Adaptive Modulation Coding in MIMO-OFDM forWiMAX using GNU Radio

B. Siva Kumar Reddy and Lakshmi BoppanaDepartment of Electronics and Communication Engineering

National Institute of Technology, WarangalAndhra Pradesh, India

Abstract-Mobile WiMAX is a broadband wireless accessbased on OFDM/OFDMA technology which employs Adap-tive Modulation and Coding (AMC) scheme to attain higherdata rates. In this paper, a selection strategy is incorporatedwith GNU Radio for the determination of Modulation andCoding Scheme (MCS) level dependent upon channel esti-mation parameter over AWGN and Rayleigh fading channels.MCS level choice has been done for different threshold valuesby varying channel model and FFT size. BER (Bit Error Rate)execution of WiMAX physical layer is investigated utilizingConvolutional coder, RMG (Reed-Muller-Golay) coder andRM (Reed-Muller) coders over AWGN and Binary SymmetricChannels by changing number of bits for every byte andmodulation schemes in GNU Radio Companion. In this paper,various 2x2 MIMO frameworks are analysed under digitalmodulations and Convolutional code rates. The aim of thispaper is to provide a thought about the benefits of multipleantenna systems over single antenna systems deploymentsusing GNU Radio. keywords- AMC, GNU Radio, MIMO,OFDM, STBC, WiMAX.

I. INTRODUCTION

Latest requirements in wireless communications have in-creased the need for WiMAX (Worldwide Interoperabilityfor Microwave Access) broadband wireless access technology[1] and it supports both fixed and mobile wireless broad-band (Fixed WiMAX (IEEE 802.16d), mobile WiMAX (IEEE802.16e-2005)). As of late, researchers have shown an in-creased interest in OFDM (Orthogonal Frequency-DivisionMultiplexing) [2] as the present transmission plan to empowerhigh-speed data, multimedia and video communications. Mul-tiple access is possible in OFDMA (a multi-user versionof the OFDM scheme) [3] by distributing subsets of sub-carriers to some clients. This allows simultaneous low data ratetransmission from number of clients. OFDM is a broadbandwireless connectivity for higher data transmission. MIMO(Multi Input Multi Output) is one thought to enhance linkcapacity and spectral efficiency. The thoughts of MIMO andOFDM have been combined to structure another class ofMIMO-OFDM [4] framework to get higher throughput andhigher data rate simultaneously for WiMAX provisions.

WiMAX standard supports a full-range of smart antennatechniques like spatial transmit diversity and Spatial Multi-plexing (SM) [5]. Spatial transmit diversity is accomplished

by utilizing Alamouti’s Space-Time coding [6]. SM can alsobe utilized to add the error-free maximum throughput. Higherorder modulation schemes with SM improve the link through-put, however require high SNR to get low Packet ErrorRates (PER). Space-Time Block Coding (STBC) [7] allowsfor strong diversity gain, however couldn’t pick up the linkthroughput without utilization of Adaptive Modulation andCoding (AMC) [7].

Software Defined Radio (SDR) [8] is a radio communicationframework where the hardware components (e.g. mixers, am-plifiers, filters, detectors, modulators/demodulators, and so on.)executed by method of programming on a personal computer.In this paper, SDR utilizes USRP N210 (Universal SoftwareRadio Peripheral) [8] as a hardware stage and GNU Radio [9]as a software. The execution of data transmission over wirelesschannels is well captured by observing their BER, which is acapacity of SNR at the receiver. The WiMAX PHY layer isexecuted utilizing different coders (Convolutional Coder, RMG(Reed-Muller-Golay) coder and RM (Reed-Muller) coder) inGNU Radio.

II. SOFTWARE DEFINED RADIO

In this paper, GNU Radio [9] is the programming partof the SDR platform. GNU Radio is an open source toolcompartment for developing software radios, in which all thesignal handling operations might be performed by utilizingprogramming. GNU Radio gives a library of signal transform-ing blocks for executing different applications. GNU Radiocould be used as an Open Source Data Acquisition System byadding/creating essential blocks. In this paper python scriptfor MCS determination and Alamouti STBC coder is mixedwith OFDM module.

III. MIMO-OFDM TRANSCEIVER

The SISO model is extended to MIMO-OFDM by includingAlamouti encoder [4] as shown in Fig 1. Main blocks arereported as follows:

A. Alamouti STBC coder

The basic principle of Alamouti encoder is that, first groupthe symbols into pairs of two. In the first time slot, send x1

and x2 from the first and second antenna. In second time slotsend −x∗

2 and x∗1 from the first and second antenna. In the

third time opening, send x3 and x4 from the first and second

2014 IEEE Region 10 Symposium

978-1-4799-2027-3/14/$31.00 ©2014 IEEE 618

Fig. 1. A basic MIMO-OFDM Transeiver model

antenna. In fourth time space, send −x∗4 and x∗

3 from the firstand second antenna and so on.

The received signal in the first time slot is given by [6],[y11y12

]=

[h11 h12

h21 h22

] [x1

x2

]+

[n11

n12

]. (1)

Assuming that the channel remains constant for the secondtime slot. The received signal in the second time slot is,[

y21y22

]=

[h11 h12

h21 h22

] [−x∗

2

x∗1

]+

[n21

n22

]. (2)

where y11 , y12 are the received information at time slot 1 on

gain receive antenna 1, 2 separately; y21 , y22 are the gained data

at time opening 2 on receive antenna 1, 2 individually; hij isthe channel from ith get receiving antenna to jth transmitreception device; x1, x2 are the transmitted symbols; n1

1, n12

are the noise at time space 1 on appropriate antenna 1, 2individually; n2

1, n22 are the noise at time slot 2 on receive

antenna 1, 2 separately.Combining the equations at time slot 1 and 2,⎡

⎢⎢⎣y11y12y2∗1y2∗2

⎤⎥⎥⎦ =

⎡⎢⎢⎣h11 h12

h21 h22

h∗12 −h∗

11

h∗22 −h∗

21

⎤⎥⎥⎦[

x1

x2

]+

⎡⎢⎢⎣

n11

n12

n2∗1

n2∗2

⎤⎥⎥⎦ . (3)

We know, for a general m x n matrix, the pseudo inverse isdefined as, H+ = (HHH)−1HH

(HHH) =

[|h11|

2 + |h21|2 + |h12|

2 + |h22|2 0

0 |h11|2 + |h21|

2 + |h12|2 + |h22|

2

].

(4)Since this is a diagonal matrix, the inverse is just the inverse

of the diagonal elements, i.e

(HHH)−1 =

[1

|h11|2+|h21|2+|h12|2+|h22|20

0 1

|h11|2+|h21|2+|h12|2+|h22|2

].

(5)The estimate of the transmitted symbol is,

[x1

x∗2

]= (HHH)−1HH

⎡⎢⎢⎣y11y12y2∗1y2∗2

⎤⎥⎥⎦ . (6)

B. CHANNEL MODEL

1) Rayleigh fading model: The phase of each path canchange by 2π radian when the delay τn(t) adjusts by 1

fc.

Assuming that fc is extensive, relative little varieties in themedium can cause change of 2π radians. Since the separationbetween the devices are significantly more than the wavelengthof the carrier frequency, it is sensible to assume that the stageis consistently conveyed between 0 and 2π radians and thephases of each path are independent.

The point when there are more number of paths, utiliz-ing Central Limit Theorem, each way might be acted likecircularly symmetric complex Gaussian irregular variable byrequiring time as the variable. This model might be called asRayleigh fading channel model.

A circularly symmetric complex Gaussian random variableis as z = x+ jy, here real and imaginary parts are zero meaniid Gaussian random variables. For a circularly symmetriccomplex random variable [10],

E[Z] = E[ejθZ] = ejθE[Z] (7)

The statistics of a circularly symmetric complex Gaussianrandom variable is completely assigned by the variance, σ2 =E[Z2]. The probability density of the magnitude |Z| is,

p(z) =z

σ2e−z

2

2σ2 , z ≥ 0 (8)

is called as a Rayleigh random variable. Hence, Rayleighfading channel model is reasonable for an environment wherethere are large number of reflectors.

C. Receiver

All the opposite operations could be performed in thissegment as indicated in Fig. 1. Excessively, channel estimationand Adaptive Modulation and Coding might be performedat receiver, are illustrated obviously in the accompanyingsections.

IV. ADAPTIVE MODULATION AND CODING

WiMAX supports a sort of modulation and coding schemesand takes into consideration the plan to change on a burst-by-burst support for every connection, in light of channel

2014 IEEE Region 10 Symposium

978-1-4799-2027-3/14/$31.00 ©2014 IEEE 619

conditions. Using the channel quality feedback indicator, themobile can provide the base station with feedback on thedownlink channel quality as indicated in Fig. 1. For the uplink,the base station estimates the channel quality, taking intoaccount the received signal quality.

Fig. 2. A selection strategy for AMC selection

Fig. 3. BER performance of 2x2 STBC MIMO-OFDM through Rayleighfading channel (FFT size=512)

0 5 10 15 20 2510

−5

10−4

10−3

10−2

10−1

100

SNR

BE

R

1/2 QPSK1/2 16−QAM1/2 64−QAM3/4 QPSK3/4 16−QAM3/4 64−QAM

Fig. 4. BER performance of SISO-OFDM through Rayleigh fading channel(FFT size=1024)

The channel estimator parameter (P) may be SNR/CINR orchannel attenuation factor (k). In the Fig. 2, the thresholdsare given by the letters A, B, C, D, E and F; where A is the

0 5 10 15 20 2510

−5

10−4

10−3

10−2

10−1

Eb/No, dB

Bit E

rror

Rate

theory (nTx=1,nRx=1)theory (nTx=1,nRx=2, MRC)theory (nTx=2, nRx=1, Alamouti)sim (nTx=2, nRx=2, Alamouti)

Fig. 5. BER for 2x2 Almouti STBC over Rayleigh fade channel

Fig. 6. Throughput performance of 2x2 SM-MIMO-OFDM system [5]

lowest threshold value, i.e., A < B < C < D < E < F . TheModulation and Coding Scheme (MCS) has picked dependentupon estimation parameter (P) as per limits given by the clientmodel. The threshold values might be picked carefully fromthe BER vs SNR performance curves. Threshold values varywith the channel model and with size of FFT utilized. Figs.3, 4 show the BER vs SNR performance through Rayleighfading channel for FFT measure 512, 1024 individually and itcan be observed that the BER performance MIMO system with2x2 STBC gives a gain of about 5 dB over the correspondingSISO system at a BER of 10−3. From Fig. 5, it can beobserved that the BER performance of 2x2 is better than1x2, because the effective channel combining the data from 2receive antennas over two symbols results in a diversity orderof 4. Generally, in case of Alamouti STBC, with k receiveantennas the diversity order for 2 transmit antenna is 4k. Table1 shows the threshold values noted from SNR vs BER curvesdrawn for Fixed WiMAX (FFT size is 256) through AWGNchannel (These SNR vs BER curves are not shown in thepaper). The point when AMC is incorporated in WiMAX; BERperformance & throughput are improved as demonstrated in

2014 IEEE Region 10 Symposium

978-1-4799-2027-3/14/$31.00 ©2014 IEEE 620

TABLE IAMC SELECTION ACOORDING TO SNR THRESHOLDS (IN DB) OVER AWGN CHANNEL (FFT SIZE-256)

Modulation SNR SNR SNRSchemes BER− 10−2 BER− 10−3 BER− 10−4

BPSK 1/2 0.5 < SNR < 3.5 2.5 < SNR < 5.5 4 < SNR < 7BPSK 3/4 3.5 < SNR < 4 3.5 < SNR < 6 7 < SNR < 7.5QPSK 1/2 4 < SNR < 7 6 < SNR < 9 7.5 < SNR < 10.5QPSK 3/4 7 < SNR < 8 6 < SNR < 9 7.5 < SNR < 10.58QAM 1/2 8 < SNR < 10.5 10 < SNR < 12.5 11.5 < SNR < 148QAM 3/4 11 < SNR < 13.5 13.5 < SNR < 15.5 15 < SNR < 17

16QAM 1/2 10.5 < SNR < 11 12.5 < SNR < 13.5 14 < SNR < 1516QAM 3/4 13.5 < SNR < 16.5 15.5 < SNR < 18.5 17 < SNR < 2032QAM 1/2 13.5 < SNR < 16.5 15.5 < SNR < 18.5 17 < SNR < 2032QAM 3/4 16.5 < SNR < 19.5 18.5 < SNR < 22 20 < SNR < 2364QAM 1/2 16.5 < SNR < 19.5 18.5 < SNR < 22 20 < SNR < 2364QAM 3/4 SNR > 19.5 SNR > 22 SNR > 23

Figs. 3,4 and 6 (Coded vs Uncoded OFDM characteristics areshown in ref [10]). Increase in modulation order causes toimprovement in throughput is indicated in Fig. 6. The STBCraises the best execution at low to medium values of SNRbecause of its strength in poor channel conditions and SM isthe best decision at high SNR due to increased error-free datarate as shown in Fig. 7. The switching point between STBCand SM is 20 dB. This quality will improve with expandingspatial correspondence.

Fig. 7. AMC and switching point between STBC and SM systems

V. EXPERIMENTAL RESULTS

Because of adaptability in the physical layer of WiMAX,data rate execution differs dependent upon the operatingparameters. Parameters that have a significant effect on thephysical-layer information rate are channel bandwidth and themodulation and coding scheme used. Different parameters,such as number of subchannels, OFDM guard time, and over-sampling rate, also have an impact. The BER execution hasbeen analyzed by associating the blocks through BSC (Binarysymmetric channel) as demonstrated in Fig. 8. A 2.4 GHzsignal is captured from laboratory environment by utilizingUSRP N210 hardware. This signal is given as file source (input

signal) for all the recreations. Throttle block is incorporatedto reduce the load on CPU (Central Processing Unit) andafterwards the signal has encoded by the convolutional encoderand next passed through the Binary Symmetric Channel anddecoded. To think about the effects between coded signal anduncoded signal, a BER block has been associated. To observeoutput signals, different sinks (Number sink, Scope sink) areconnected as indicated in Fig. 8. Convolutional encoder isswapped with RMG coder, RM coder and outcomes are notedby varying number of bits for every byte as indicated in TableII. The coded and uncoded BER waveforms are indicated inFigs 9 and 10 respectively. It can be seen that the uncodedversion reflects higher BER than coded version. From theTable II, it can be concluded that BER performance has beenimproved as number of bits per byte increased and BER ismore for Convolutional coder compared to RMG coder andRM coders.

Fig. 9. BER for Convolutional coded signal over BSC channel, seen at scopesink 1.

As indicated in Fig. 11, the incoming signal from the filesource is channel coded by the scrambler, RMG encoderand interleaving separately and passed through the OFDMmodulator to produce OFDM symbols and afterwards passedthrough the multiply constant block and channel model. The

2014 IEEE Region 10 Symposium

978-1-4799-2027-3/14/$31.00 ©2014 IEEE 621

Fig. 8. GNU Schematic for BER for uncoded and Convolutional coded transmission over BSC channel.

TABLE IIRESULTS OBTAINED FOR BER PERFORMANCE WITH CHANNEL CODING OVER AWGN CHANNEL

Coder Mod Scheme Bits per byte BER valueRMG Coder BPSK 1 0.5001434684RMG Coder BPSK 4 0.4068774879RMG Coder BPSK 8 0.3892548680

Average 0.43209194RMG Coder QAM64 1 0.5004814267RMG Coder QAM64 4 0.4189103246RMG Coder QAM64 8 0.4092760682

Average 0.44288927CCSDS Coder BPSK 1 0.4585958719CCSDS Coder BPSK 4 0.5740551949CCSDS Coder BPSK 8 0.5869382620

Average 0.53986311CCSDS Coder QAM64 1 0.4601847827CCSDS Coder QAM64 4 0.5721712112CCSDS Coder QAM64 8 0.5870822072

Average 0.53981274RM Coder BPSK 1 0.5000710487RM Coder BPSK 4 0.4210021496RM Coder BPSK 8 0.3852755427

Average 0.43544958RM Coder QAM64 1 0.5001475811RM Coder QAM64 4 0.42152449419RM Coder QAM64 8 0.4092907906

Average 0.44365444

multiply constant block is utilized to enhance the amplitude ofthe OFDM symbols. The channel model could be reconfiguredby changing frequency offset, noise parameters. The generatedOFDM symbols are demodulated, deinterleaved, decoded anddescrambled respectively. The RMG coder is replaced withConvolutional coder, RM coder and results are noted in TableIII by varying modulation schemes and bits per byte in BERblock.

VI. CONCLUSIONS

This paper has put forth an itemized investigation of thebenefit of MIMO when applied to WiMAX. To get higher

throughput, higher data rate; MIMO and OFDM are examined.SISO-OFDM has augmented to MIMO-OFDM by integratingSTBC Almoutis encoder with SISO model. BER executionhas analyzed for different modulation schemes through variouschannels (Rayleigh, AWGN and Binary symmetric channels)by changing distinctive encoders, such as Convolutional, RMGand RM coders. The simulation results demonstrated thatconvolutional encoder has better BER performance contrastedwith remaining two. A selector block has made and combinedwith OFDM block to select proper MCS level dependentupon the channel estimation parameter (SNR/CINR, Channel

2014 IEEE Region 10 Symposium

978-1-4799-2027-3/14/$31.00 ©2014 IEEE 622

Fig. 11. GNU Schematic for BER of 64QAM-OFDM with RMG coder channel coding.

Fig. 10. BER for uncoded signal over BSC channel, seen at scope sink 2.

TABLE IIIRESULTS OBTAINED FOR BER UNCODED AND CODED SIGNAL OVER BSC

CHANNEL

Coder Bits Uncoded Codedper byte BER BER

RMG 1 0.0010421536 0.0099786464RMG 4 0.2802865505 0.0024868969RMG 8 0.3480649889 0.0012434485

CCSDS 1 0.5416055322 0.0099835679CCSDS 4 0.5438777804 0.0024312227CCSDS 8 0.5534156561 0.0012434485

RM 1 0.0202364717 0.0105615864RM 4 0.3020897806 0.0105615864RM 8 0.3504898846 0.0013201983

attenuation factor etc.). The outcomes also presented that, atmore level qualities of SNR, STBC is preferred and at highSNR Adaptive MIMO Switching will be utilized to switch toSM.

REFERENCES

[1] Andrews, Jeffrey G and Ghosh, Arunabha and Muhamed, Rias, ”Fun-damentals of WiMAX: understanding broadband wireless networking,”Pearson Education publications, 2007.

[2] B.Siva Kumar Reddy, Dr.B. Lakshmi ”Concatenated Coding in OFDMfor WiMAX using USRP N210 and GNU Radio” International Journalof Wireless & Mobile Networks, pp.55-68, vol. 5, no. 6, 2013.

[3] Kivanc, Didem and Li, Guoqing and Liu, Hui ”Computationallyefficient bandwidth allocation and power control for OFDMA,” IEEETransactions on Wireless Communications, pp. 1150-1158, vol 2, no.3, 2003.

[4] Li, Qinghua and Li, Guangjie and Lee, Wookbong and Lee, Moon-il and Mazzarese, David and Clerckx, Bruno and Li, Zexian ”MIMOtechniques in WiMAX and LTE: a feature overview,” IEEE Communi-cations Magazine, vol 42, no.5, pp 86-92, 2010.

[5] Zerrouki, Hadj and Feham, Mohamed, ”High Throughput of WiMAXMIMO OFDM Including Adaptive Modulation and Coding,”arXivpreprint arXiv:1002.1954, 2010.

[6] Gong, Yi and Letaief, Khaled Ben ”Low complexity channel estimationfor space-time coded wideband OFDM systems,” IEEE Transactionson Wireless Communications, pp. 876-882, vol. 2, no. 5, 2003.

[7] Fantacci, Romano and Marabissi, Dania and Tarchi, Daniele and Habib,Ibrahim, ”Adaptive modulation and coding techniques for OFDMAsystems,” IEEE Transactions on Wireless Communications, pp 4876-4883, 2009.

[8] B.Siva Kumar Reddy, Dr.B. Lakshmi, ”Channel Coding and Clippingin OFDM for WiMAX using SDR,”International Journal on RecentTrends in Engineering & Technology, pages 66-74, vol. 9 , no. 1, 2013.

[9] Tucker, D Casey and Tagliarini, Gene A, ”Prototyping with GNU radioand the USRP-where to begin,” Southeastcon, 2009. SOUTHEAST-CON’09. IEEE, pp. 50-54, 2009.

[10] B.Siva Kumar Reddy, Dr.B. Lakshmi,et al. ”Modulation switching inOFDM for WiMAX through Rayleigh fading channel using GNUradio,” IEEE International Conference on Advanced Electronic Systems(ICAES), pp. 331-333, 2013.

2014 IEEE Region 10 Symposium

978-1-4799-2027-3/14/$31.00 ©2014 IEEE 623