# Optimal Detectors For 4g Lte Communication Biology Essay

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Multiple Input Multiple Output techniques are used to realize practical high data rate systems which laid the foundation of Long Term Evolution. Various transmission techniques like Transmit Diversity (TxD), Open Loop Spatial Multiplexing (OLSM) and Closed Loop Spatial Multiplexing (CLSM) are deployed in the realm of MIMO. The spectral efficiency is improved with the help Orthogonal Frequency Division Multiplexing (OFDM). In this paper we will focus on CLSM, to evaluate its performance with the help of Zero Forcing (ZF), Minimum Mean Sqaure Error (MMMSE), SoftSphere Decoder (SSD), SSD K-Best (SSDKB) and SIC receivers to find the optimal decoder in LTE environment. The SSD, SSD-KB and SIC uses MMSE based equalizers. The channel environment used are Additive White Gaussian (AWGN), Vehicular A (VehA), Vehicular B (VehB) and an outdoor Pedestrian (Ped B) channel model . A Least Square (LS) estimated feedback obtained by the averaging of two channel instances is used to improve BLER in the case of fading channels.

Keywords-VehB, SSD, SIC, CLSM, LTE , and LS.

the parameters specified by the 3GPP working group [4]. In the following paper Section II describes the channel model and receiver algorithm. In Section III, the CLSM mode of transmission is explained. The Section IV explains outcome of these simulations and observations. Conclusions are given in Section V.

II. CHANNEL MODEL

The proposed MIMO [2] system model consisting of NT transmit antennas and MR receive

antennas can be defined by the following Equation (1).

where y is the received vector, H is the

channel coefï¬cient matrix of the dimensions M

deï¬ning

the channel gains and is the noise.

z is assumed to be (i.i.d) Zero Mean Circularly Symmetric

Complex Gaussian (ZMCSCG). The channel H is deï¬ned by

the channel delay proï¬le.

The input is divided into different streams of data with the

help of spatial demultiplexer. The streams are than processed

by the turbo decoder to provide communication at low values

of SNR. IFFT is used to provide computational efï¬ciency and

cyclic preï¬x is added to maintain synchronization.The streams

are passed through the inter-leaver after the channel coding

is applied. The inter-leaver processes the input such that the

consecutive bits are placed far apart to avoid burst error due

to fading. The modulation scheme is than applied which in

this case is 16-QAM with an effective coding rate of 0.6016.

The modulated data is passed through the serial to parallel

converter. On reception data is processed with the decoder.

I. INTRODUCTION

Wireless communications continue to strive for higher data rates and a better link reliability in order to provide more ad- vanced services on the go. The use of multiple antennas at both the transmitter and receiver side, i.e., multiple-input multiple- output (MIMO) communications, is one of the most promising technologies to fulfill these demands. Indeed, MIMO systems are capable of achieving increased data rates and an improved link reliability compared to single-antenna systems without the aid of additional bandwidth or transmit power. These im- provements, however, require the use of more computationally intensive data detection algorithms at the receiver side. In particular, optimum data detection can easily become complex. Conventional sub-optimum detection techniques have a low computational cost but their performance is in general less significant to that of optimum data detection. Thus, there is a strong demand for computationally efficient data detection algorithms that are able to reduce this performance gap.

In this paper we mainly focus on Zero Forcing (ZF), Minimum Mean Sqaure Error (MMSE), SoftSphere Decoder (SSD), SSD K-Best (SSDKB) and SIC receivers to find the optimal decoder in LTE environment. The SSD, SSD-KB and SIC uses MMSE based equalizers. The channel environment used are Additive White Gaussian (AWGN), Vehicular A (VehA), Vehicular B (VehB) and an outdoor Pedestrian (Ped B) channel model .

These simulation results achieved meet industrial standards with the help of link level LTE simulator [1] compliant with

hMR ,1 hMR ,2 Â· Â· Â· hMR ,NT

where y= [y1 y2 Â· Â· Â· yMR ] is the received vector, H is the channel coefficient matrix of the dimensions MR Ã- NT defin- ing the channel gains and z = [z1 z2 Â· Â· Â· zMR ] is the noise. z is assumed to be (i.i.d) Zero Mean Circularly Symmetric Complex Gaussian (ZMCSCG). The channel H is defined by the channel delay profile.

The input is divided into different streams of data with the help of spatial demultiplexer. The streams are than processed by the turbo decoder to provide communication at low values of SNR. IFFT is used to provide computational efficiency and cyclic prefix is added to maintain synchronization.The streams are passed through the inter-leaver after the channel coding is applied. The inter-leaver processes the input such that the consecutive bits are placed far apart to avoid burst error due to fading. The modulation scheme is than applied which in this case is 16-QAM with an effective coding rate of 0.6016. The modulated data is passed through the serial to parallel converter. On reception data is processed with the decoder.

A. Receiver Algorithm

A brief description of the receivers is given below:

1) ZF Receiver: Zero-Forcing (ZF) detection is the simplest and effective technique for retrieving multiple transmitted data streams at the receiver with very little complexity.

The probability density function (PDF) for the signal-to noise-plus-interference ratio (SINR) at the output of a zero

Fig. 1. Block diagram of a MIMO transmission scheme.

forcing (ZF) detector in a flat fading channel was derived in

[3], [4].

The zero-forcing (ZF) technique nullifies the interference by the following weight matrix:

1

and canceling unwanted interference, such that the signal-to interference-and-noise ratio (SINR) is maximized.

In [5], receive antennas are used for spatial diversity to increase the desired signal power, while in [6], receive an-

tennas are used to cancel interference from the strongest

WZ F = H H H âˆ’

H H , (3)

interferer nodes. In [7], MMSE receivers are used and the

where (.)H denotes the Hermitian transpose operation. In other words, it inverts the effect of channel as

xËœZ F = WZ F y;

= x + zËœZ F , (4)

1

average spectral efficiency, a per-link performance measure, was obtained in the large antenna regime. In [8], [9], [10], by using sub-optimal and MMSE linear receivers, the results of transmission capacity were shown to scale linearly with the number of receive antennas.

In order to maximize the post-detection signal-to-

where zËœZ F = WZ F z = H H H âˆ’

H H z. Note that the error

interference plus noise ratio (SINR), the MMSE weight matrix

performance is directly connected to the power of zËœZ F . (i.e.,

kzZËœF k2 ). The post-detection can be calculated using SVD as

is given as

WM M SE

= (HH

H + Ïƒ2 I )âˆ’1 H H

, (9)

2 H H )âˆ’1 H H

(5)

2

Note that the MMSE receiver requires the statistical infor-

= V X .2 V H âˆ’1 V X U H z

V X .âˆ’1 U 2

(6)

(7)

mation of noise Ïƒ2 . Note that the ith row vector wi,M M SE

of the weight matrix in Equation 9 is given by solving the

following optimization equation:

Since kQxk

= xH QH Qx = xH x = kxk2

for a unitary ma- W

= arg min

|whi | Ex ,

trix Q, the expected value of the noise poweris given as

i,M M SE

w =(w1 ,...,wNT

) j=1,j=i |whi |

+ kwk 2

2

(10)

E nkzZËœF k2 o = E

X .âˆ’1 U H z

Using the MMSE weight in Equation 9, we obtain the

2 2

following relationship:

= E ntr(X .âˆ’1 U H zzH U X .âˆ’1 )o

= tr(X .âˆ’1 U H E zzH U X .âˆ’1 )

= tr(Ïƒ2 X .âˆ’1 U H U X .âˆ’1 )

= Ïƒ2 tr(X .âˆ’2 )

xËœM M SE = WM M SE y (11)

= (H H + Ïƒ2 I )âˆ’1 H H z

= xËœ + zËœM M SE

NT 2

H 2 âˆ’1 H

= X Ïƒz

where zËœM M SE = ((H

+ Ïƒz I )

H z). Using SVD, the

2

i=1 i

(8)

post detection noise poweris expressed as

âˆ’1

2) MMSE Receiver: Multiple antennas offer significant per-

E {kzËœM M SE k} = E

X +Ïƒ2 X .âˆ’1

U H z

formance improvements in wireless communication systems

NT 2 2

by providing higher data rates and more reliable communica-

X Ïƒz Ïƒi

2

(12)

tion. A practical method which can achieve high data rates is to employ spatial multiplexing transmission with low complexity linear receivers, like minimum-mean-squared-error (MMSE) receiver.

The MMSE receiver is particularly important as it uses its receive degrees of freedom (DOF) to optimally trade off strengthening the energy of the desired signal of interest

i=1 (Ïƒ2 z

i + Ïƒ2 )

For a MMSE receiver it is preferable to have a high density of single-stream transmissions than a low density of multi- stream transmissions. This is because in MMSE detection, the interference powers from the strongest interferers source remaining after interference-cancellation are weaker for single stream transmission than multi-stream transmission.

Fig. 2. Illustration of the sphere in sphere decoding.

3) Soft Sphere Decoder: SSD gives the ML solution with soft outputs. These ML symbols are chosen from a reduced set of vectors within the radius of a given sphere rather than a complete vector length. The radius of the sphere is adjusted so that there exists only one ML symbol within the given radius. SSD provides sub optimal ML solution [11] with reduced complexity. MMSE is used to estimate the channel. The Soft Sphere Decoder (SSD) solution is given by the following equation.

argmin ky âˆ’ Hxk = argmin(x âˆ’ xË†)T HT H(x âˆ’ xË†), (13)

Fig. 4. Block diagram of a MIMO Transmission using CLSM.

III. TRANSMISSION MODELS

MIMO improve the spatial and multiplexing gains by the use of diversity and spatial multiplexing [12]. The methods used to enhance the diversity and multiplexing gains is CLSM.

A. Closed Loop Spatial Multiplexing

Independent data streams are transmitted from the NT transmit antennas in CLSM 4. In CLSM essential amount of CSI is used as feedback which enables us to achieve high throughput with lower BLER.

x x

where (Â·)T denotes the transpose of matrix. Equation 13 gives the unconstrained solution of the real time system. This means that the ML solution can be determined by the term (x âˆ’ xË†)T HT H(x âˆ’ xË†). No ML value exists outside the sphere because there ML value is greater than those which exists inside the sphere [2] hence making a unique detection as in Figure 2 .

4) K- Best Soft Sphere Decoder: The K-Best SSD is a variant of SSD, and performs its operation on K best selected optioins unlike the SSD which considers only one point.

5) Successive Interference Canceller Decoder: SIC re- ceiver is a collection of linear receiver banks which succes- sively cancels the interference which in this case are MMSE receivers, as shown in the Figure 3

Fig. 3. SIC Receiver.

IV. SIMULATION RESULTS AND DISCUSSION

In this paper, Hybrid Automatic Repeat Request (HARQ) is set to a maximum value of 03 to provide retransmission in the case of fading i.e. block fading in this scenario. Soft decisions are made using the max log map criterion for lower probability of error. VehA and VehB channels are considered for observing the LTE link behavior. The feedback for supporting CLSM transmission mode is obtained by channel averaging of two channel realizations. A complete detail of the parameters used in the simulations are given by the Table 1.

Parameters Values

Receivers ZF, MMSE, SSD, SSDKB, SIC Channel Veh A, Veh B, PedB, AWGN User Speed 30 Km/h, 120 Km/h and 3Km/h Fading Type Block Fading Retransmission Algo. HARQ

No of Retransmissions 03

Soft Demapper Max Log Map

Modulation 16 QAM, CQI 9

Feedback Estimation Least Square

Feedback Bits 01

Resource Blocks 06

TABLE I

LTE SI M U L AT I O N PA R A M E T E R S .

In case of AWGN channel, from Figures 5 and 6 it can be seen that at higher values of SNR all the receivers are per- forming equally good giving almost the same throughput and BLER. In case of lower SNR, in AWGN channel SIC receiver gives a better output as compared to all other receivers.

In case of VehA channel, from Figures 7 and 8 it can be seen that at higher values of SNR, SIC receiver is giving the

0

8 10

SIC 2x2

7 SIC 4x4

ZF 4x4

ZF 2x2

6

MMSE 4x4

MMSE 2x2

5 SSD 4x4

SSD 2x2

MMSEâˆ’SIC 4x4

âˆ’1 MMSEâˆ’SIC 2x2

4 SSDKB 4x4

SSDKB 2x2

10

ZF 4x4

ZF 2x2

3

2

1

âˆ’2

0 10

MMSE 4x4

MMSE 2x2

SSD 4x4

SSD 2x2

SSDKB 4x4

SSDKB 2x2

âˆ’5 0 5 10 15 20 25 30

SNR [dB]

âˆ’5 0 5 10 15 20 25 30

SNR [dB]

Fig. 5. Receivers throughput in AWGN Channel using CLSM.

Fig. 8. Receivers BLER in VehA Channel using CLSM.

0

10

SIC 2x2

âˆ’1 SIC 4x4

10

ZF 4x4

ZF 2x2

MMSE 4x4

MMSE 2x2

SSD 4x4

SSD 2x2

SSDKB 4x4

âˆ’2 SSDKB 2x2

10

8

MMSEâˆ’SIC 4x4

7 MMSEâˆ’SIC 2x2

ZF 4x4

ZF 2x2

6

SSD 4x4

MMSE 2x2

5 MMSE 4x4

SSD 2x2

4 SSDKB 4x4

SSDKB 2x2

3

2

1

0

âˆ’5 0 5 10 15 20 25 30

SNR [dB]

âˆ’5 0 5 10 15 20 25 30

SNR [dB]

Fig. 6. Receivers BLER in AWGN Channel using CLSM.

Fig. 9. Receivers throughput in VehB Channel using CLSM.

0

8 10

MMSEâˆ’SIC 4x4

7 MMSEâˆ’SIC 2x2

ZF 4x4

ZF 2x2

6

MMSE 4x4

MMSE 2x2

5 SSD 4x4

SSD 2x2

MMSEâˆ’SIC 4x4

âˆ’1 MMSEâˆ’SIC 2x2

4 SSDKB 4x4

SSDKB 2x2

10

ZF 4x4

ZF 2x2

3

2

1

âˆ’2

0 10

SSD 4x4

MMSE 2x2

MMSE 4x4

SSD 2x2

SSDKB 4x4

SSDKB 2x2

âˆ’5 0 5 10 15 20 25 30

SNR [dB]

âˆ’5 0 5 10 15 20 25 30

SNR [dB]

Fig. 7. Receivers throughput in VehA Channel using CLSM.

best out put in terms of throughput and BLER while SSD- KB is providing a sub optimal output. For the lower values of SNR, SIC is the best performer among all the receivers while SSD is the second best.

Fig. 10. Receivers BLER in VehB Channel using CLSM.

In case of VehB channel, from Figures 9 and 10 it can be seen that at higher values of SNR, SIC receiver is the best performer in terms of throughput and BLER while SSD-KB is providing a sub optimal output. For the lower values of

8

SIC 4x4

7 SIC 2x2

ZF 4x4

ZF 2x2

6

MMSE 4x4

MMSE 2x2

5 SSD 4x4

SSD 2x2

4 SSDKB 4x4

and BLER requirements of the user keeping in view the performance/complexity trade-off in case of both high and low values of SNR. There is a great room for improvement in terms of throughput and BLER with the help of CLSM, if we are able to develop a way to enhance the effect of feedback without increasing the overhead.

R

SSDKB 2x2

3

2

1

0

âˆ’5 0 5 10 15 20 25 30

SNR [dB]

Fig. 11. Receivers throughput in PedB Channel using CLSM.

0

10

SIC 4x4

âˆ’1 SIC 2x2

10

ZF 4x4

ZF 2x2

MMSE 4x4

MMSE 2x2

SSD 4x4

SSD 2x2

SSDKB 4x4

âˆ’2 SSDKB 2x2

10

âˆ’5 0 5 10 15 20 25 30

SNR [dB]

Fig. 12. Receivers BLER in PedB Channel using CLSM.

SNR, SIC is the best performer among all the receivers while SSD is the second best.The BLER in this case is worst among all the channel conditions and the reception of correct data is hardly expected.

In case of outdoor pedestrian channel model Ped B, from Figures 11 and 12 the performance of SIC is no different as in the case of VehA and VehB channel. SSD and SSDKB performs almost same at the higher values of SNR. At the lower values of SNR, the 2x2 version of SIC receiver is performing better than the 4x4 versions of SSD, SSDKB , MMSE and ZF receivers in terms of throughput and SNR.

V. CONCLUSIONS

In order to achieve higher through put in LTE, SIC receiver must be used in all channel models. Considering the perfor- mance/complexity trade off SSD and SSDKB receivers pro- vide a reasonable output in terms of throughput and BLER as compared with the SIC receiver. This performance/complexity trade-off makes SSD and and its variant SSDKB as the optimal receivers. A carefully designed mechanism is needed to select the optimal receiver according to the throughput

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