**7. Simulation results**

Simulations are divided into 3 parts. In the first part, we look at the performance of the proposed interference-aware receiver structure for the multi-user MIMO mode in LTE while second part is dedicated to the sensitivity analysis of this receiver structure to the knowledge of the constellation of interference. This sensitivity analysis is motivated by the fact that the DCI formats in the transmission mode 5 (multi-user MIMO) do not include the information of the constellation of the co-scheduled UE. Third part looks at the diversity order of the EGT in both single-user and multi-user MIMO modes in LTE.

For the first part (Figs. 5 and 6), we consider the downlink of 3GPP LTE which is based on BICM OFDM transmission from the eNodeB equipped with two antennas using rate-1/3 LTE turbo code1 [16] with rate matching to rate 1/2 and 1/4. We deliberate on both the cases of single and dual-antenna UEs. We consider an ideal OFDM system (no ISI) and analyze it in the frequency domain where the channel has iid Gaussian matrix entries with unit variance and is independently generated for each channel use. We assume no power control in the multi-user MIMO mode so two UEs have equal power distribution. Furthermore, all mappings of the coded bits to QAM symbols use Gray encoding. We focus on the FER while the frame length is fixed to 1056 information bits. As a reference, we consider the fall-back transmit diversity scheme (LTE mode 2 - Alamouti code) and compare it with the single-user and multi-user MIMO modes employing single-user receivers and

<sup>1</sup> The LTE turbo decoder design was performed using the coded modulation library www.iterativesolutions.com

22 Recent Trends in Multiuser MIMO Communications

10−3

MF EGT MU MIMO

in both single-user and multi-user MIMO modes in LTE.

10−2

FER

MU MIMO

puncturing patterns.

MF MU MIMO

**7. Simulation results**

10−1

100

9 10 11 12 13 14 15 16 17

**Figure 5.** Downlink fast fading channel with the dual-antenna eNodeB and 2 single-antenna UEs. IA Rx indicates the low-complexity interference-aware receiver while SU Rx indicates the single-user receiver. MU MIMO and SU MIMO indicate multi-user and single-user MIMO respectively. To be fair in comparison amongst different schemes, sum rates are fixed, i.e. if 2 users are served with QPSK with rate 1/2 in the multi-user mode, then one user is served with QAM16 with rate 1/2 in the single-user mode thereby equating the sum rate in both cases to 2bps/Hz. 3GPP LTE rate 1/3 turbo code is used with different

Simulations are divided into 3 parts. In the first part, we look at the performance of the proposed interference-aware receiver structure for the multi-user MIMO mode in LTE while second part is dedicated to the sensitivity analysis of this receiver structure to the knowledge of the constellation of interference. This sensitivity analysis is motivated by the fact that the DCI formats in the transmission mode 5 (multi-user MIMO) do not include the information of the constellation of the co-scheduled UE. Third part looks at the diversity order of the EGT

For the first part (Figs. 5 and 6), we consider the downlink of 3GPP LTE which is based on BICM OFDM transmission from the eNodeB equipped with two antennas using rate-1/3 LTE turbo code1 [16] with rate matching to rate 1/2 and 1/4. We deliberate on both the cases of single and dual-antenna UEs. We consider an ideal OFDM system (no ISI) and analyze it in the frequency domain where the channel has iid Gaussian matrix entries with unit variance and is independently generated for each channel use. We assume no power control in the multi-user MIMO mode so two UEs have equal power distribution. Furthermore, all mappings of the coded bits to QAM symbols use Gray encoding. We focus on the FER while the frame length is fixed to 1056 information bits. As a reference, we consider the fall-back transmit diversity scheme (LTE mode 2 - Alamouti code) and compare it with the single-user and multi-user MIMO modes employing single-user receivers and

<sup>1</sup> The LTE turbo decoder design was performed using the coded modulation library www.iterativesolutions.com

LTE mode 5 SU MIMO MF SU MIMO

LTE mode 2 IA Rx IA Rx IA Rx

SNR

MF EGT SU MIMO

LTE mode 6

Transmit Diversity

MU MIMO LTE mode 5 SU Rx

4bps/Hz

**Figure 6.** Downlink fast fading channel with the dual-antenna eNodeB and 2 dual-antenna UEs. IA indicates the low-complexity interference-aware receiver while SU indicates the single-user receiver. 3GPP LTE rate 1/3 turbo code is used with different puncturing patterns.

low-complexity interference-aware receivers. To analyze the degradation caused by the low-resolution and EGT of LTE precoders, we also look at the system performance employing the unquantized MF and unquantized MF EGT precoders. To be fair in the comparison of the LTE multi-user MIMO mode (mode 5) employing the geometric scheduling algorithm with the multi-user MIMO mode employing unquantized MF and MF EGT precoders, we consider the geometric scheduling algorithm (Section 4) based on the spatial angle between the two channels (equation (22)). Perfect CSIT is assumed for the case of MF and MF EGT precoding while error free feedback of 2 bits (PMI) to the eNodeB is assumed for LTE precoders. It is assumed that the UE has knowledge of the constellation of co-scheduled UE in the multi-user MIMO mode. It is further assumed that the UE knows its own channel from the eNodeB. So in multi-user MIMO mode, the UE can find the effective interference channel based on the fact that the eNodeB schedules the second UE on the same RE whose precoder is 180◦ out of phase of the precoder of the first UE. Fig. 5 shows the results for the case of single-antenna UEs. It shows enhanced performance of the multi-user MIMO mode once the UEs resort to intelligent detection by employing the low-complexity interference-aware receivers. The performance is severely degraded once the UEs resort to single-user detection. An interesting result is almost the equivalent performance of the unquantized MF EGT and low-resolution LTE precoders which shows that the loss with respect to the unquantized CSIT is attributed to the EGT rather than the low-resolution of LTE precoders.

Fig. 6 shows the results for the case of dual-antenna UEs and focuses on different LTE modes employing LTE precoders. It shows the degraded performance of single-user detection which is due to the fact that the rate with single-user detection gets saturated at high SNR due to the increased interference strength as was shown in Section. 4. So the performance of single-user detection is degraded as the spectral efficiency is higher than the rate or mutual information of the single-user detection. For single-user MIMO (Mode 6), there is no saturation of the rate at high SNR as there is no interference. So mode 6 performs better than mode 5 at

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10 15 20 25 30

Codebook

MU MIMO - Enhanced MU MIMO - LTE

MU MIMO - Angular

Resolution Codebook

Levels

SNR

Lower bound MU MIMO - Random

**Figure 8.** Proposed precoder codebook. Downlink channel with dual-antenna eNodeB and two single-antenna UEs. The figure illustrates the performance for the sum rate of 4bps/Hz. SNR is the transmit SNR while sum rate is same for single-user and multi-user MIMO, i.e. if two UEs are served with QPSK, rate 1/2, in multi-user mode, then one UE is served with QAM16,

its modulation order. As the complexity of this receiver structure is independent of the constellation of interference, the assumption of higher order modulation does not add to the

In the third set of simulations, we look at the diversity order of the single-user MIMO and multi-user MIMO schemes in LTE. The system settings are same as in the first part but now we consider slow fading environment, i.e. the channel remains constant for the duration of one codeword. Fig. 8 shows significant improvement in the performance of the multi-user MIMO mode when additional codebook entries are employed to increase the levels of transmission as compared to the case of increasing the angular resolution of precoders. However creating two levels of transmission leads to significant improvement as the performance moves closer to the upper bound. This hypothetical upper bound is the performance curve for MF precoder in multi-user MIMO mode without any interference, i.e. the eNodeB serves two UEs with their respective MF based precoders and the two UEs do not see any interference. The change of the slope of FER curve with increased levels of transmission indicates improved diversity as compared to the case of increased angular resolution. On the other hand, little gain is observed in the single-user mode (LTE transmission mode 6) with additional codebook entries which is expected as the standard LTE precoders have been optimized for the single-user transmission [22]. For comparison purposes, we have also considered the case of random codebooks. The main advantage of random codebooks is that they indicate some sort of performance lower bound and with any

4bps/Hz

Multi-user MIMO in LTE and LTE-Advanced - Receiver Structure and Precoding Design

10−2

SU MIMO - Angular Resolution

SU MIMO - Enhanced Levels

complexity of detection.

SU MIMO - LTE Codebook

intelligent feedback design, system is bound to perform better.

MU MIMO

rate 1/2, in the single-user mode. SU MIMO and MU MIMO indicate single-user and multi-user MIMO.

10−1

FER

100

**Figure 7.** Interference sensitivity for the multi-user MIMO mode in LTE. Three sets of simulations are shown. QPSK-QPSK indicates that both *x*<sup>1</sup> and *x*<sup>2</sup> belong to QPSK. UE-1 does not know the constellation of interference (*x*2) and assumes it to be QPSK, QAM16 and QAM64.

high SNR once UEs employ single-user detection. However if UEs resort to the intelligent interference-aware detection, the multi-user MIMO mode shows enhanced performance over other transmission modes in LTE. No degradation of LTE multi-user MIMO mode is observed at higher spectral efficiencies once UEs have receive diversity (dual antennas).

In the second part of simulations, we look at the sensitivity of the proposed receiver structure to the knowledge of the constellation of co-scheduled UE for the multi-user MIMO mode in LTE. The simulation settings are same as of the first part except that we consider the case when UE has no knowledge of the constellation of co-scheduled UE. The UE assumes this unknown interference constellation to be QPSK, QAM16 or QAM64 and the results for these different assumptions are shown in Fig. 7. Results show that there is negligible degradation in the performance of the proposed receiver if the interfering constellation is assumed to be QAM16 or QAM64. However, there is significant degradation if the interference is assumed to be QPSK when it actually comes from QAM64. It indicates that assuming interference to be from a higher order modulation amongst the possible modulation alphabets leads to the best compromise as this assumption includes the lower modulation orders as special cases (with proper scaling). However the converse is not true, i.e. assuming interference from lower modulation order cannot include higher order modulations. As LTE and LTE-Advanced restrict the transmission to three modulations ( QPSK, QAM16 and QAM64 ), assuming interference to be QAM64 (or even QAM16) leads to better performance. If the interference constellation also includes QAM256, then assuming interference to be QAM256 (or even QAM64) would lead to better results. These results have not been shown here as LTE and LTE-Advanced do not support QAM256 modulation. The proposed receiver structure, therefore, can still exploit the discrete nature of the interference even if it does not know

24 Recent Trends in Multiuser MIMO Communications

10−4

Interference (x2)

10−3

10−2

FER of x1

QPSK, QAM16 and QAM64.

10−1

100

0 2 4 6 8 10 12 14 16

QPSK−QPSK QAM64−QAM64

QAM16−QAM16

SNR

QAM16 assumed to be QAM64 assumed to be QPSK

**Figure 7.** Interference sensitivity for the multi-user MIMO mode in LTE. Three sets of simulations are shown. QPSK-QPSK indicates that both *x*<sup>1</sup> and *x*<sup>2</sup> belong to QPSK. UE-1 does not know the constellation of interference (*x*2) and assumes it to be

high SNR once UEs employ single-user detection. However if UEs resort to the intelligent interference-aware detection, the multi-user MIMO mode shows enhanced performance over other transmission modes in LTE. No degradation of LTE multi-user MIMO mode is observed

In the second part of simulations, we look at the sensitivity of the proposed receiver structure to the knowledge of the constellation of co-scheduled UE for the multi-user MIMO mode in LTE. The simulation settings are same as of the first part except that we consider the case when UE has no knowledge of the constellation of co-scheduled UE. The UE assumes this unknown interference constellation to be QPSK, QAM16 or QAM64 and the results for these different assumptions are shown in Fig. 7. Results show that there is negligible degradation in the performance of the proposed receiver if the interfering constellation is assumed to be QAM16 or QAM64. However, there is significant degradation if the interference is assumed to be QPSK when it actually comes from QAM64. It indicates that assuming interference to be from a higher order modulation amongst the possible modulation alphabets leads to the best compromise as this assumption includes the lower modulation orders as special cases (with proper scaling). However the converse is not true, i.e. assuming interference from lower modulation order cannot include higher order modulations. As LTE and LTE-Advanced restrict the transmission to three modulations ( QPSK, QAM16 and QAM64 ), assuming interference to be QAM64 (or even QAM16) leads to better performance. If the interference constellation also includes QAM256, then assuming interference to be QAM256 (or even QAM64) would lead to better results. These results have not been shown here as LTE and LTE-Advanced do not support QAM256 modulation. The proposed receiver structure, therefore, can still exploit the discrete nature of the interference even if it does not know

at higher spectral efficiencies once UEs have receive diversity (dual antennas).

assumed to be

Interference (x2) Interference (x2)

**Figure 8.** Proposed precoder codebook. Downlink channel with dual-antenna eNodeB and two single-antenna UEs. The figure illustrates the performance for the sum rate of 4bps/Hz. SNR is the transmit SNR while sum rate is same for single-user and multi-user MIMO, i.e. if two UEs are served with QPSK, rate 1/2, in multi-user mode, then one UE is served with QAM16, rate 1/2, in the single-user mode. SU MIMO and MU MIMO indicate single-user and multi-user MIMO.

its modulation order. As the complexity of this receiver structure is independent of the constellation of interference, the assumption of higher order modulation does not add to the complexity of detection.

In the third set of simulations, we look at the diversity order of the single-user MIMO and multi-user MIMO schemes in LTE. The system settings are same as in the first part but now we consider slow fading environment, i.e. the channel remains constant for the duration of one codeword. Fig. 8 shows significant improvement in the performance of the multi-user MIMO mode when additional codebook entries are employed to increase the levels of transmission as compared to the case of increasing the angular resolution of precoders. However creating two levels of transmission leads to significant improvement as the performance moves closer to the upper bound. This hypothetical upper bound is the performance curve for MF precoder in multi-user MIMO mode without any interference, i.e. the eNodeB serves two UEs with their respective MF based precoders and the two UEs do not see any interference. The change of the slope of FER curve with increased levels of transmission indicates improved diversity as compared to the case of increased angular resolution. On the other hand, little gain is observed in the single-user mode (LTE transmission mode 6) with additional codebook entries which is expected as the standard LTE precoders have been optimized for the single-user transmission [22]. For comparison purposes, we have also considered the case of random codebooks. The main advantage of random codebooks is that they indicate some sort of performance lower bound and with any intelligent feedback design, system is bound to perform better.

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(49)

**Appendix A**

form as

H *<sup>X</sup>*1|*Y*1, **<sup>h</sup>**† 1, **P** = ∑*x*1 *y*1 **h**† <sup>1</sup>**p**<sup>1</sup> **h**† <sup>1</sup>**p**<sup>2</sup> *p x*1, *y*1, **h**†

= ∑*x*1 ∑*x*2 *y*1 **h**† <sup>1</sup>**p**<sup>1</sup> **h**† <sup>1</sup>**p**<sup>2</sup> *p* 

where *x* ′

*<sup>X</sup>*1|*Y*1, **<sup>h</sup>**†

H  <sup>1</sup> <sup>∈</sup> *<sup>χ</sup>*<sup>1</sup> and *<sup>x</sup>*

1, **P** <sup>=</sup> <sup>1</sup> *M*1*M*<sup>2</sup>

where *<sup>M</sup>*<sup>2</sup> = |*χ*2|, **<sup>x</sup>** = [*x*<sup>1</sup> *<sup>x</sup>*2]

for UE-1 can be rewritten as

*I* 

**Mutual information for finite alphabets**

*x*1, *x*2, *y*1, **h**†

source of randomness, i.e. noise. So (50) can be extended as

∑**x**

∑**x**

*Ez*<sup>1</sup> log

*Ez*<sup>1</sup> log

*<sup>T</sup>*, **x** ′ = *x* ′ 1 *x* ′ 2 *T*

<sup>∑</sup>**x**′ exp

<sup>∑</sup>**x**′ exp

∑*x* ′ 2 exp − 1 *N*<sup>0</sup> **h**† 1**P x** − **x** ′ 2 + *z*<sup>1</sup> 2

<sup>=</sup> log *<sup>M</sup>*<sup>1</sup> <sup>−</sup> <sup>1</sup>

with *Nz* realizations of noise and *Nh*<sup>1</sup> realizations of the channel **<sup>h</sup>**†

matrix depends on the channel. So we can rewrite (52) as (53)

− 1 *N*<sup>0</sup> **h**†

∑*x* ′ 2 exp − 1 *N*<sup>0</sup> **h**†

> − 1 *N*<sup>0</sup> **h**† 1**P x** − **x** ′ +*z*<sup>1</sup> 2

and **x** ′ <sup>2</sup> = *x*<sup>1</sup> *x* ′ 2 *T*

*Ez*<sup>1</sup> log

∑**x**′ *p <sup>y</sup>*1|**<sup>x</sup>** ′ , **h**† 1, **P** 

∑*x* ′ 2 *p <sup>y</sup>*1|**<sup>x</sup>** ′ <sup>2</sup>, **<sup>h</sup>**† 1, **P**

*<sup>M</sup>*1*M*<sup>2</sup> <sup>∑</sup>**<sup>x</sup>**

The above quantities can be easily approximated using sampling (Monte-Carlo) methods

′

<sup>=</sup> <sup>1</sup> *M*1*M*<sup>2</sup>

*<sup>Y</sup>*1; *<sup>X</sup>*1|**h**†

1, **P**  <sup>1</sup>**p**1, **<sup>h</sup>**† <sup>1</sup>**p**<sup>2</sup> log ∑*x* ′ 1 ∑*x* ′ 2 *p <sup>y</sup>*1|*<sup>x</sup>* ′ <sup>1</sup>, *x* ′ <sup>2</sup>, **<sup>h</sup>**† <sup>1</sup>**p**1, **<sup>h</sup>**† <sup>1</sup>**p**<sup>2</sup> 

*I Y*1; *X*<sup>1</sup> **h**† 1, **P** = H *X*1 **h**† 1, **P** − H *X*1 *<sup>Y</sup>*1, **<sup>h</sup>**† 1, **P** 

The mutual information for UE-1 for finite size QAM constellation with |*χ*1| = *<sup>M</sup>*<sup>1</sup> takes the

<sup>=</sup> log *<sup>M</sup>*<sup>1</sup> − H

where H (.) = −*E* log *p* (.) is the entropy function. The second term of (49) is given as

<sup>1</sup>**p**1, **<sup>h</sup>**† <sup>1</sup>**p**<sup>2</sup> 

> ∑*x* ′ 2 *p <sup>y</sup>*1|*x*1, *<sup>x</sup>* ′ <sup>2</sup>, **<sup>h</sup>**† <sup>1</sup>**p**1, **<sup>h</sup>**† <sup>1</sup>**p**<sup>2</sup>

*X*1 *<sup>Y</sup>*1, **<sup>h</sup>**† 1, **P** 

log <sup>1</sup> *p <sup>x</sup>*1|*y*1, **<sup>h</sup>**†

Multi-user MIMO in LTE and LTE-Advanced - Receiver Structure and Precoding Design

<sup>2</sup> <sup>∈</sup> *<sup>χ</sup>*2. Conditioned on the channel and the precoder, there is one

1**p**1*x*1+**h**†

<sup>1</sup>**p**1, **<sup>h</sup>**† <sup>1</sup>**p**<sup>2</sup>

1**p**2*x*2+*z*1−**h**†

<sup>1</sup>**p**2*x*<sup>2</sup> <sup>+</sup> *<sup>z</sup>*<sup>1</sup> <sup>−</sup> **<sup>h</sup>**†

*dy*1*d*(**h**†

*dy*1*d*(**h**†

<sup>1</sup>**p**1*x* ′ 1−**h**† <sup>1</sup>**p**2*x* ′ 2 2 

<sup>1</sup>**p**2*x* ′ 2 2 

(51)

. The mutual information

(52)

<sup>1</sup> where the precoding

1**p**1)*d*(**h**†

1**p**1)*d*(**h**†

<sup>1</sup>**p**2)

<sup>1</sup>**p**2)

(50)

**Figure 9.** Performance of the proposed precoder codebook in 3GPP LTE channel models [18]. Black continuous lines show the Extended Pedestrian A model (EPA), blue dashed lines show Extended Vehicular A model (EVA), while red dotted lines show Extended Typical Urban model (ETU).

Fig. 9 shows the case where we have considered 3GPP LTE channel model introduced in [18] for three representative scenarios, i.e. pedestrian, vehicular and typical urban scenario. The transmission chain is dominantly LTE compliant with 15 KHz subcarrier-spacing and 20 MHz system bandwidth. The results confirm the earlier findings of the improved performance of proposed codebook design (enhanced levels of transmission) for multi-user transmission mode. Pedestrian channel offers less diversity in the channel as compared to the vehicular channel, so the performance of LTE precoders for multi-user MIMO in severely degraded in the former case. However as the proposed precoder design recovers the lost order of diversity, there is an improvement of 6dB at the target FER of 10<sup>−</sup>1.
