Analysis of Large MIMO DS-CDMA Systems With Imperfect ... - NTNU

(a) δ tx ∈ (0.1, 16), uncorrelated receive antennas and optimum LMMSE

channel estimator (spatial correlation known perfectly).

(b) δ rx ∈ (0.1, 16), correlated transmit antennas δ tx =3and optimum

LMMSE, Type-1 or Type-2 mismatched LMMSE channel estimator.

Figure 1. Spectral efficiency vs. angular spread (in degrees) at the (a) transmitter δ tx, and (b) receiver δ rx. Equal transmit power per antenna, 4 × 4 **MIMO**

channel, coherence time **of** T = 50 symbols, number **of** pilots per fading block τ p =4and average SNR per receive antenna snr = 10 dB.

In Fig. 1(b) the spectral efficiency **of** LMMSE MUD and

SUMF for the CEs defined in Examples 1 and 2 is plotted as

a function **of** angular spread at the receiver side δ rx for load

α =2. Angular spread **of** d tx =3degrees (high correlation)

at the transmitter is assumed. As expected, when antenna

correlation at the receiver’s side decreases, a significant gain

in spectral efficiency is observed. If the optimum LMMSE

CE instead **of** the covariance mismatched CE that neglects

transmit correlation is used, C qpsk roughly doubles for both

the LMMSE and SUMF MUDs for all values **of** δ rx . As a

consequence, in this scenario it is in fact preferable to have

the optimum LMMSE CE with SUMF instead **of** Type-1 CE

and LMMSE MUD.

VI. CONCLUSIONS

The effect **of** antenna correlation on the spectral efficiency

**of** **MIMO** **DS**-**CDMA** was studied. The analysis took into

account the CSI mismatch caused by pilot-aided channel

estimation. The results indicated that the ergodic spectral

efficiency achieved with uncorrelated transmit antennas could

be more than doubled by using highly correlated transmit

antennas. No information at the transmitter was required, but

the channel estimator needed knowledge about the spatial

correlation in advance.

ACKNOWLEDGMENT

The work **of** M. Vehkaperä was supported by the Norwegian

Research Council under grant 171133/V30. K. Takeuchi was in

part supported by the Grant-in-Aid for Young Scientists (Startup)

(No. 21860035) from MEXT, Japan. Tanaka and Takeuchi

acknowledge support through Grant-in-Aid for Scientific Research

on Priority Areas (No. 18079010) from MEXT, Japan.

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