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Large System Performance of Linear Multiuser Receivers in Multipath Fading ChannelsAuthors – Jamie Evans & David Tse Presented by RajathaRaghavendra
Outline • Multi user receivers • Performance measures • Data estimator performance • Impact of channel estimation • Simulation results • Conclusions
Conventional receiver for CDMA • Matched filter - Correlation of received signal with all PN sequences. • Detection - Highest peak for autocorrelation. • But PN sequences are not fully orthogonal in practice. • Results in Multiple Access Interference(MAI).
Multi-User Detection receiver • Knowledge of other user’s channel and signature code helps in mitigating MAI at output of matched filter. • Types of linear receivers: • Decorrelator – requires signature sequence. Applies inverse of correlation to output of matched filter. • LMMSE - requires channel knowledge. Minimizes the error between estimated data and actual data with the help of training sequences.
Block diagram of M.U.D. • Data estimator estimates the data of each user by observing the received data over one symbol period. • Needs channel estimates which are time-varying due to multipath fading.
Performance measure of MUD • SIR is a measure of performance. • SIR for random signature sequence is random. • David Tse – asymptotically, for large number of users, SIR converges to a deterministic quantity. • Extension – Channel has multipath fading components. • Only channel estimates(mean & covariance) are known.
Concept of Effective Interference • System with K users, N spreading gain, ak received power where where - Effective interference of k users on user1 • For estimated channel where - The estimated channel gain of user k - The error variance
Data Estimator performance • For a multipath fading channel with L resolvable paths where • Interference looks like (L-1) users with power and one user with power
Data Estimator performance • Overall interference caused by user k • When channel is known perfectly, then the interferer looks like a single interferer with power • When no channel knowledge is available, the interferer looks like L interferers with power
Data Estimator performance • One high power interferer is weaker than several low powered interferers with same total power. • Therefore channel estimation is an important factor in improving the performance. • Uncertainty results in single interferer becoming L dimensional.
Channel Estimation • Performed during training sequences. • Estimation window size is less than coherence time. • Mean Square Error where • As estimation window length increases, is approximated to which is the same as absence of other users.
Simulation Results • Asymptotically, normalized SIR converges to the theoretical value of 0.38 • K/N = 0.5 • N= 32, 64, 128, 256
Simulation Results Ideal LMMSE (o), worst case LMMSE (+), Decorrelator (x), and matched filter (*) • Ideal LMMSE & worst case LMMSE performance is almost the same in frequency flat fading channel.
Simulation Results Results are shown for Frequency Selective fading . The matched filter (*), the Decorrelator (X), and the LMMSE receiver (o). Curves are shown for estimation window lengths of (from the top) infinity (perfectly known channel), 10, 2, and finally for the case when nothing is known about the channels.
Simulation Results Plots of performance loss for the LMMSE receiver for Flat fading channel(L=1). Results are shown for channel estimator window lengths of (from the top) = 1, 2, and 5.
Conclusions • Asymptotic performance with random sequences is equal to the performance when the sequences are independent. • In multipath fading, the receivers making accurate channel estimates performs better than those without channel knowledge. • LMMSE performs better than decorrelator and matched filter.