MCCDMA vs DSCDMA M des Noes and D

MC-CDMA vs DS-CDMA M. des Noes and D. Ktenas (presented by Sylvie Mayrargue) COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

Outline • Context of the comparison : Ø Simulation assumptions Ø Asymptotic analysis • DS and MC-CDMA system models. • For each detector : Ø Linear filter description Ø Simulation results • Interpretation • Conclusion and future work COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

Context of the comparison • Downlink : Base station to mobile. • No channel coding. • No inter-cell interferences • Perfect channel estimation and synchronization • Linear detectors : MRC, SU-MMSE and MU-MMSE Comparison of BER based on simulations (Monte Carlo) and asymptotic analysis (theory). COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

Asymptotic analysis 1/3 • Symbol estimated at the output of a linear detector for DS or MC-CDMA system : • k and k depend on the channel, spreading codes and code power matrices. • k results from the filtering of the MAI plus the background noise. COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

Asymptotic analysis 2/3 The main results of the asymptotic analysis are the followings: • As N, K and =K/N is fixed, k converges to a limit . • As N, K and =K/N is fixed, k becomes gaussian and its variance converges to a limit V 2 • An analytical expression of the asymptotic SINR is obtained. It is independent of the spreading codes. These demonstrations are based on the so-called ‘free probability theory’. Zhang, Chong, Tse « Output MAI distribution of linear MMSE multi-user receivers in CDMA systems » Information Theory March 2001 COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

Asymptotic analysis Fixed Gaussian noise 3/3 AWGN transmission ! Signal to Interference plus Noise Ratio (SINR) : COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

References Ø MC CDMA M. Debbah, W. Hachem, P. Loubaton, M. de Courville « MMSE Analysis of Certain Large Isometric Random Precoded Systems » – IEEE Trans on Information Theory Vol 49, n° 5, May 2003 Ø DS CDMA – J. M. Chaufray, W. Hachem, Ph. Loubaton « Asymptotical Analysis of Optimum and Sub optimum CDMA Downlink MMSE Receivers » – Can be downloaded at http: //syscom. univmlv. fr/~loubaton/index. html COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

DS-CDMA system model N d 1(n) 1/2 c 1(z) v[n] X[n] h(z) N d. K(n) Y[n] c. K(z) • Channel : • C=(c 1 c 2 … c. K), d(n) = (d 1(n), …, d. K(n))T, P = diag(P 1, …, PK) • Y(n) = (Y 1(n) , …, YN(n))T • N : spreading factor , K : number of codes • W : delay spread of the channel (W< N) COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

DS-CDMA system model 2/2 Received signal : Useful + MAI ISI+MAI Noise N(0, 2 I) COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

d. K(n) x 1(n) 1: N x. N(n) 1/2 s 1 N: N P/S IFFT S/P d 1(n) Spreading MC CDMA System model s. N GI Insertion z[i] N: 1 COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

MC CDMA System model Received signal : Tap delay channel : where is the channel impulse response. COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability. 2/2

MRC: Maximum Ratio Combining DS-CDMA MC-CDMA COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

MRC: Simulation vs. Asymptotic DS-CDMA COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

MRC: Simulation vs. Asymptotic MC-CDMA COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

MRC: Comparison MC-CDMA DS-CDMA COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

SU-MMSE DS-CDMA MC-CDMA COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

SU-MMSE : simulation vs asymptotic – MC CDMA COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

SU-MMSE : Comparison DS-CDMA – MC CDMA COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

MU-MMSE Multiple User MMSE (for DS-CDMA) MU-MMSE : equalize the global channel : h(z) c(z) Asymptotic SINR : Distribution of powers : Kc classes of powers COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

MU-MMSE Multiple User MMSE (for MC-CDMA) Asymptotic SINR COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

MU-MMSE : simulation vs asymptotic – DS CDMA COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

MU-MMSE : DS-CDMA – MC CDMA COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

Interpretation 1(N, K) DS-CDMA 2(N, K) DS-CDMA with Cyclic Prefix 2(N, K)- 1(N, K) 2 N, K 0 Both systems have the same asymptotic SINR COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

Interpretation • Both matrices have the same eigenvalue distribution. • When computing the asymptotic SINR, we only use the eigenvalue distribution. • MC-CDMA and DS-CDMA have the same asymptotic SINR. COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.

Conclusion • With our assumptions : MC-CDMA = DS-CDMA in an uncoded scenario. • MC-CDMA receiver is less complex than a DS-CDMA receiver ? Ø DS-CDMA : possibility to perform frequency domain equalization (with the same performance), but needs one FFT and one IFFT at the receiver side. Ø MC-CDMA gains one FFT on the complexity for a MS. Ø Need to take into account the overall complexity (including channel estimation, synchronization , …, RF). ØFuture work: coding impact? . COST 289 30 -31 Oct 2003 (Kosice) MATRICE project The information in this document is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information as its sole risk and liability.