#### Transcript Multiuser detection in CDMA systems

Multiuser Detection in CDMA A. Chockalingam Assistant Professor Indian Institute of Science, Bangalore-12 [email protected] http://ece.iisc.ernet.in/~achockal Outline Near-Far Effect in CDMA CDMA System Model Conventional MF Detector Optimum Multiuser Detector Sub-optimum Multiuser Detectors – Linear Detectors » MMSE, Decorrelator – Nonlinear Detectors » Subtractive Interference cancellers (SIC, PIC) » Decision Feedback Detectors Dr. A. Chockalingam Dept of ECE, IISc, Bangalore 2 DS-CDMA Efficient means of sharing a given RF spectrum by different users User data is spread by a PN code before transmission Base station Rx distinguishes different users based on different PN codes assigned to them All CDMA users simultaneously can occupy the entire spectrum » So system is Interference limited Dr. A. Chockalingam Dept of ECE, IISc, Bangalore 3 DS-SS DS-SS signal is obtained by multiplying the information bits with a wideband PN signal Information Bits Carrier Modulation Tb PN Signal Information Bits Tb = N Tc N : Processing Gain Dr. A. Chockalingam t Tc PN Signal t Dept of ECE, IISc, Bangalore 4 Processing Gain Ratio of RF BW (W) to information rate (R) Gp W (e.g., In IS-95A, W = 1.25 MHz, R = 9.6 Kbps R 1 . 25 X 10 System K i.e., Gp 9 . 6 X 10 3 133 21 dB ) Capacity (K) proportional to G p G pG vG A ( E b / I o )G f G v 2 . 67 (voice activity gain) G A 2 . 4 (sectorization gain) G f 1 .6 (other cell interference loss) E b / I o 6 dB Dr. A. Chockalingam 6 Dept of ECE, IISc, Bangalore (typically required) 5 Near-Far Effect in DS-CDMA Assume K users in the system. Let Ps be the average Rx power of each signal. Model interference from K 1 users as AWGN. E Ps T SNR at the desired user is b I0 N 0 ( K 1) Ps T c Let one user is near to BS establishes a stronger Rx signal equal to aPs , a 1 SNR then becomes Eb I0 When a Ps T N 0 aP s T c ( K 2 ) Ps T c is large, SNR degrades drastically. To maintain same SNR, K 2 has to be reduced Dr. A. Chockalingam Dept of ECE, IISc, Bangalore i.e., loss in capacity. 6 Near-Far Effect Factors causing near-far effect (unequal Rx Signal powers from different users) in cellular CDMA – Distance loss – Shadow loss – Multipath fading (Most detrimental. Dynamic range of fade power variations: about 60 dB) Two common approaches to combat near-far effect – Transmit Power Control – Near-far Resistant Multiuser Detectors Dr. A. Chockalingam Dept of ECE, IISc, Bangalore 7 CDMA System Model Data of User 1 Chip shaping filter 1 Spreading Sequence of user 1 Data of User 1 AWGN Chip shaping filter 2 Chip shaping filter K Spreading Sequence of user 2 Data of User 1 r (t ) To Demod/ Detector Spreading Sequence of user K Dr. A. Chockalingam Dept of ECE, IISc, Bangalore 8 Matched Filter Detector (MFD) ^ nT r1 MF User 1 ^ nT ^ nT rK MF User K rk E k bk E jbj jk b 2 (n ) r2 MF User 2 r (t ) b1 (n ) b K (n ) r RA b n nk jk E [ nn ] R T Dr. A. Chockalingam 2 R: Correlation Matrix A diag Dept of ECE, IISc, Bangalore E1 , E 2 ,..., EK 9 MFD Performance: Near-Far Scenario 2-User system: NFR Interferin Desired 0.4 g User' s Rx Power User' s Rx Power NFR = 20 dB 0.1 NFR = 10 dB Bit Error Rate NFR = 5 dB NFR = 0 dB E/b/No (dB) • Problem with MF Detector: Treats other user interference (MAI) as merely noise • But MAI has a structure which can be exploited in the Dr. A. Chockalingam Dept of ECE, IISc, Bangalore detection process 10 Optimum Multiuser Detector Jointly detect all users data bits Optimum Multiuser Detector – Maximum Likelihood Sequence Detector Selects the mostly likely sequences of data bits given the observations Needs knowledge of side information such as – received powers of all users – relative delays of all users – spreading sequences of all users Dr. A. Chockalingam Dept of ECE, IISc, Bangalore 11 Optimum Multiuser Detector Optimum ML detector computes the likelihood fn (b ) T 0 r (t ) 2 E k b k c k ( t ) dt K k 1 the sequence bk ,1 k K that and selects minimizes (b ) The above function can be expressed in the form T c(r , b) B r B R B where r r1 , r2 ,..., rK T B T and T E 1 b1 , E 2 b 2 ,..., E K bK is the correlation matrix with elements T where ij ( ) c i ( t ) c j ( t ) dt 0 Dr. A. Chockalingam Dept of ECE, IISc, Bangalore 12 Optimum Multiuser Detector results in 2 K choices of the bits of the K users { b1 , b 2 ,..., b K } Thus Optimum Multiuser Detector is highly complex – complexity grows exponentially with number of users – Impractical even for moderate number of users Need to know the received signal energies of all the users Dr. A. Chockalingam Dept of ECE, IISc, Bangalore 13 Suboptimum Detectors Prefer – Better near-far resistance than Matched Filter Detector – Lesser complexity (linear complexity) than Optimum Detector Linear suboptimum detectors – Decorrelating detector – MMSE detector Dr. A. Chockalingam Dept of ECE, IISc, Bangalore 14 Decorrelating Detector r1 r2 Linear Transformation and Detector Decision 1 ^ R r b sgn() rK p For the case of 2 users (k ) and p e Q Dr. A. Chockalingam R 2 E k (1 ) 1 xx (k ) e Q Ek R 1 kk 1 1 2 Dept of ECE, IISc, Bangalore 15 Decorrelating Detector For the case of 2 users and R 1 1 2 1 1 1 R 1 1 1 R r E 1 b1 E 2 b2 n1 n 2 2 1 n 2 n1 2 1 – R 1 r operation has completely eliminated MAI components at the output (.e., no NF effect) – Noise got enhanced (variance increased by a factor of Dr. A. Chockalingam Dept of ECE, IISc, Bangalore 1 1 16 2 ) Decorrelating Detector Alternate representation of Decorrelating detector ^ T b1 0 r (t ) c1 ( t ) c 2 ( t ) ^ T b2 0 c1 ( t ) c 2 ( t ) – By correlating the received signal with the modified signature waveforms, the MAI is tuned out (decorrelated) – Hence the name decorrelating detector Dr. A. Chockalingam Dept of ECE, IISc, Bangalore 17 MMSE Detector • Choose the linear transformation that minimizes the mean square error between the MF outputs and the transmitted data vector b r1 r2 Linear Transformation and Detector 1 A r rK Dr. A. Chockalingam Dept of ECE, IISc, Bangalore Decision ^ b sgn() 18 MMSE Detector 0 • Choose the linear transformation b A r where A is determined so as to minimize the mean square error (MSE) J ( b ) E [( b A r ) ( b A r )] T • Optimum choice of A that minimizes J (b ) is A R I 0 Dr. A. Chockalingam 2 1 Dept of ECE, IISc, Bangalore 19 MMSE Detector r1 r2 Linear Transformation and Detector R I 2 1 r rK Decision ^ b sgn() • When 2 is small compared to the diagonal elements of R MMSE performance approaches Decorrelating detector performance • When 2 is large A 0 becomes 2 I (i.e., AWGN becomes dominant) Dr. A. Chockalingam Dept of ECE, IISc, Bangalore 20 Adaptive MMSE Estimate of the data bits Linear Transversal Filter Adaptive Algorithm Several Re() Training bits adaptation algorithms – LMS – RLS Blind techniques Dr. A. Chockalingam Dept of ECE, IISc, Bangalore 21 Performance Measures Bit Error Rate Asymptotic k Lt efficiency: Ratio of SNRs with and without interference 0 Asymptotic Dr. A. Chockalingam ke k represents loss due to multiuser interference efficiency easy to compute than BER Dept of ECE, IISc, Bangalore 22 Performance Measures Optimum Detector DC 1.0 MMSE k MF Detector 0.0 -20.0 Dr. A. Chockalingam -10.0 0.0 Dept of ECE, IISc, Bangalore 10.0 20.0 E2 E 1 dB 23 Subtractive Interference Cancellation Multistage interference Cancellation approaches – Serial (or successive) Interference Canceller (SIC) » sequentially recovers users (recover one user per stage) » data estimate in each stage is used to regenerate the interfering signal which is then subtracted from the original received signal » Detects and removes the strongest user first – Parallel Interference Canceller (PIC) » Similar to SIC except that cancellations are done in parallel Dr. A. Chockalingam Dept of ECE, IISc, Bangalore 24 SIC ^ ^ b1 bm MF Detector MF Detector r (t ) Matched Filter Remodulate & Cancel e2 em Stage-1 Dr. A. Chockalingam e m 1 Remodulate & Cancel Stage-m Dept of ECE, IISc, Bangalore 25 m-th Stage in SIC MF Detector MF User m ^ em bm Select Strongest User MF User K cm ^ Remodulate & Cancel Dr. A. Chockalingam Dept of ECE, IISc, Bangalore Em e m 1 26 Performance of SIC Good near-far resistance Most performance gain in achieved using just 2 to 3 stages High NFR can result in good performance! – Provided accurate estimates of amptitude and timing are available Sensitive to amplitude and timing estimation errors – increased loss in performance for amplitude estimation errors > 20 % Some amount of power control may be required to compensate for the near-far resistance loss due to imperfect estimates and low NFR Dr. A. Chockalingam Dept of ECE, IISc, Bangalore 27 PIC MF User 1 (1 ) 1 r ^ (1 ) b1 r r (t ) ^ ( j) ( j) 1 ^ ( j 1 ) K b1 1i Ei bi i 1 i 1 MF User K r (1 ) K ^ (1 ) bK ( j) rK Stage 1 Dept of ECE, IISc, Bangalore bK ^ ( j 1 ) K i 1 i K Dr. A. Chockalingam ^ ( j) Ki Ei bi Stage j 28 Performance of PIC Performance of PIC Good near-far resistance Similar performance observations as in SIC Performance of PIC depends more heavily on the relative amplitude levels than on the cross-correlations of the user spreading codes Hybrid SIC/PIC architectures Dr. A. Chockalingam Dept of ECE, IISc, Bangalore 29 DFE Detector Tc T 1 ^ MF User 1 b1 FFF Centralized Decision Feedback ^ bK Tc T K MF User K FFF • Feedback current data decisions of the stronger users as well • DFE multiuser detectors outperform linear adaptive receivers • Complexity, error propagation issues Dr. A. Chockalingam Dept of ECE, IISc, Bangalore 30