**2.1. LTE - A brief overview**

In 3GPP LTE, a 2 × 2 configuration for MIMO is assumed as the baseline configuration, however configurations with four transmit or receive antennas are also foreseen and reflected in the specifications [17]. LTE restricts the transmission of maximum of two codewords in the downlink which can be mapped onto different layers where one codeword represents an output from the channel encoder. Number of layers available for the transmission is equal to the rank of the channel matrix (maximum 4). In this chapter, we restrict ourselves to the baseline configuration with the eNodeB (LTE notation for the base station) equipped with 2 antennas while we consider single and dual antenna user equipments (UEs). Physical layer technology employed for the downlink in LTE is OFDMA combined with bit interleaved coded modulation (BICM) [4]. Several different transmission bandwidths are possible, ranging from 1.08 MHz to 19.8 MHz with the constraint of being a multiple of 180 kHz. Resource Blocks (RBs) are defined as groups of 12 consecutive resource elements (REs - LTE notation for the subcarriers) with a bandwidth of 180 kHz thereby leading to the constant RE spacing of 15 kHz. Approximately 4 RBs form a subband and the feedback is generally done on subband basis. Seven operation modes are specified in the downlink of LTE, however, we shall focus on the following four modes:

2 Recent Trends in Multiuser MIMO Communications

detection.

**2. LTE system model**

**2.1. LTE - A brief overview**

assumption that users employ simple single-user receivers.

about the feasibility of this mode of transmission [22, page 244]. This strong perception is based on the fact that users can not cooperate in multi-user scenario and further on the

In this chapter, we focus on a new paradigm of multi-user MIMO where users exploit the discrete structure of interference, instead of ignoring it or assuming it to be Gaussian and merging it in noise. We compare the two strategies of interference exploitation and interference cancellation in multi-user scenario. For the former, we look at low complexity multi-user detectors. Though multi-user detection has been extensively investigated in the literature for the uplink (multiple access channel), its related complexity has so far prohibited its employment in the downlink (broadcast channel). For the multiple access channel, several multi-user detection techniques exist in the literature starting from the optimal multi-user receivers [25] to their near-optimal reduced complexity counterparts (sphere decoders [3]). The complexity associated with these techniques led to the investigation of low-complexity solutions as sub-optimal linear multi-user receivers [20], iterative multi-user receivers [26, 28], and decision-feedback receivers [5, 12]. Since in practice, most wireless systems employ error control coding combined with the interleaving , recent work in this area has addressed multi-user detection for coded systems based on soft decisions [13, 23]. We focus in this chapter on a low-complexity interference-aware receiver structure which not only reduces one complex dimension of the system but is also characterized by exploiting the interference structure in the detection process. Considering this receiver structure, we investigate the effectiveness of the low-resolution LTE precoders for the multi-user MIMO mode and show that multi-user MIMO can bring significant gains in future wireless systems if the users resort to intelligent interference-aware detection as compared to the sub-optimal single-user

In an effort of bridging the gap between the theoretical and practical gains of multi-user MIMO, this chapter investigates the structure of LTE codebook by analyzing the pairwise error probability (PEP) expressions. The analysis shows that LTE precoders suffer from the loss of diversity when being employed in multi-user MIMO transmission mode but no such loss is observed in single-user MIMO mode. Based on this analysis, a new codebook design is proposed and it is shown that with a nominal increase in the feedback, the performance of multi-user MIMO improves to within 1.5 dB from the lower bound (single-user MIMO). To verify the proposed codebook design, widely studied Gaussian random codebooks [11], [2] are considered for comparison. Note that though the overall discussion in this chapter has generally been on LTE and LTE-Advanced framework, the proposed feedback and precoding design can serve as a guideline for multi-user MIMO modes in any other modern wireless

In 3GPP LTE, a 2 × 2 configuration for MIMO is assumed as the baseline configuration, however configurations with four transmit or receive antennas are also foreseen and reflected in the specifications [17]. LTE restricts the transmission of maximum of two codewords in the downlink which can be mapped onto different layers where one codeword represents an output from the channel encoder. Number of layers available for the transmission is equal

system which employs limited feedback schemes for CSIT acquisition.


In the case of transmit diversity and closed-loop precoding, one codeword (data stream) is transmitted to each UE using Alamouti code in the former case and LTE precoders in the latter case. Time-frequency resources are orthogonal to the different UEs in these modes thereby avoiding interference in the system. However, in the multi-user MIMO mode, parallel codewords are transmitted simultaneously, one for each UE, sharing the same time-frequency resources. Note that LTE restricts the transmission of one codeword to each UE in the multi-user MIMO mode.

For closed-loop transmission modes (mode 4, 5 and 6), precoding mechanisms are employed at the transmit side with the objective of maximizing throughput. The precoding is selected and applied by the eNodeB to the data transmission to a target UE based on the channel feedback received from that UE. This feedback includes a precoding matrix indicator (PMI), a channel rank indicator (RI) and a channel quality indicator (CQI). PMI is an index in the codebook for the preferred precoder to be used by the eNodeB. The granularity for the computation and signaling of the precoding index can range from a couple of RBs to the full bandwidth. For transmission mode 5, the eNodeB selects the precoding matrix to induce high orthogonality between the codewords so that the interference between UEs is minimized. In transmission modes 4 and 6, the eNodeB selects the precoding vector/matrix such that codewords are transmitted to the corresponding UEs with maximum throughput.

In order to avoid excessive downlink signaling, transmission mode for each UE is configured semi-statically via higher layer signaling, i.e. it is not allowed for a UE to be scheduled in one subframe in the multi-user MIMO mode and in the next subframe in the single-user MIMO mode. For transmission modes 4, 5 and 6, low-resolution precoders are employed which are based on the principle of EGT. For the case of eNodeB with two antennas, LTE

**Figure 1.** eNodeB in multi-user MIMO mode. *π*<sup>1</sup> denotes the random interleaver, *µ*<sup>1</sup> the labeling map and *χ*<sup>1</sup> the signal set for the codeword of UE-1. **P** indicates the precoding matrix.

proposes the use of following four precoders for transmission mode 5 and 6:

$$\mathbf{p} = \left\{ \frac{1}{\sqrt{4}} \begin{bmatrix} 1 \\ 1 \end{bmatrix}, \frac{1}{\sqrt{4}} \begin{bmatrix} 1 \\ -1 \end{bmatrix}, \frac{1}{\sqrt{4}} \begin{bmatrix} 1 \\ j \end{bmatrix}, \frac{1}{\sqrt{4}} \begin{bmatrix} 1 \\ -j \end{bmatrix} \right\} \tag{1}$$

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65

1,*k***p**2,*kx*2,*<sup>k</sup>* + *z*1,*<sup>k</sup>* (3)

*<sup>n</sup>*,*<sup>k</sup>* <sup>∈</sup> **<sup>C</sup>**1×<sup>2</sup> symbolizes the

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

+ **z**1,*<sup>k</sup>* (4)

*<sup>k</sup>***p***kxk* + *zk* (5)

<sup>1</sup>**p**2*x*<sup>2</sup> + *z*<sup>1</sup> (7)

**y***<sup>k</sup>* = **H***k***p***kxk* + **z***<sup>k</sup>* (6)

<sup>2</sup> . **<sup>h</sup>**†

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

channels. Cascading IFFT at the eNodeB and FFT at the UE with the cyclic prefix extension,

where *y*1,*<sup>k</sup>* is the received symbol at UE-1 and *z*1,*<sup>k</sup>* is zero mean circularly symmetric complex white Gaussian noise of variance *N*0. *x*1,*<sup>k</sup>* is the complex symbol for UE-1 with the variance

spatially uncorrelated flat Rayleigh fading MISO channel from eNodeB to the *n*-th UE (*n* = 1, 2) at the *k*-th RE. Its elements can therefore be modeled as independent and identically distributed (iid) zero mean circularly symmetric complex Gaussian random variables with a variance of 0.5 per dimension. Note that **<sup>C</sup>**1×<sup>2</sup> denotes a 2-dimensional complex space. **<sup>p</sup>***n*,*<sup>k</sup>* denotes the precoding vector for the *n*-th UE at the *k*-th RE and is given by (1). For the dual

**p**1,*kx*1,*<sup>k</sup>* + **p**2,*kx*2,*<sup>k</sup>*

where **<sup>y</sup>**1,*k*, **<sup>z</sup>**1,*<sup>k</sup>* <sup>∈</sup> **<sup>C</sup>**2×<sup>1</sup> are the vectors of the received symbols and circularly symmetric complex white Gaussian noise of double-sided power spectral density *N*0/2 at the 2 receive antennas of UE-1 respectively. **<sup>H</sup>**1,*<sup>k</sup>* <sup>∈</sup> **<sup>C</sup>**2×<sup>2</sup> is the channel matrix from eNodeB to UE-1.

In transmission mode 6, only one UE will be served in one time-frequency resource.

where **p***<sup>k</sup>* is given by (1). For the dual antenna UEs, the system equation for mode 6 is

We now look at the effectiveness of the low-resolution LTE precoders for the multi-user MIMO mode. We first consider a geometric scheduling strategy [8] based on the selection of

As the processing at the UE is performed on a RE basis for each received OFDM symbol, the dependency on RE index can be ignored for notational convenience. The system equation

<sup>1</sup>**p**1*x*<sup>1</sup> <sup>+</sup> **<sup>h</sup>**†

for the case of single-antenna UEs for the multi-user mode is

*y*<sup>1</sup> = **h**†

the transmission at the *k*-th RE for UE-1 in transmission mode 5 can be expressed as

1,*k***p**1,*kx*1,*<sup>k</sup>* <sup>+</sup> **<sup>h</sup>**†

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

<sup>1</sup> and *<sup>x</sup>*2,*<sup>k</sup>* is the complex symbol for UE-2 with the variance *<sup>σ</sup>*<sup>2</sup>

antenna UEs, the system equation for transmission mode 5 is modified as

Therefore the system equation for single-antenna UEs at the *k*-th RE is given as

*yk* = **<sup>h</sup>**†

**y**1,*<sup>k</sup>* = **H**1,*<sup>k</sup>*

*σ*2

modified as

**3. Multi-user MIMO mode**

UEs with orthogonal precoders.

**3.1. Scheduling strategy**

The number of precoders increases to sixteen in the case of four transmit antennas however in this chapter we restrict to the case of two transmit antennas. For transmission mode 4, LTE proposes the use of following two precoder matrices on subband basis.

$$\mathbf{P} = \left\{ \frac{1}{\sqrt{4}} \begin{bmatrix} 1 & 1\\ 1 & -1 \end{bmatrix}, \frac{1}{\sqrt{4}} \begin{bmatrix} 1 & 1\\ j & -j \end{bmatrix} \right\} \tag{2}$$

Note that there is a possibility of swapping the columns in **P** but the swap must occur over the entire band.

#### **2.2. System model**

We first consider the system model for transmission mode 5, i.e. the multi-user MIMO mode in which the eNodeB transmits one codeword each to two single-antenna UEs using the same time-frequency resources. Transmitter block diagram is shown in Fig. 1. During the transmission for UE-1, the code sequence **<sup>c</sup>**<sup>1</sup> is interleaved by *<sup>π</sup>*<sup>1</sup> and is then mapped onto the signal sequence **<sup>x</sup>**1. *<sup>x</sup>*<sup>1</sup> is the symbol of **<sup>x</sup>**<sup>1</sup> over a signal set *<sup>χ</sup>*<sup>1</sup> ⊆ C with a Gray labeling map where <sup>|</sup>*χ*1<sup>|</sup> <sup>=</sup> *<sup>M</sup>*<sup>1</sup> and *<sup>x</sup>*<sup>2</sup> is the symbol of **<sup>x</sup>**<sup>2</sup> over signal set *<sup>χ</sup>*<sup>2</sup> where <sup>|</sup>*χ*2<sup>|</sup> <sup>=</sup> *<sup>M</sup>*2. The bit interleaver for UE-1 can be modeled as *π*<sup>1</sup> : *k* ′ → (*k*, *i*) where *k* ′ denotes the original ordering of the coded bits *ck* ′ , *k* denotes the RE of the symbol *x*1,*<sup>k</sup>* and *i* indicates the position of the bit *ck* ′ in the symbol *x*1,*k*. Note that each RE corresponds to a symbol from a constellation map *χ*<sup>1</sup> for UE-1 and *χ*<sup>2</sup> for UE-2. Selection of the normal or extended cyclic prefix (CP) for each OFDM symbol converts the downlink frequency-selective channel into parallel flat fading channels. Cascading IFFT at the eNodeB and FFT at the UE with the cyclic prefix extension, the transmission at the *k*-th RE for UE-1 in transmission mode 5 can be expressed as

$$\mathbf{y}\_{1,k} = \mathbf{h}\_{1,k}^{\dagger} \mathbf{p}\_{1,k} \mathbf{x}\_{1,k} + \mathbf{h}\_{1,k}^{\dagger} \mathbf{p}\_{2,k} \mathbf{x}\_{2,k} + z\_{1,k} \tag{3}$$

where *y*1,*<sup>k</sup>* is the received symbol at UE-1 and *z*1,*<sup>k</sup>* is zero mean circularly symmetric complex white Gaussian noise of variance *N*0. *x*1,*<sup>k</sup>* is the complex symbol for UE-1 with the variance *σ*2 <sup>1</sup> and *<sup>x</sup>*2,*<sup>k</sup>* is the complex symbol for UE-2 with the variance *<sup>σ</sup>*<sup>2</sup> <sup>2</sup> . **<sup>h</sup>**† *<sup>n</sup>*,*<sup>k</sup>* <sup>∈</sup> **<sup>C</sup>**1×<sup>2</sup> symbolizes the spatially uncorrelated flat Rayleigh fading MISO channel from eNodeB to the *n*-th UE (*n* = 1, 2) at the *k*-th RE. Its elements can therefore be modeled as independent and identically distributed (iid) zero mean circularly symmetric complex Gaussian random variables with a variance of 0.5 per dimension. Note that **<sup>C</sup>**1×<sup>2</sup> denotes a 2-dimensional complex space. **<sup>p</sup>***n*,*<sup>k</sup>* denotes the precoding vector for the *n*-th UE at the *k*-th RE and is given by (1). For the dual antenna UEs, the system equation for transmission mode 5 is modified as

$$\mathbf{y}\_{1,k} = \mathbf{H}\_{1,k} \left[ \mathbf{p}\_{1,k} \mathbf{x}\_{1,k} + \mathbf{p}\_{2,k} \mathbf{x}\_{2,k} \right] + \mathbf{z}\_{1,k} \tag{4}$$

where **<sup>y</sup>**1,*k*, **<sup>z</sup>**1,*<sup>k</sup>* <sup>∈</sup> **<sup>C</sup>**2×<sup>1</sup> are the vectors of the received symbols and circularly symmetric complex white Gaussian noise of double-sided power spectral density *N*0/2 at the 2 receive antennas of UE-1 respectively. **<sup>H</sup>**1,*<sup>k</sup>* <sup>∈</sup> **<sup>C</sup>**2×<sup>2</sup> is the channel matrix from eNodeB to UE-1.

In transmission mode 6, only one UE will be served in one time-frequency resource. Therefore the system equation for single-antenna UEs at the *k*-th RE is given as

$$y\_k = \mathbf{h}\_k^\dagger \mathbf{p}\_k x\_k + z\_k \tag{5}$$

where **p***<sup>k</sup>* is given by (1). For the dual antenna UEs, the system equation for mode 6 is modified as

$$\mathbf{y}\_k = \mathbf{H}\_k \mathbf{p}\_k \mathbf{x}\_k + \mathbf{z}\_k \tag{6}$$

#### **3. Multi-user MIMO mode**

4 Recent Trends in Multiuser MIMO Communications

Encoder-1

Encoder-2 Turbo

for the codeword of UE-1. **P** indicates the precoding matrix.

**p** =

interleaver for UE-1 can be modeled as *π*<sup>1</sup> : *k*

 1 √4 1 1 , 1 √4 1 −1 , 1 √4 1 *j* , 1 √4 1 −*j* 

**P** =

Turbo

π1

c1

c2

µ1, χ<sup>1</sup>

x1

x2

P

′

denotes the original ordering

OFDM

insertion) (IFFT + CP

1

2

(1)

(2)

OFDM (IFFT + CP

insertion)

µ2, χ<sup>2</sup>

**Figure 1.** eNodeB in multi-user MIMO mode. *π*<sup>1</sup> denotes the random interleaver, *µ*<sup>1</sup> the labeling map and *χ*<sup>1</sup> the signal set

The number of precoders increases to sixteen in the case of four transmit antennas however in this chapter we restrict to the case of two transmit antennas. For transmission mode 4,

Note that there is a possibility of swapping the columns in **P** but the swap must occur over

We first consider the system model for transmission mode 5, i.e. the multi-user MIMO mode in which the eNodeB transmits one codeword each to two single-antenna UEs using the same time-frequency resources. Transmitter block diagram is shown in Fig. 1. During the transmission for UE-1, the code sequence **<sup>c</sup>**<sup>1</sup> is interleaved by *<sup>π</sup>*<sup>1</sup> and is then mapped onto the signal sequence **<sup>x</sup>**1. *<sup>x</sup>*<sup>1</sup> is the symbol of **<sup>x</sup>**<sup>1</sup> over a signal set *<sup>χ</sup>*<sup>1</sup> ⊆ C with a Gray labeling map where <sup>|</sup>*χ*1<sup>|</sup> <sup>=</sup> *<sup>M</sup>*<sup>1</sup> and *<sup>x</sup>*<sup>2</sup> is the symbol of **<sup>x</sup>**<sup>2</sup> over signal set *<sup>χ</sup>*<sup>2</sup> where <sup>|</sup>*χ*2<sup>|</sup> <sup>=</sup> *<sup>M</sup>*2. The bit

′

′ in the symbol *x*1,*k*. Note that each RE corresponds to a symbol from a constellation map *χ*<sup>1</sup> for UE-1 and *χ*<sup>2</sup> for UE-2. Selection of the normal or extended cyclic prefix (CP) for each OFDM symbol converts the downlink frequency-selective channel into parallel flat fading

→ (*k*, *i*) where *k*

′ , *k* denotes the RE of the symbol *x*1,*<sup>k</sup>* and *i* indicates the position of the bit

π2

proposes the use of following four precoders for transmission mode 5 and 6:

LTE proposes the use of following two precoder matrices on subband basis.

 1 √4 1 1 1 −1 , <sup>1</sup> √4 1 1 *j* −*j*

Source

(Bits)

the entire band.

**2.2. System model**

of the coded bits *ck*

*ck*

(Bits)

Source

We now look at the effectiveness of the low-resolution LTE precoders for the multi-user MIMO mode. We first consider a geometric scheduling strategy [8] based on the selection of UEs with orthogonal precoders.

#### **3.1. Scheduling strategy**

As the processing at the UE is performed on a RE basis for each received OFDM symbol, the dependency on RE index can be ignored for notational convenience. The system equation for the case of single-antenna UEs for the multi-user mode is

$$y\_1 = \mathbf{h}\_1^\dagger \mathbf{p}\_1 \mathbf{x}\_1 + \mathbf{h}\_1^\dagger \mathbf{p}\_2 \mathbf{x}\_2 + z\_1 \tag{7}$$

The scheduling strategy is based on the principle of maximizing the desired signal strength while minimizing the interference strength. As the decision to schedule a UE in the single-user MIMO, multi-user MIMO or transmit diversity mode will be made by the eNodeB, each UE would feedback the precoder which maximizes its received signal strength. So this selected precoder by the UE would be the one closest to its matched filter (MF) precoder in terms of the Euclidean distance.

10.5772/57134

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

(9)

′ ∈

(10)

*y*<sup>1</sup> and *y*<sup>2</sup> =

(11)

Λ*i* 1 *y*1, *ck* ′ 

where *χ<sup>i</sup>*

to

Λ*i* 1 *y*1, *ck* ′ 

= min *x*1∈*χ<sup>i</sup>* 1,*c k* ′ ,*x*2∈*χ*<sup>2</sup>

where *ρ*<sup>12</sup> =

O (|*χ*1| |*χ*2|).

written as

Λ*i* 1 *y*1, *ck* ′ 

where

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

1,*c k*

Viterbi algorithm, <sup>1</sup>

≈ min *x*1∈*χ<sup>i</sup>* 1,*c k* ′ ,*x*2∈*χ*<sup>2</sup> *y*1−**h**†

> |*y*1| 2+ **h**† <sup>1</sup>**p**1*x*<sup>1</sup> 2 + **h**† <sup>1</sup>**p**2*x*<sup>2</sup> 2 −2 **h**† 1**p**1*x*1*y*<sup>∗</sup> 1 *R*

 **h**† <sup>1</sup>**p**<sup>1</sup> ∗ **h**†

Here we have used the relation |*a* − *b*|

*<sup>y</sup>*1. Ignoring |*y*1|

≈ min *x*1∈*χ<sup>i</sup>* 1,*c k* ′ ,*x*2∈*χ*<sup>2</sup> = log *p*

≈ log *p*

= log ∑ *x*1∈*χ<sup>i</sup>* 1,*c k* ′

≈ min *x*1∈*χ<sup>i</sup>* 1,*c k* ′ ,*x*2∈*χ*<sup>2</sup>

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

In (10), we now introduce two terms as the outputs of MF, i.e. *y*<sup>1</sup> =

 **h**† <sup>1</sup>**p**1*x*<sup>1</sup> 2 + **h**† <sup>1</sup>**p**2*x*<sup>2</sup> 2 <sup>−</sup><sup>2</sup> (*y*<sup>∗</sup>

 *ck* ′ |*y*1, **<sup>h</sup>**† 1, **P** 

 *<sup>y</sup>*1|*ck* ′ , **h**† 1, **P** 

> ∑*x*2∈*χ*<sup>2</sup> *p*

> > 1 *N*0 *y*<sup>1</sup> <sup>−</sup> **<sup>h</sup>**†

{0, 1} in the position *<sup>i</sup>*. Here we have used the log-sum approximation, i.e. log <sup>∑</sup>*<sup>j</sup> zj* = max*<sup>j</sup>* log *zj* and this bit metric is therefore termed as max log MAP bit metric. As LLR is the difference of two bit metrics and these will be decoded using a conventional soft-decision

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

<sup>2</sup> = |*a*|

indicates the real part. Note that the complexity of the calculation of bit metric (10) is

*<sup>ψ</sup><sup>A</sup>* <sup>=</sup> *<sup>ρ</sup>*12,*Rx*1,*<sup>R</sup>* <sup>+</sup> *<sup>ρ</sup>*12,*<sup>I</sup> <sup>x</sup>*1,*<sup>I</sup>* <sup>−</sup> *<sup>y</sup>*2,*<sup>R</sup> <sup>ψ</sup><sup>B</sup>* <sup>=</sup> *<sup>ρ</sup>*12,*Rx*1,*<sup>I</sup>* <sup>−</sup> *<sup>ρ</sup>*12,*<sup>I</sup> <sup>x</sup>*1,*<sup>R</sup>* <sup>−</sup> *<sup>y</sup>*2,*<sup>I</sup>*

<sup>2</sup> + |*b*|

′ denotes the subset of the signal set *<sup>x</sup>*<sup>1</sup> <sup>∈</sup> *<sup>χ</sup>*<sup>1</sup> whose labels have the value *ck*

*<sup>N</sup>*<sup>0</sup> (a common scaling factor to all LLRs) can be ignored thereby leading

<sup>1</sup>**p**<sup>2</sup> indicates the cross correlation between the two effective channels.

<sup>2</sup> (independent of the minimization operation), the bit metric is

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

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

1, **P** 

<sup>+</sup><sup>2</sup> (*ρ*12*x*<sup>∗</sup>

<sup>1</sup> *<sup>x</sup>*2)*<sup>R</sup>* <sup>−</sup> <sup>2</sup>

<sup>2</sup> <sup>−</sup> <sup>2</sup> (*a*∗*b*)*<sup>R</sup>* where the subscript (.)*<sup>R</sup>*

 **h**† <sup>1</sup>**p**<sup>1</sup> ∗

<sup>1</sup> *<sup>x</sup>*1)*R*+2*ψAx*2,*R*+2*ψBx*2,*<sup>I</sup>*

 **h**† 1**p**2*x*2*y*<sup>∗</sup> 1 *R* 

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

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

For the multi-user MIMO mode, the eNodeB needs to ensure good channel separation between the co-scheduled UEs. Therefore the eNodeB schedules two UEs on the same RBs which have requested opposite (orthogonal) precoders, i.e. the eNodeB selects as the second UE to be served in each group of allocatable RBs, one of the UEs whose requested precoder **<sup>p</sup>**<sup>2</sup> is 180◦ out of phase from the precoder **<sup>p</sup>**<sup>1</sup> of the first UE to be served on the same RBs. So if UE-1 has requested **<sup>p</sup>**<sup>1</sup> = <sup>√</sup> 1 4 1 *q* , *q* ∈ {±1, ±*j*}, then eNodeB selects the second UE which has requested **<sup>p</sup>**<sup>2</sup> = <sup>√</sup> 1 4 1 −*q* . This transmission strategy also remains valid also for the case of dual-antenna UEs where the UEs feedback the indices of the precoding vectors which maximize the strength of their desired signals, i.e. �**Hp**�<sup>2</sup> . For the multi-user MIMO mode, the eNodeB schedules two UEs on the same RE which have requested 180◦ out of phase precoders. The details of this geometric scheduling strategy can be found in [7].

Though this precoding and scheduling strategy would ensure minimization of the interference under the constraint of low-resolution LTE precoders, the residual interference would still be significant. Single-user detection i.e. Gaussian assumption of the residual interference and its subsequent absorption in noise would lead to significant degradation in the performance. On the other hand, this residual interference is actually discrete belonging to a finite alphabet and its structure can be exploited in the detection process. However intelligent detection based on its exploitation comes at the cost of enhanced complexity. Here we propose a low-complexity interference-aware receiver structure [9] which on one hand reduces one complex dimension of the system while on the other hand, it exploits the interference structure in the detection process.

#### **3.2. Low-complexity interference-aware receiver**

First we consider the case of single-antenna UEs. Soft decision of the bit *ck* ′ of *x*1, also known as log-likelihood ratio (LLR), is given as

$$\text{LLR}^i\_1 \left( c\_{k'} | y\_{1'}, \mathbf{h}\_{1'}^\dagger \mathbf{P} \right) = \log \frac{p \left( c\_{k'} = 1 | y\_{1'}, \mathbf{h}\_{1'}^\dagger \mathbf{P} \right)}{p \left( c\_{k'} = 0 | y\_{1'}, \mathbf{h}\_{1'}^\dagger \mathbf{P} \right)} \tag{8}$$

We introduce the notation Λ*<sup>i</sup>* 1 *y*1, *ck* ′ for the bit metric which is developed on the lines similar to the equations (7) and (9) in [4], i.e.

$$\begin{split} \Lambda\_{1}^{\hat{d}} \left( y\_{1} c\_{\boldsymbol{k'}} \right) &= \log p \left( c\_{\boldsymbol{k'}} \middle| y\_{1}, \mathbf{h}\_{1}^{\dagger}, \mathbf{P} \right) \\ &\approx \log p \left( y\_{1} \middle| c\_{\boldsymbol{k'}}, \mathbf{h}\_{1}^{\dagger}, \mathbf{P} \right) \\ &= \log \sum\_{\mathbf{x}\_{1} \in \mathcal{X}\_{\boldsymbol{k'}, \boldsymbol{c}\_{\boldsymbol{k'}}}^{\top}} \sum\_{\mathbf{x}\_{2} \in \mathcal{X}\_{2}} p \left( y\_{1} \middle| \mathbf{x}\_{1}, \mathbf{x}\_{2}, \mathbf{h}\_{1}^{\dagger}, \mathbf{P} \right) \\ &\approx \min\_{\mathbf{x}\_{1} \in \mathcal{X}\_{\boldsymbol{k'}, \boldsymbol{c}\_{\boldsymbol{k'}}}^{\top}, \mathbf{x}\_{2} \in \mathcal{X}\_{2}} \frac{1}{\mathcal{N}\_{0}} \left| y\_{1} - \mathbf{h}\_{1}^{\dagger} \mathbf{p}\_{1} \mathbf{x}\_{1} - \mathbf{h}\_{1}^{\dagger} \mathbf{p}\_{2} \mathbf{x}\_{2} \right|^{2} \end{split} \tag{9}$$

where *χ<sup>i</sup>* 1,*c k* ′ denotes the subset of the signal set *<sup>x</sup>*<sup>1</sup> <sup>∈</sup> *<sup>χ</sup>*<sup>1</sup> whose labels have the value *ck* ′ ∈ {0, 1} in the position *<sup>i</sup>*. Here we have used the log-sum approximation, i.e. log <sup>∑</sup>*<sup>j</sup> zj* = max*<sup>j</sup>* log *zj* and this bit metric is therefore termed as max log MAP bit metric. As LLR is the difference of two bit metrics and these will be decoded using a conventional soft-decision Viterbi algorithm, <sup>1</sup> *<sup>N</sup>*<sup>0</sup> (a common scaling factor to all LLRs) can be ignored thereby leading to

$$\begin{split} \Lambda\_{1}^{\dagger} \left( y\_{1}, c\_{k'} \right) &\approx \min\_{\mathbf{x}\_{1} \in \chi\_{\mathbf{1}\_{k'}}^{\dagger}, x\_{2} \in \chi\_{2}^{\dagger}} \left| y\_{1} - \mathbf{h}\_{1}^{\dagger} \mathbf{p}\_{1} \mathbf{x}\_{1} - \mathbf{h}\_{1}^{\dagger} \mathbf{p}\_{2} \mathbf{x}\_{2} \right|^{2} \\ &= \min\_{\mathbf{x}\_{1} \in \chi\_{\mathbf{1}\_{k'}}^{\dagger}, x\_{2} \in \chi\_{2}^{\dagger}} \left\{ \left| y\_{1} \right|^{2} + \left| \mathbf{h}\_{1}^{\dagger} \mathbf{p}\_{1} \mathbf{x}\_{1} \right|^{2} + \left| \mathbf{h}\_{1}^{\dagger} \mathbf{p}\_{2} \mathbf{x}\_{2} \right|^{2} - 2 \left( \mathbf{h}\_{1}^{\dagger} \mathbf{p}\_{1} \mathbf{x}\_{1} y\_{1}^{\*} \right)\_{R} + 2 \left( \rho\_{12} \mathbf{x}\_{1}^{\*} \mathbf{x}\_{2} \right)\_{R} - 2 \left( \mathbf{h}\_{1}^{\dagger} \mathbf{p}\_{2} \mathbf{x}\_{2} y\_{1}^{\*} \right)\_{R} \right] \end{split} \tag{10}$$

where *ρ*<sup>12</sup> = **h**† <sup>1</sup>**p**<sup>1</sup> ∗ **h**† <sup>1</sup>**p**<sup>2</sup> indicates the cross correlation between the two effective channels. Here we have used the relation |*a* − *b*| <sup>2</sup> = |*a*| <sup>2</sup> + |*b*| <sup>2</sup> <sup>−</sup> <sup>2</sup> (*a*∗*b*)*<sup>R</sup>* where the subscript (.)*<sup>R</sup>* indicates the real part. Note that the complexity of the calculation of bit metric (10) is O (|*χ*1| |*χ*2|).

In (10), we now introduce two terms as the outputs of MF, i.e. *y*<sup>1</sup> = **h**† <sup>1</sup>**p**<sup>1</sup> ∗ *y*<sup>1</sup> and *y*<sup>2</sup> = **h**† <sup>1</sup>**p**<sup>2</sup> ∗ *<sup>y</sup>*1. Ignoring |*y*1| <sup>2</sup> (independent of the minimization operation), the bit metric is written as

$$\Lambda\_1^i \left( y\_1, c\_{k'} \right) \approx \min\_{\mathbf{x}\_1 \in \chi\_{1, c\_{k'}}^i, \mathbf{x}\_2 \in \chi\_2} \left\{ \left| \mathbf{h}\_1^\dagger \mathbf{p}\_1 \mathbf{x}\_1 \right|^2 + \left| \mathbf{h}\_1^\dagger \mathbf{p}\_2 \mathbf{x}\_2 \right|^2 - 2 \left( \overline{y}\_1^\* \mathbf{x}\_1 \right)\_R + 2 \psi\_A \mathbf{x}\_{2,R} + 2 \psi\_B \mathbf{x}\_{2,I} \right\} \tag{11}$$

where

6 Recent Trends in Multiuser MIMO Communications

precoder in terms of the Euclidean distance.

1 4 1 *q* 

which maximize the strength of their desired signals, i.e. �**Hp**�<sup>2</sup>

1 4 1 −*q* 

interference structure in the detection process.

as log-likelihood ratio (LLR), is given as

We introduce the notation Λ*<sup>i</sup>*

**3.2. Low-complexity interference-aware receiver**

LLR*i* 1 *ck* ′ |*y*1, **<sup>h</sup>**† 1, **P** = log

similar to the equations (7) and (9) in [4], i.e.

1 *y*1, *ck* ′

First we consider the case of single-antenna UEs. Soft decision of the bit *ck*

So if UE-1 has requested **<sup>p</sup>**<sup>1</sup> = <sup>√</sup>

which has requested **<sup>p</sup>**<sup>2</sup> = <sup>√</sup>

The scheduling strategy is based on the principle of maximizing the desired signal strength while minimizing the interference strength. As the decision to schedule a UE in the single-user MIMO, multi-user MIMO or transmit diversity mode will be made by the eNodeB, each UE would feedback the precoder which maximizes its received signal strength. So this selected precoder by the UE would be the one closest to its matched filter (MF)

For the multi-user MIMO mode, the eNodeB needs to ensure good channel separation between the co-scheduled UEs. Therefore the eNodeB schedules two UEs on the same RBs which have requested opposite (orthogonal) precoders, i.e. the eNodeB selects as the second UE to be served in each group of allocatable RBs, one of the UEs whose requested precoder **<sup>p</sup>**<sup>2</sup> is 180◦ out of phase from the precoder **<sup>p</sup>**<sup>1</sup> of the first UE to be served on the same RBs.

the case of dual-antenna UEs where the UEs feedback the indices of the precoding vectors

mode, the eNodeB schedules two UEs on the same RE which have requested 180◦ out of phase precoders. The details of this geometric scheduling strategy can be found in [7].

Though this precoding and scheduling strategy would ensure minimization of the interference under the constraint of low-resolution LTE precoders, the residual interference would still be significant. Single-user detection i.e. Gaussian assumption of the residual interference and its subsequent absorption in noise would lead to significant degradation in the performance. On the other hand, this residual interference is actually discrete belonging to a finite alphabet and its structure can be exploited in the detection process. However intelligent detection based on its exploitation comes at the cost of enhanced complexity. Here we propose a low-complexity interference-aware receiver structure [9] which on one hand reduces one complex dimension of the system while on the other hand, it exploits the

> *p ck*

> *p ck*

′ = <sup>1</sup>|*y*1, **<sup>h</sup>**†

′ = <sup>0</sup>|*y*1, **<sup>h</sup>**†

1, **P** 

1, **P**

for the bit metric which is developed on the lines

, *q* ∈ {±1, ±*j*}, then eNodeB selects the second UE

. This transmission strategy also remains valid also for

. For the multi-user MIMO

′ of *x*1, also known

(8)

$$\begin{aligned} \psi\_A &= \rho\_{12,R} \mathbf{x}\_{1,R} + \rho\_{12,I} \mathbf{x}\_{1,I} - \overline{y}\_{2,R} \\ \psi\_B &= \rho\_{12,R} \mathbf{x}\_{1,I} - \rho\_{12,I} \mathbf{x}\_{1,R} - \overline{y}\_{2,I} \end{aligned}$$

Note that the subscript (.)*<sup>I</sup>* indicates the imaginary part.

For *x*<sup>1</sup> and *x*<sup>2</sup> belonging to equal energy alphabets, **h**† <sup>1</sup>**p**1*x*<sup>1</sup> 2 and **h**† <sup>1</sup>**p**2*x*<sup>2</sup> 2 can be ignored as they are independent of the minimization operation. The values of *x*2,*<sup>R</sup>* and *x*2,*<sup>I</sup>* which minimize (11) need to be in the opposite directions of *ψ<sup>A</sup>* and *ψ<sup>B</sup>* respectively thereby avoiding search on the alphabets of *x*<sup>2</sup> and reducing one complex dimension in the detection, i.e.

$$\Lambda\_1^i \left( y\_1, c\_{\boldsymbol{k'}} \right) \approx \min\_{\mathbf{x}\_l \in \chi\_{1, \boldsymbol{\ell'}}^i} \left\{ -2 \overline{y}\_{1, \mathcal{R}} \mathbf{x}\_{1, \mathcal{R}} - 2 \overline{y}\_{1, \mathcal{I}} \mathbf{x}\_{1, \mathcal{I}} - 2 \left| \psi\_A \right| \left| \mathbf{x}\_{2, \mathcal{R}} \right| - 2 \left| \psi\_B \right| \left| \mathbf{x}\_{2, \mathcal{I}} \right| \right\} \tag{12}$$

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(16)

the metric (15) reduces it to merely two operations thereby trimming down one complex dimension in the detection, i.e. the detection complexity is independent of |*χ*2| and reduces

As a particular example of the discretization of continuous values in (15), we consider the case of *x*<sup>2</sup> belonging to QAM16 . The values of *x*2,*<sup>R</sup>* and *x*2,*<sup>I</sup>* for the case of QAM16 are

2 + (−1)

2 + (−1)

Now we look at the receiver structure for the case of dual-antenna UEs. The system equation

For comparison purposes, we also consider the case of single-user receiver, for which the bit

1

Table 1 compares the complexities of different receivers in terms of the number of real-valued multiplications and additions for getting all LLR values per RE/subcarrier. Note that *nr* denotes the number of receive antennas. This complexity analysis is independent of the number of transmit antennas as the operation of finding effective channels bears same

*I* � |*ψA*|<*σ*<sup>2</sup>

*I* � |*ψB*|<*σ*<sup>2</sup>

� 1 if *a* < *b* 0 otherwise <sup>2</sup>|**h**† 1**p**2| 2 √<sup>10</sup> � 

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

<sup>2</sup>|**h**† 1**p**2| 2 √<sup>10</sup> �

**y**<sup>1</sup> = **H**<sup>1</sup> [**p**1*x*<sup>1</sup> + **p**2*x*2] + **z**<sup>1</sup> (17)

<sup>1</sup> being replaced by **H**1, i.e. the channel from

**y**<sup>1</sup> and *y*<sup>2</sup> = (**H**1**p**2)

2 

† **y**1

(18)

†

† **<sup>H</sup>**1**p**<sup>2</sup> is the cross-correlation between two effective

so their magnitudes in (14) are given as

1 √10

1 √10 *I* (*a* < *b*) =



and *I* (.) is the indicator function defined as

The receiver structure would remain same with **h**†

≈ min *x*1∈*χ<sup>i</sup>* 1,*c k* ′

are the MF outputs while *<sup>ρ</sup>*<sup>12</sup> <sup>=</sup> (**H**1**p**1)

channels.

metric is given as

Λ*i* 1 � *y*1, *ck* ′ �

eNodeB to the two antennas of UE-1. Subsequently *y*<sup>1</sup> = (**H**1**p**1)

 

� |*ρ*12| 2 *σ*2 <sup>2</sup> + � � � **h**† <sup>1</sup>**p**<sup>1</sup> � � � 2 *N*0 � � � � � *<sup>y</sup>*1<sup>−</sup> � � � **h**† <sup>1</sup>**p**<sup>1</sup> � � � 2 *x*1 � � � �

for UE-1 (ignoring the RE index) is

to O (|*χ*1|).

<sup>10</sup> , <sup>±</sup> <sup>√</sup> 3*σ*<sup>2</sup> 10 �

� ± <sup>√</sup>*σ*<sup>2</sup>

As an example we consider the case of QPSK for which the values of *<sup>x</sup>*2,*<sup>R</sup>* and *<sup>x</sup>*2,*<sup>I</sup>* are ± <sup>√</sup>*σ*<sup>2</sup> 2 , so the bit metric is written as

$$\Lambda\_1^i \left( y\_1, c\_{k'} \right) \approx \min\_{\mathbf{x}\_1 \in \chi\_{1, \varepsilon\_{k'}}^i} \left\{ -2\overline{y}\_{1, \mathbb{R}} \mathbf{x}\_{1, \mathbb{R}} - 2\overline{y}\_{1, I} \mathbf{x}\_{1, I} - \sqrt{2}\sigma\_2 \left| \psi\_A \right| - \sqrt{2}\sigma\_2 \left| \psi\_B \right| \right\} \tag{13}$$

For *x*<sup>1</sup> and *x*<sup>2</sup> belonging to non-equal energy alphabets, the bit metric is same as (13) but **h**† <sup>1</sup>**p**1*x*<sup>1</sup> 2 and **h**† <sup>1</sup>**p**2*x*<sup>2</sup> 2 can no longer be ignored thereby leading to

$$\Lambda\_{1}^{i} \left( y\_{1}, c\_{\mathbf{z}'} \right) \approx \min\_{\mathbf{x}\_{1} \in \chi\_{1\mathbf{z}\_{\mathbf{z}'}}^{i}} \left\{ \left| \mathbf{h}\_{1}^{\dagger} \mathbf{p}\_{1} \right|^{2} \left| \mathbf{x}\_{1,R} \right|^{2} + \left| \mathbf{h}\_{1}^{\dagger} \mathbf{p}\_{1} \right|^{2} \left| \mathbf{x}\_{1,I} \right|^{2} + \left| \mathbf{h}\_{1}^{\dagger} \mathbf{p}\_{2} \right|^{2} \left| \mathbf{x}\_{2,R} \right|^{2} + \left| \mathbf{h}\_{1}^{\dagger} \mathbf{p}\_{2} \right|^{2} \left| \mathbf{x}\_{2,I} \right|^{2} - \left| \mathbf{y}\_{1} \right|^{2} \right\} \tag{14}$$
 
$$2\overline{y}\_{1,R} \mathbf{x}\_{1,R} - 2\overline{y}\_{1,I} \mathbf{x}\_{1,I} - 2\left| \psi\_{A} \right| \left| \mathbf{x}\_{2,R} \right| - 2\left| \psi\_{B} \right| \left| \mathbf{x}\_{2,I} \right| \right\} \tag{14}$$

Note that the minimization is independent of *χ*<sup>2</sup> though *x*<sup>2</sup> appears in the bit metric. The reason of this independence is as follows. The decision regarding the signs of *x*2,*<sup>R</sup>* and *x*2,*<sup>I</sup>* in (14) will be taken in the same manner as for the case of equal energy alphabets. For finding their magnitudes that minimize the bit metric (14), it is the minimization problem of a quadratic function, i.e. differentiating (14) w.r.t |*x*2,*R*| and |*x*2,*I*| to find the global minimas which are given as

$$|\chi\_{2,R}| \to \frac{|\psi\_A|}{\left|\mathbf{h}\_1^\dagger \mathbf{p}\_2\right|^2}, \qquad |\chi\_{2,I}| \to \frac{|\psi\_B|}{\left|\mathbf{h}\_1^\dagger \mathbf{p}\_2\right|^2} \tag{15}$$

where → indicates the discretization process in which amongst the finite available points of *x*2,*<sup>R</sup>* and *x*2,*I*, the point closest to the calculated continuous value is selected. So if *x*<sup>2</sup> belongs to QAM256, then instead of searching 256 constellation points for the minimization of (14), the metric (15) reduces it to merely two operations thereby trimming down one complex dimension in the detection, i.e. the detection complexity is independent of |*χ*2| and reduces to O (|*χ*1|).

As a particular example of the discretization of continuous values in (15), we consider the case of *x*<sup>2</sup> belonging to QAM16 . The values of *x*2,*<sup>R</sup>* and *x*2,*<sup>I</sup>* for the case of QAM16 are � ± <sup>√</sup>*σ*<sup>2</sup> <sup>10</sup> , <sup>±</sup> <sup>√</sup> 3*σ*<sup>2</sup> 10 � so their magnitudes in (14) are given as

$$\begin{aligned} |\mathbf{x}\_{2,R}| &= \sigma\_2 \frac{1}{\sqrt{10}} \left( 2 + (-1)^{I \left( \left| \psi\_A \right| < \sigma\_2 \frac{2 \left| \mathbf{h}\_1^\mathbf{1} \mathbf{P}\_2 \right|}{\sqrt{10}} \right)}{2} \right) \\ |\mathbf{x}\_{2,I}| &= \sigma\_2 \frac{1}{\sqrt{10}} \left( 2 + (-1)^{I \left( \left| \psi\_B \right| < \sigma\_2 \frac{2 \left| \mathbf{h}\_1^\mathbf{1} \mathbf{P}\_2 \right|}{\sqrt{10}} \right)} \right) \end{aligned} \tag{16}$$

and *I* (.) is the indicator function defined as

8 Recent Trends in Multiuser MIMO Communications

i.e.

 **h**† <sup>1</sup>**p**1*x*<sup>1</sup> 2 and **h**† <sup>1</sup>**p**2*x*<sup>2</sup> 2

> Λ*i* 1 *y*1, *ck* ′ ≈ min *x*1∈*χ<sup>i</sup>* 1,*c k* ′ **h**† <sup>1</sup>**p**<sup>1</sup> 2 |*x*1,*R*| 2 + **h**† <sup>1</sup>**p**<sup>1</sup> 2 |*x*1,*I*| 2+ **h**† <sup>1</sup>**p**<sup>2</sup> 2 |*x*2,*R*| 2+ **h**† <sup>1</sup>**p**<sup>2</sup> 2 |*x*2,*I*| 2 −

which are given as

Λ*i* 1 *y*1, *ck* ′ 

so the bit metric is written as

Λ*i* 1 *y*1, *ck* ′ 

Note that the subscript (.)*<sup>I</sup>* indicates the imaginary part.

 **h**† <sup>1</sup>**p**1*x*<sup>1</sup> 2 and **h**† <sup>1</sup>**p**2*x*<sup>2</sup> 2

<sup>−</sup>2*y*1,*Rx*1,*<sup>R</sup>* <sup>−</sup> <sup>2</sup>*y*1,*<sup>I</sup> <sup>x</sup>*1,*<sup>I</sup>* <sup>−</sup> <sup>2</sup> <sup>|</sup>*ψA*<sup>|</sup> <sup>|</sup>*x*2,*R*<sup>|</sup> <sup>−</sup> <sup>2</sup> <sup>|</sup>*ψB*| |*x*2,*I*<sup>|</sup>

<sup>2</sup>*σ*<sup>2</sup> <sup>|</sup>*ψA*<sup>|</sup> <sup>−</sup> <sup>√</sup>

<sup>2</sup>*σ*<sup>2</sup> |*ψB*|

<sup>2</sup> (15)

as they are independent of the minimization operation. The values of *x*2,*<sup>R</sup>* and *x*2,*<sup>I</sup>* which minimize (11) need to be in the opposite directions of *ψ<sup>A</sup>* and *ψ<sup>B</sup>* respectively thereby avoiding search on the alphabets of *x*<sup>2</sup> and reducing one complex dimension in the detection,

As an example we consider the case of QPSK for which the values of *x*2,*<sup>R</sup>* and *x*2,*<sup>I</sup>* are

<sup>−</sup>2*y*1,*Rx*1,*<sup>R</sup>* <sup>−</sup> <sup>2</sup>*y*1,*<sup>I</sup> <sup>x</sup>*1,*<sup>I</sup>* <sup>−</sup> <sup>√</sup>

For *x*<sup>1</sup> and *x*<sup>2</sup> belonging to non-equal energy alphabets, the bit metric is same as (13) but

can no longer be ignored thereby leading to

<sup>2</sup>*y*1,*Rx*1,*<sup>R</sup>* <sup>−</sup>2*y*1,*<sup>I</sup> <sup>x</sup>*1,*I*−<sup>2</sup> <sup>|</sup>*ψA*<sup>|</sup> <sup>|</sup>*x*2,*R*|−<sup>2</sup> <sup>|</sup>*ψB*| |*x*2,*I*<sup>|</sup>

<sup>2</sup> , <sup>|</sup>*x*2,*I*<sup>|</sup> <sup>→</sup> <sup>|</sup>*ψB*<sup>|</sup>

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

Note that the minimization is independent of *χ*<sup>2</sup> though *x*<sup>2</sup> appears in the bit metric. The reason of this independence is as follows. The decision regarding the signs of *x*2,*<sup>R</sup>* and *x*2,*<sup>I</sup>* in (14) will be taken in the same manner as for the case of equal energy alphabets. For finding their magnitudes that minimize the bit metric (14), it is the minimization problem of a quadratic function, i.e. differentiating (14) w.r.t |*x*2,*R*| and |*x*2,*I*| to find the global minimas

where → indicates the discretization process in which amongst the finite available points of *x*2,*<sup>R</sup>* and *x*2,*I*, the point closest to the calculated continuous value is selected. So if *x*<sup>2</sup> belongs to QAM256, then instead of searching 256 constellation points for the minimization of (14),

<sup>|</sup>*x*2,*R*<sup>|</sup> <sup>→</sup> <sup>|</sup>*ψA*<sup>|</sup> **h**† <sup>1</sup>**p**<sup>2</sup>  can be ignored

 ± <sup>√</sup>*σ*<sup>2</sup> 2 ,

(12)

(13)

(14)

For *x*<sup>1</sup> and *x*<sup>2</sup> belonging to equal energy alphabets,

≈ min *x*1∈*χ<sup>i</sup>* 1,*c k* ′ 

> ≈ min *x*1∈*χ<sup>i</sup>* 1,*c k* ′

$$I\left(a < b\right) = \begin{cases} 1 \text{ if } a < b\\ 0 \text{ otherwise} \end{cases}$$

Now we look at the receiver structure for the case of dual-antenna UEs. The system equation for UE-1 (ignoring the RE index) is

$$\mathbf{y}\_1 = \mathbf{H}\_1 \left[ \mathbf{p}\_1 \mathbf{x}\_1 + \mathbf{p}\_2 \mathbf{x}\_2 \right] + \mathbf{z}\_1 \tag{17}$$

The receiver structure would remain same with **h**† <sup>1</sup> being replaced by **H**1, i.e. the channel from eNodeB to the two antennas of UE-1. Subsequently *y*<sup>1</sup> = (**H**1**p**1) † **y**<sup>1</sup> and *y*<sup>2</sup> = (**H**1**p**2) † **y**1 are the MF outputs while *<sup>ρ</sup>*<sup>12</sup> <sup>=</sup> (**H**1**p**1) † **<sup>H</sup>**1**p**<sup>2</sup> is the cross-correlation between two effective channels.

For comparison purposes, we also consider the case of single-user receiver, for which the bit metric is given as

$$\Lambda\_1^i \left( y\_1, c\_{k'} \right) \approx \min\_{\mathbf{x}\_1 \in \mathcal{X}\_{1c\_{k'}}^i} \left\{ \frac{1}{\left( |\rho\_{12}|^2 \sigma\_2^2 + \left| \mathbf{h}\_1^\dagger \mathbf{p}\_1 \right|^2 N\_0 \right)} \left| \overline{\mathbf{y}}\_1 - \left| \mathbf{h}\_1^\dagger \mathbf{p}\_1 \right|^2 \mathbf{x}\_1 \right|^2 \right\} \tag{18}$$

Table 1 compares the complexities of different receivers in terms of the number of real-valued multiplications and additions for getting all LLR values per RE/subcarrier. Note that *nr* denotes the number of receive antennas. This complexity analysis is independent of the number of transmit antennas as the operation of finding effective channels bears same

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(19)

(20)

(21)

<sup>2</sup> which is

<sup>1</sup> and **<sup>h</sup>**†

<sup>0</sup>◦ <sup>≤</sup> *<sup>φ</sup>* <sup>≤</sup> <sup>90</sup>◦ (22)

structure as compared to using single-user receivers except that the UE needs to know the

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

*<sup>Y</sup>*2; *<sup>X</sup>*2|**h**†

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

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

> <sup>2</sup> + |*h*21| 2 � *h*<sup>11</sup> *h*21 �

� 1 *h*∗

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

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

�

**<sup>p</sup>** <sup>=</sup> <sup>1</sup> � |*h*11|

**<sup>p</sup>** <sup>=</sup> <sup>1</sup> √2

the spatial space into 4 quadrants according to the spatial angle between **h**†

 

� � � **h**† <sup>1</sup>**h**<sup>2</sup> � � � �**h**1� �**h**2�

*<sup>φ</sup>* <sup>=</sup> cos−<sup>1</sup>

2, **P** �

�

*<sup>Y</sup>*2; *<sup>X</sup>*2|**h**†

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

2, **P** �

is the mutual information of UE-1

is the mutual information of UE-2

constellation of interference.

**4. Information theoretic perspective** Sum rate of the downlink channel is given as

where **P** = [**p**<sup>1</sup> **p**2] is the precoder matrix, *I*

once it sees interference from UE-2 and *I*

Appendix-A for simplicity and lucidity.

For EGT, the unquantized MF precoder is given as

given as

I = *I* � *Y*1; *X*<sup>1</sup> � �**h**† 1, **P** � + *I* �

**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.


**Table 1.** Comparison of receivers complexity

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 structure as compared to using single-user receivers except that the UE needs to know the constellation of interference.
