Stochastic least-symbol-error-rate adaptive equalization for pulse-amplitude modulation

Adaptive minimum error-rate filtering design: A review

“…10 ðþÞ R for the two beamforming designs given SNR ¼ 6 dB, where the beamformer's weight vector w was normalised to a unit length. It can be seen that the distribution pðyjs d ðkÞ ¼ þ1Þ is symmetric with respect to the R½y and I½y axes for the MMSE design, and this was a direct consequence of the minimisation of the MSE criterion (18). By contrast, the MBER design appeared to be more intelligent and was able to shape pðyjs d ðkÞ ¼ þ1Þ in such a way that the distance between the decision threshold y R ¼ 0 and the signal subset Y ðþÞ R was maximised.…”

“…Furthermore, at the time of writing there exists no theoretical result for analysing the steady-state BER misadjustment of the LBER algorithm, but in practice we have observed that the steady-state BER misadjustment can often be made very small by carefully tuning the two algorithmic parameters. Convergence behaviour and steady-state BER misadjustment of the LBER algorithm have been extensively investigated in the previous publications [11,14,18,20,25,26,29,31,35,36,38,39,[41][42][43][44].…”

“…In the past decade, significant advances have been made in the design of adaptive minimum BER (MBER) filtering for a variety of communication applications, including classical single-user channel equalisation [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], multiuser detection in codedivision multiple-access (CDMA) systems [21][22][23][24][25][26][27][28][29][30], adaptive beamforming assisted receiver for multiple-antenna aided systems [31][32][33][34][35][36][37][38][39], space-time equalisation assisted multiuser detection for spacedivision multiple-access (SDMA) induced multipleinput multiple-output (MIMO) systems [40][41][42][43][44], and orthogonal frequency division multiplexing (OFDM) and other multi-carrier systems [45][46][47][48][49][50]. The ...…”

Adaptive minimum symbol-error-rate CDMA linear multiuser detector for pulse-amplitude modulation

“…where AE × AE × Å is the number of points in Ð . Following [13], it can be shown that the SER of the user linear detector with weight vector Û is…”

“…A steepest-descent or simplified conjugate gradient algorithm [12], [13] can be used to minimize the SER expression (13) to arrive at the MSER solution. It is computationally advantageous to normalize Û to a unit-length after each iteration as Û Û Ô Û Ì Û. Computational requirements can further be simplified by considering the subset Ð with Ð ½ • Å ¾, which results in × Ð ½ ¼ .…”