster than [13], although [13] may convergence to a lower steady-state error. Under a 10-dB near-far ratio and with imperfect amplitude information, the soft-decision SIC achieves a BER performance within 0.4 dB of the single-user bound, as will be described in Section VI.…”

“…The performance of the proposed SIC in (9) can also be compared to an SIC using a Gibbs sampler [13]. The Gibbs sampler introduces randomness into the SIC cancellation, where the hard data bit decision is made by choosing a sample from a conditional probability density function (pdf) of the soft data bit estimate.…”

“…Since a wrong hard bit decision is made, i.e., , its regenerated signal for interference cancellation is . Assuming that the data bit error and the amplitude estimation error are independent, the introduced interference variance can be calculated as (12) Combining the above cases, the average interference variance contribution from one bit of user conditioned on its amplitude is (13) If the received user signals have unequal powers, we may assume that the received amplitudes are uniformly distributed between and , where is the amplitude of the weakest user and is the ratio of . The average interference variance contribution from user can be calculated by averaging (13) over the distribution of , which is assumed uniform in [ ].…”

“…Assuming that the data bit error and the amplitude estimation error are independent, the introduced interference variance can be calculated as (12) Combining the above cases, the average interference variance contribution from one bit of user conditioned on its amplitude is (13) If the received user signals have unequal powers, we may assume that the received amplitudes are uniformly distributed between and , where is the amplitude of the weakest user and is the ratio of . The average interference variance contribution from user can be calculated by averaging (13) over the distribution of , which is assumed uniform in [ ]. Denote the expectation (14) and by using the approximation (15) Substituting (14) and (15) into (13), the total interference for all users including the channel noise variance is the solution to (16) For example, for an amplitude averaging length of bits, signal-to-noise ratio (SNR) of 10 dB, near-far ratio of 10 dB, spreading factor of , and number of users , the loss to the single-user bound is about 0.35 dB for threshold , 0.68 dB for , and 1.93 dB for .…”