**4. Information theoretic perspective**

10 Recent Trends in Multiuser MIMO Communications

QPSK

Interference-aware receiver (Equal energy alphabets) 8*nr* + 2

Interference-aware receiver (Non Equal energy alphabets) 12*nr* + 4*M* + <sup>7</sup>

SNR (dB) @ FER=10−2

**Table 1.** Comparison of receivers complexity

<sup>101</sup> <sup>102</sup> <sup>103</sup> <sup>104</sup> <sup>0</sup>

Number of real−valued multiplications for LLR per RE

Receiver Real Multiplications Real Additions

Max-log MAP receiver 2*M*2*nr* + 8*Mnr* 6*M*2*nr* + 4*Mnr* + log(*M*) − *M*<sup>2</sup>

√

2 √

*M* + 2*M* 8*nr* + 10*M* + log(*M*) − 4

*M* 12*nr* + 18*M* + log(*M*) − 6

**Figure 2.** eNodeB has two antennas. Continuous lines indicate the case of single-antenna UEs while dashed lines indicate dual-antenna UEs. 3GPP LTE rate 1/2 punctured turbo code is used. Simulation settings are same as in the first part of Sec.7.

Single-user receiver (Equal energy alphabets) 10*nr* + 6 10*nr* − 3 Single-user receiver (Non Equal energy alphabets) <sup>10</sup>*nr* <sup>+</sup> <sup>3</sup>*<sup>M</sup>* <sup>+</sup> <sup>√</sup>*M*/2 <sup>+</sup> <sup>4</sup> <sup>10</sup>*nr* <sup>+</sup> <sup>3</sup>*<sup>M</sup>* <sup>+</sup> log(*M*) <sup>−</sup> <sup>3</sup>

complexity in all receiver structures. Moreover UEs can also directly estimate their effective channels if the pilot signals are also precoded. The comparison shows that the complexity of the interference-aware receiver is of the same order as of single-user receiver while it is far less than the complexity of the max log MAP receiver. Fig. 2 further shows the performance-complexity trade off of different receivers for multi-user MIMO mode in LTE. The performance of the receivers is measured in terms of the SNR at the frame error rate (FER) of 10−<sup>2</sup> whereas the complexity is determined from Table.1. It shows that the performance of the single-user receiver is severely degraded as compared to that of the interference-aware receiver. In most cases, the single-user receiver fails to achieve the requisite FER in the considered SNR range. On the other hand, interference-aware receiver achieves same performance as max log MAP receiver but with much reduced complexity. The interference-aware receiver is therefore not only characterized by low complexity but it also resorts to intelligent detection by exploiting the structure of residual interference. Moreover, this receiver structure being based on the MF outputs and devoid of any division operation can be easily implemented in the existing hardware. However the proposed receiver needs both the channel knowledge and the constellation of interference (co-scheduled UE). As the UE already knows its own channel from the eNodeB and the requested precoder, it can determine the effective channel of the interference based on the geometric scheduling algorithm, i.e. the precoder of the co-scheduled UE is 180◦ out of phase of its own precoder. Consequently there is no additional complexity in utilizing this receiver

QAM16

 Single−user Rx Interference−Aware Rx Max−log MAP Rx

QAM64

Sum rate of the downlink channel is given as

$$\mathcal{L} = I\left(Y\_1; \mathbf{X}\_1|\mathbf{h}\_1^\dagger, \mathbf{P}\right) + I\left(Y\_2; \mathbf{X}\_2|\mathbf{h}\_2^\dagger, \mathbf{P}\right) \tag{19}$$

where **P** = [**p**<sup>1</sup> **p**2] is the precoder matrix, *I* � *Y*1; *X*<sup>1</sup> � �**h**† 1, **P** � is the mutual information of UE-1 once it sees interference from UE-2 and *I* � *<sup>Y</sup>*2; *<sup>X</sup>*2|**h**† 2, **P** � is the mutual information of UE-2 once it sees interference from UE-1. Note that *Y*<sup>1</sup> is the received symbol at UE-1 while *X*<sup>1</sup> is the symbol transmitted by the eNodeB to UE-1. Note that interference is present in the statistics of *Y*<sup>1</sup> and *Y*2. No sophisticated power allocation is employed to the two streams as the downlink control information (DCI) in the multi-user mode in LTE includes only 1-bit power offset information, indicating whether a 3 dB transmit power reduction should be assumed or not. We therefore consider equal-power distribution between the two streams. For the calculation of mutual information, we deviate from the unrealistic Gaussian assumption for the alphabets and consider them from discrete constellations. The derivations of the mutual information expressions for the case of finite alphabets have been relegated to Appendix-A for simplicity and lucidity.

We focus on the LTE precoders but to analyze the degradation caused by the low-level quantization and the characteristic of EGT of these precoders, we also consider some other transmission strategies. Firstly we consider unquantized MF precoder [27] which is given as

$$\mathbf{p} = \frac{1}{\sqrt{|h\_{11}|^2 + |h\_{21}|^2}} \begin{bmatrix} h\_{11} \\ h\_{21} \end{bmatrix} \tag{20}$$

For EGT, the unquantized MF precoder is given as

$$\mathbf{p} = \frac{1}{\sqrt{2}} \begin{bmatrix} 1 \\ h\_{11}^\* h\_{21} / \left| h\_{11} \right| \left| h\_{21} \right| \end{bmatrix} \tag{21}$$

To be fair in comparison with the geometric scheduling algorithm for multi-user MIMO in LTE, we introduce a geometric scheduling algorithm for unquantized precoders. We divide the spatial space into 4 quadrants according to the spatial angle between **h**† <sup>1</sup> and **<sup>h</sup>**† <sup>2</sup> which is given as

$$\phi = \cos^{-1}\left(\frac{\left|\mathbf{h}\_1^\dagger \mathbf{h}\_2\right|}{||\mathbf{h}\_1|| \, ||\mathbf{h}\_2||}\right) \qquad 0^\diamond \le \phi \le 90^\diamond \tag{22}$$

73

http://dx.doi.org/10.5772/57134

rate is not adapted with the SNR in these simulations, i.e. the constellation size is fixed to QAM64 and is not increased with the increase in the SNR. At high SNR, the rate of each UE gets saturated to its constellation size (6 bits for QAM64) if the UE resorts to intelligent interference-aware detection. However the approach to this saturation point (slope of the

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

Another interesting result is the effect of the two characteristics of LTE precoders, i.e. low-resolution and EGT. There is a slight improvement in the sum rate at medium SNR when the restriction of low-resolution (LTE quantized precoders) is relaxed, i.e. eNodeB employs MF EGT precoders however there is a significant improvement in the sum rate when the restriction of EGT is eliminated, i.e the eNodeB employs MF precoders. This shows that the loss in spectral efficiency due to the employment of LTE precoders is mainly attributed to

We now focus on the EGT characteristic of the LTE precoders and carry out the performance analysis of the EGT in single-user and multi-user MIMO systems. We restrict to the case of

> 1 2

<sup>1</sup> *<sup>h</sup>*21,*kh*<sup>∗</sup>

1,*k***p**1,*kx*1,*<sup>k</sup>* + *z*1,*<sup>k</sup>* (23)

*T*

. So the received signal

*z*1,*<sup>k</sup>* (24)

′ can be written as

(25)

2 

11,*k* |*h*21,*<sup>k</sup>* ||*h*11,*<sup>k</sup>* |

> *h*11,*<sup>k</sup> <sup>h</sup>*11,*<sup>k</sup>*

rate curve) depends on the quantization of channel information.

the EGT rather than their low resolution (quantization).

single-antenna UEs while the eNodeB has two antennas.

For EGT, the precoder vector is given by **<sup>p</sup>**1,*<sup>k</sup>* = <sup>√</sup>

*yN* 1,*<sup>k</sup>* <sup>=</sup> <sup>1</sup> √2 *<sup>h</sup>*11,*<sup>k</sup>* <sup>+</sup> *<sup>h</sup>*21,*<sup>k</sup> x*1,*<sup>k</sup>* +

The conditional PEP i.e *<sup>P</sup>* (**c**<sup>1</sup> <sup>→</sup> **<sup>c</sup>**ˆ1|**h**1) is given as

<sup>|</sup>*h*11,*<sup>k</sup>* <sup>|</sup> is given by

≈ min *x*1∈*χ<sup>i</sup>* 1,*c k* ′  1 *N*0 *yN* 1,*<sup>k</sup>* <sup>−</sup> <sup>1</sup> √2 *<sup>h</sup>*11,*<sup>k</sup>* <sup>+</sup> *<sup>h</sup>*21,*<sup>k</sup> x*1 

For the single-user case, the received signal at the *k*-th RE is given by

*<sup>y</sup>*1,*<sup>k</sup>* = **<sup>h</sup>**†

*y*1,*k*. The max log MAP bit metric [4] for the bit *ck*

**5. Performance analysis**

**5.1. Single-user MIMO**

after normalization by *<sup>h</sup>*11,*<sup>k</sup>*

1,*<sup>k</sup>* <sup>=</sup> *<sup>h</sup>*11,*<sup>k</sup>* |*h*11,*<sup>k</sup>* |

> Λ*i* 1 *yk*, *ck* ′

where *y<sup>N</sup>*

**Figure 3.** Sum rates of different transmission schemes for the downlink channel with dual-antenna eNodeB and 2 single-antenna UEs. 'No Scheduling - SU Rx' indicates the case once the eNodeB uses the LTE precoders without employing the geometric scheduling strategy. In all other cases, the eNodeB employs the geometric scheduling strategy along with the LTE precoders, MF EGT precoders and MF precoders. SU Rx indicates the cases when UEs employ single-user detection while IA Rx indicates the cases when UEs resort to the intelligent detection by employing the low-complexity interference-aware receivers.

The geometric scheduling algorithm ensures that the eNodeB chooses the second UE to be served on the same RE as the first UE such that their channels **h**† <sup>1</sup> and **<sup>h</sup>**† <sup>2</sup> lie in the opposite quadrants.

Fig. 3 shows the sum rates of a broadcast channel with the dual-antenna eNodeB and 2 single-antenna UEs for QAM64 alphabets. SNR is the transmit SNR, i.e. *<sup>σ</sup>*<sup>2</sup> <sup>1</sup> **<sup>p</sup>**<sup>1</sup><sup>2</sup> +*σ*<sup>2</sup> <sup>2</sup> **<sup>p</sup>**<sup>2</sup><sup>2</sup> *N*0 whereas the two UEs have equal power distribution, i.e. *σ*<sup>2</sup> <sup>1</sup> <sup>=</sup> *<sup>σ</sup>*<sup>2</sup> <sup>2</sup> . MF and MF EGT precoders are the unquantized precoders given in (20) and (21) respectively while LTE precoders are the quantized precoders given in (1). The sum rates of unquantized precoders along with those of LTE quantized precoders are shown for the case of single-user receivers and for the case of low-complexity interference-aware receivers. The results show that under the proposed transmission strategy, the sum rate can be significantly improved (unbounded in SNR) if the low-complexity interference-aware receivers are used as compared to the case when the UEs resort to sub-optimal single-user detection where rates are bounded (in SNR). The behavior of single-user detection is attributed to the fact that this detection strategy considers interference as noise so the SINR is low once no geometric scheduling has been employed by the eNodeB while the SINR improves due to the reduction of interference once geometric scheduling is employed. However the rates remain bounded in the SNR if the UEs resort to the single-user detection which is due to the fact that increasing the SNR (transmit SNR) also increases the interference strength thereby bounding the SINR at high values of the transmit SNR. On the other hand, there is significant improvement in the sum rate once UEs resort to intelligent detection by employing the low-complexity interference-aware receivers. In this case, the sum rate is unbounded if the rate (constellation size) of each UE is adapted with the SNR. Note that the quantized CSIT (LTE precoders) appears to have no effect at high SNR once UEs resort to intelligent interference-aware detection. This behavior is because the rate is not adapted with the SNR in these simulations, i.e. the constellation size is fixed to QAM64 and is not increased with the increase in the SNR. At high SNR, the rate of each UE gets saturated to its constellation size (6 bits for QAM64) if the UE resorts to intelligent interference-aware detection. However the approach to this saturation point (slope of the rate curve) depends on the quantization of channel information.

Another interesting result is the effect of the two characteristics of LTE precoders, i.e. low-resolution and EGT. There is a slight improvement in the sum rate at medium SNR when the restriction of low-resolution (LTE quantized precoders) is relaxed, i.e. eNodeB employs MF EGT precoders however there is a significant improvement in the sum rate when the restriction of EGT is eliminated, i.e the eNodeB employs MF precoders. This shows that the loss in spectral efficiency due to the employment of LTE precoders is mainly attributed to the EGT rather than their low resolution (quantization).
