MIMO Performance

7/28/2019 MIMO Performance

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UE is supposed to feedback the preferred number of data

streams depending on the observed channel. The UE can also

feedback an index to a matrix in a codebook, which can be

used by eNodeB as a precoder. The precoder is chosen such

that throughput is maximized. The granularity for computation

and signaling of the precoding index can range from a couple

of RBs to the full bandwidth.

In MU-MIMO operation two or more UEs share the same

time-frequency resources. Several parallel data streams are

transmitted simultaneously, one for each UE. It is assumed

that the UE feeds back a quantized version of the observed

channel, so that eNodeB can schedule in MU-MIMO mode

those terminals with good channel separation (cf Section IV

and Section VII). The transmitted data is precoded such that

each data stream is transmitted to the corresponding UE

with maximum throughput. The precoder must be designed

jointly for all data streams, such that interference between datastreams can be minimized, as seen in Section IV.

III . SIGNAL MODEL

Let us define Ns as the number of streams transmitted

simultaneously to each user, Nt and Nr as the number of trans-

mit and receive antennas, respectively, and Nu as the number

of users transmitting simultaneously at the same subcarrier. For

each subcarrier, we can write the received symbol estimates for

the l-th user after receiver filtering as

xl = WR,lHl

Nu

u=1

WT,uxu +WR,ln, (1)

where the Nt Ns matrix WT,l and the Ns Nr matrixWR,l are the transmitter precoding filter and receiver baseband

processing filter for the l-th user, respectively, Hl is the

MIMO channel matrix for the l-th user, xl are the transmitted

symbols, and n is the circularly-complex Gaussian white noise.

The dependency on subcarrier index and time instant is not

explicitly indicated in (1), since the processing is assumed to

be performed on a subcarrier basis for each received OFDM

symbol.

IV. PRECODER COMPUTATION

The singular value decomposition (SVD) of the Nr Ntchannel H is given by H = UVH. Since matrices U andV are unitary, the SVD decouples the channel into orthogonal

directions. Assuming the receiver is given by the left singular

vectors, U, and that we are interested in the channel direction

that corresponds to the largest singular value, we can write the

equivalent channel seen by the l-th user as

Heq,l = lvHl , (2)

where vl denotes the first column ofV and l is the first

element of the main diagonal of. The equivalent channel is

quantized to a codebook before it is fed back to eNodeB [1].

The quantized version of the equivalent channel is denoted by

Heq,l and computed as

Heq,l = arg maxc

Heq,lcH, (3)

where c denotes a vector that belongs to the codebook.

Zero-Forcing (ZF) precoding is a potential precoder design

technique for DL MU-MIMO. The main benefits of ZF pre-

coding is that the interference is pre-canceled at the transmitter

side. This implies that eNodeB has most of the computational

complexity in designing the precoder, and each terminal needs

only information regarding its own data streams for reception.

The ZF precoder can be designed using the Moore-Penrose

pseudo-inverse as

WT = HH

eq

HeqH

H

eq

1

, (4)

where

Heq =HT

eq,1 . . . HT

eq,Nu

T(5)

WT =

WT,1 . . . WT,Nu

(6)

In practice, the precoder has to be quantized to a codebook

as well, or else dedicated pilots must be used for channel

estimation. Detailed description of codebook definitions for

MIMO operation in LTE can be found in [1].

A special case of the ZF precoder is obtained when the

equivalent channel observed by different users are orthogonal

to each other. In this case the expression for the transmitter in

(4) simplifies to

WT = HH

eq . (7)

When the scheduler imposes the constraint that only users with

orthogonal channels can be multiplexed, the resulting multi-

plexing scheme is known as unitary precoding. In principle,unitary precoding is more robust to channel quantization and

variation than ZF precoding. However, the probability that any

two users feedback orthogonal channels decreases with the

number of codewords in the codebook, assuming the codebook

is designed such that all codewords are fed back with non-zero

probability. If the number of codewords is small, then only a

coarse quantization of the channel is possible, which limits

the precoding gain. Hence, with unitary precoding there is a

trade-off between multiplexing and precoding gains.

V. RECEIVER

In principle, there is no need to cancel the interferenceof the other user at the receiver, since the ZF precoder is

designed such that the received signal is free from multi-

user interference. However, due to channel quantization and

feedback delay, some MU interference will exist. An LMMSE

receiver can be employed at the receiver to reduce the interfer-

ence and improve system performance, but this requires that

the precoding vectors applied to the streams transmitted to

different users are known. This information could be signaled

in downlink control channel, or else estimated from dedicated

pilots. In both cases, this implies additional overhead. The

LMMSE receiver for the l-th user is given by

WR = WHT,lHHl HlWT(HlWT)H + 2nI1 , (8)where 2n is the noise variance.

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In LTE, the working assumption in the ongoing standard-

ization [1] is that only one stream can be transmitted to a

user in MU-MIMO mode, i.e. Ns = 1. Hence, if the receiveris not aware of the precoding vectors applied to the streams

transmitted to the other users, the receiver is not able to reject

the interference from the other users, and can only maximize

the received power. Hence the LMMSE receiver in (8) is

equivalent to the Maximum Ratio Combiner (MRC).

VI. CHANNEL FEEDBACK

Feedback from the terminal is crucial in order to design pre-

coders taking into account current channel state. The terminal

is supposed to feed back a Precoding Matrix Indication (PMI)

which is an index in the codebook for the preferred precoder.

It is not practical to feedback one PMI for each subcarrier, and

hence the terminal feeds back one PMI for a given group of

subcarriers.For each subcarrier the optimum precoding vector is given

by the right singular vector corresponding to the largest singu-

lar value. The vector is then quantized to the codebook using

the metric in equation (3) for all subcarriers in the group.

Moreover, accurate Channel Quality Indication (CQI) is

important for proper link adaptation at eNodeB. Otherwise, low

rate modulation and coding schemes should be used in order

to avoid detection errors, resulting in reduced throughput.CQI definition for MU-MIMO is still an open issue in LTE,

and in this paper we assume that the terminal reports the Signal

to Interference plus Noise Ratio (SINR) assuming a single-

stream, single-user transmission. The eNodeB then applies a

reduction factor in order to take into account the reducedpower in each stream and other losses due to, e.g. interference.

As seen in Section V, for the single-stream transmission the

LMMSE receiver is equivalent to the MRC receiver, and the

SNR is given by

=|Heq,lWT,l |

2

2n, (9)

where WT,l is the preferred (quantized) precoding vector,

Heq,l is the equivalent channel given by equation (2), and 2

n

is the noise variance.

VII. USE R SCHEDULING ALGORITHMS

In SU-MIMO transmission, several parallel data streamsare transmitted to the same terminal, while in MU-MIMO

transmission the streams are transmitted to different users who

share the same time-frequency resources. In the 3GPP LTE

system, it is assumed that UEs are semi-statically allocated in

MU-MIMO mode, implying that it is not allowed for a UE to

be scheduled in one subframe in MU-MIMO and in Single-

User MIMO (SU-MIMO) in the next subframe. Moreover,

it is assumed that only one stream can be transmitted to a

UE operating in MU-MIMO mode (Ns = 1), as noted inSection II.

For each resource allocation the scheduler has to decide

between single-stream single-user transmission or MU-MIMOtransmission. Since the transmitted power must remain con-

stant, the power of each stream in MU-MIMO mode is the

UE 1

UE 3UE 2UE 2

Frequency

Power

Figure 1. Distribution of power over different resource blocks. The eNodeBtransmits with maximum power to UE 1 on those RBs where it is notmultiplexed with any other user.

total TX power divided by the number of streams, and hence

MU-MIMO transmission does not necessarily imply higher

data rates. We assume that the scheduler assigns one user for

transmission, and decides on transmitting in MU-MIMO modeonly if the estimated data rate in MU-MIMO mode is higher

than for single-user transmission.

For frequency-dependent (FD) scheduling it is assumed

that the same modulation and coding scheme is used for the

whole allocation, according to 3GPP LTE. The FD scheduling

algorithm can be summarized as:

Primary user selection and the resource allocation for the

primary users is done by the FD scheduler independently

in time and frequency domains. Well-known schedulers

can be used, such as Round Robin and Proportional Fair

schedulers [7].

Candidates for MU-MIMO are selected among users thathave not been scheduled as primary users.

Identify which UEs can be transmitted in MU-MIMO

mode with the primary UE.

Estimate the rate for single-stream transmission and

MU-MIMO transmission for each candidate UE. De-

cide on single-stream or MU-MIMO allocation as we

will describe in Section VII-B.

Compute the precoding matrix as in Section IV, assuming

either ZF or unitary precoding.

Limitation on the maximum number of scheduled users

per TTI due to control signaling restrictions must be taken

into account. Users can be allocated in MU-MIMO mode with different

primary users.

The selection of UEs to be scheduled and the allocation of

frequency resources are performed independently in time and

frequency domains. The evaluation of MU-MIMO allocation is

performed independently for each resource block. A terminal

is allocated in MU-MIMO mode for each resource block

depending on the precoding vector and channel condition, and

hence it is not guaranteed that a UE can be allocated in MU-

MIMO mode for all resource blocks it has been allocated

to. Hence, eNodeB does not perform power sharing in those

resource blocks where there is no actual user multiplexing, inorder to guarantee that the total output power is constant over

all subcarriers. Figure 1 illustrates this arrangement.

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A. Search for MU-MIMO candidates

The MU-MIMO candidates are identified by means of cor-

relation between the reported channel vectors. If the correlation

is below a pre-defined threshold, then the users are marked ascandidates to be scheduled in MU-MIMO mode. For unitary

precoding this threshold should be zero and for ZF precoding

the threshold can be close to unity.

However, even for the ZF case it is not recommended

to accept terminals with similar channels as candidates. The

reason is that the ZF solution can be more sensitive to errors

if the channels are highly correlated. Hence, by setting a

more conservative threshold (i.e. closer to zero) the overall

complexity of the scheduler is simplified. This is due to the

smaller number of terminals that have to be evaluated for each

RB, thus reducing the number of computed precoding matrices.

B. Decision on MU-MIMO allocationFor each candidate set, eNodeB uses fed back information

to estimate the transmission rate for single-user and multi-

user allocation. Let RSP denote the rate of the primary user

scheduled in single-user mode, RMP denote the rate of the

primary user scheduled in multi-user MIMO mode, and RMSdenote the rate of the secondary user scheduled in multi-user

MIMO mode.

With these definitions, a set of users is allocated in MU-

MIMO mode if and only if

RMP + RMS R

SP (10)

andRMP

Rmin

N, (11)

where N is the number of scheduled resources allocated to

the user and Rmin is a QoS parameter specifying the minimum

supported data rate. The rates RSP, RMP , and R

MS are estimated

from Channel Quality Indication (CQI) fed back by the UE.

The purpose of (11) is to avoid that a weak UE is forced

to transmit in MU-MIMO mode in order to favor transmission

for a much stronger UE which is a secondary user, i.e., RSPand RMP are small, but R

MS is large.

VIII. SIMULATION RESULTS

In this Section we provide system simulation results toevaluate the impact of varying precoding granularity. We also

evaluate the performance loss if the interferers precoding

vector and transmission is not known.

System simulations were done for 2x2 antenna configura-

tion, TU Case 1 channel model [8], 10 MHz bandwidth, 20

users per sector, and a regular grid of 19 cells (57 sectors).

Precoding is based on 3-bit SU-MIMO codebook agreed in

3GPP [1]. For unitary precoding, only four precoding vectors

are considered, corresponding to two unitary matrices. The

receiver is as defined in Section V. Frequency domain packet

scheduling as described in Section VII, with scheduling granu-

larity of 5RBs, i.e. the minimum allocation for a terminal is 60consecutive subcarriers, corresponding to 900 kHz. The total

number of available RBs for 10 MHz bandwidth is equal to

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 112.5

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TX correlation

Avg.sectorthroughput[Mbps]

SUMIMO

UN512

UN256

ZF512

ZF256

Figure 2. Average sector throughput for Rmin = 256 kbps and Rmin =512 kbps as a function of TX correlation. Also shown is the performance ofopen-loop SU-MIMO transmission.

50 [6]. Proportional-fair scheduling algorithm is used in both

time and frequency domains [7].

In principle, the precoder should be computed indepen-

dently for each subcarrier, as shown in Section IV. However,

such frequency granularity is not of practical use, and the same

precoding vector must be applied to a group of subcarriers.

Two different precoding granularities have been simulated:

5 RBs or 50 RBs. A granularity of 5 RBs implies that the UE

must feedback 10 PMI for each subframe, compared to a single

PMI feedback in the case of 50 RBs granularity. Moreover, the

applied precoding vectors must be transmitted in the downlink

control channel as well, especially if eNodeB is allowed to

utilize different precoding vectors than the ones signaled by

the UE. Such situation can happen if ZF precoding is used, or

if the PMI was received with error.

Figure 2 shows the average sector throughput for Rmin =256 kbps and Rmin = 512 kbps as a function of TX correlation.Performance of open-loop SU-MIMO transmission is shown

for comparison. The SU-MIMO scheme simulated in this

article is the Selective Per Antenna Rate Control (S-PARC)[9]. It can be seen from the figure that performance of open-

loop SU-MIMO degrades with increased TX correlation, as

expected. However, performance of MU-MIMO improves with

TX correlation, since this allows better separation between the

streams transmitted to each user. It is observed that the system

only benefits from the higher utilization of MU-MIMO for

very high spatial correlation. Otherwise, a more conservative

adaptation between single stream and MU-MIMO transmission

results in higher sector throughput.

Figure 3 shows the average sector throughput for unitary

precoding for different precoding granularities in frequency

domain and for different receivers. The results are shownfor a receiver that is aware of the transmission to other

users (LMMSE), and for a receiver that is not aware of

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