978-1-4799-5863-4/14/$31.00 ©2014 IEEE

Real-domain SIC for MIMO with FBMC Waveforms

V. Stanivuk, S. Tomić, M. Narandžić and S. Nedić

Faculty of Technical Sciences

University of Novi Sad

Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia

orange@uns.ac.rs

Abstract—This paper proposes 2x2 MIMO OQAM/FBMC

receiver strategy based on successive interference cancellation

(SIC) as an extension of the SISO approach which uses entirely

real-valued formulation of the transmission system model]. Both

increase of throughput and SNR gain are observed through

appropriate maximum ratio combining (MRC) of the soft

symbols pertaining to the receiver-end diversity branches. The

2x1 multi-user detection (MUD) case has been also addressed to

certain extent. Additional gains, essentially related to SISO case,

coming from the cooperative use of in-phase (I) and quadrature

(Q) branches, primarily based on the quadrature noise

components’ independence, as well as from the explicit noise

cancellation within the SIC framework, have also been outlined.

Keywords— successive interference cancellation; staggered

multicarrier waveforms; FBMC; MIMO; diversity; noise prediction

I. INTRODUCTION

Compensation of linear distortions introduced in the

subchannels of a FBMC signal with staggered, i.e. by T/2

offset, in-phase (I) and quadrature (Q) components of

transmitted QAM symbols was the first challenge towards

making it competitive to the traditional CP-OFDM

multicarrier waveform.. This issue has been further

pronounced in various forms of multiple-input multiple-output

(MIMO) configurations, where the so-called (complex-

domain) intrinsic interference [1] has been considered as an

obstacle towards attaining the performance level comparable

with CP-OFDM. To address this within the context of non-

linear data detection methods, in [2] and [3] were proposed

combined (linear) minimum mean square error (MMSE) and

maximum likelihood sequence estimation (MLSE), and the

(entirely) maximum a posteriori probability (MAP)

approaches, respectively. In these cases, to be found also in

[7][9], while relying on the transmission system model in

complex-domain, the intrinsic interference is considered as an

“annoyance”, with a lot of effort/complexity invested in its

avoidance, i.e. partial elimination. However, the orthogonality conditions for the FBMC

formats and single-input single-output (SISO) transmission are determined entirely in the real-domain. For that reason in [4] only the in-phase component of the subchannel signals was used to provide the sufficient statistic for detection of the transmitted signal in the framework of the successive interference cancellation (SIC). Thereby, the subchannel

impulse responses (one from the channel of interest and two related to adjacent channels cross-talk) are estimated as real-valued samples and further used for reconstruction of the in-phase component in an iterative process that is based on MAP-like “soft” estimated data symbols, with optional interaction with the forward error code (FEC) decoder. In the real-domain SIC formulation the intrinsic interference does not figure explicitly and the MAP detection takes places with the halved number of real-valued multiplications in the signal reconstruction step, when compared with the complex-domain formulation.

Consequently, the extension of the SIC SISO framework to the MIMO case becomes free from the notion of the intrinsic interference, in that it becomes included in the system-model description. However, the problem of the MIMO/MISO implicit MUD (multi-user detection) comes to the foreground and needs to be addressed by appropriate detection strategy that distinguishes impact of the residual interference and the additive (Gaussian) noise to the overall estimation variance.

Since the FBMC subchannels signals I-component presents sufficient statistics for the T/2 spaced real data samples, the corresponding Q-component contains the same information and, with the appropriately defined/estimated system-level impulse response, it can be used for signal detection as well. Moreover, since the noise quadrature components are independent, the two components can be processed in such a way to produce at least the AWGN diversity effect, and potentially also the fading related one. Another possibility to enhance the SIC performance for FBMC signal reception is the fact that the analysis filter-bank (AFB) complex-valued output noise samples are correlated at T/2 instants, enabling the noise prediction and cancellation without the causality constraints. This paper thus presents an attempt towards allowing for the FBMC performance to significantly exceed the CP-OFDM performance.

In the following, after presentation of general FBMC SISO transmission system model and its extension to 2x2 MIMO configuration in Section II, the proposed SIC-based receiver structure and related flat fading channels simulation results are presented in Section III, followed by the still generally „problematic‟ 2x1 MUD configuration. The noise prediction and the constructive use of the quadrature complex signal branch are explored in Section IV. The drawn conclusions and the planed future work are given in section V.

II. FBMC TRANSMISSION SYSTEM MODEL

A. SISO to MIMO Extension

In continuous time representation, the OFDM/OQAM

modulated signal is defined by the relation

)()(2

1

12

0

tdjtx k

n

k

kk

M

n

k

n

nk

. (1)

where the symbols k

nd are the real valued (Re{} and Im{}

parts of M-ary QAM) symbols that scale an orthogonal basis:

TnTtkjkn enTtgt /)2/(2)2/()( . (2)

The interfering subchannels take indices between 1k and 2k .

The elementary signal )(tg is a symmetric, real-valued,

square root Nyquist function which is normalized to have

unity power. It has finite time duration ],[ TLTL gg , with T

denoting the QAM signaling interval and its spectra occupies

bandwidth TBg /)1( , where α designates the roll off

factor of subchannels‟ spectra.

After a transmission over the channel with the (complex-

valued) impulse response )(tc , the conventional maximum

likelihood (ML) receiver is obtained by considering (in accordance with the FBMC orthogonality conditions) the real part of the scalar product between the received signal

)(')(*)()( tbtxtcty and the basis functions )(tkn :

dttnTtnTyrTL

TL

k

n

k

n

h

h )2/()2/(Re , (3)

where the over-bar denotes complex conjugation. In general, including the frequency-flat fading channel, the received signal samples can be represented [4] as the output of a MISO matrix filter with real-valued coefficients, superposed by the AFB filtered white Gaussian noise samples

1. The model of

transmission system that includes interference from adjacent subchannels is given [4][8] by the following relation:

1

1' '

',

'

'

'

k

L

Ln

k

n

kk

n

kk

nn

k

n

h

h

bhdr . (4)

where ','kk

nh designates the overall impulse responses related to

interacting subchannels: 0,

'knh is the impulse response in the

referent subchannel k, 1,

'knh represents the interferences from

the upper subchannel with index k+1 and 1,

'k

nh interferences

from the lower subchannel with index k-1. It is worth noting that while in the complex-domain formulation the subchannel impulse response has just one sample, for the real-domain system formulation the impulse response length is

1 In real-domain formulation noise samples are independent, 0

k

kn

k

nbbE ,

while in the complex-domain formulation the are correlated

)1(5.0'' jbbE kkn

kn

.

essentially 12 gh LL , where in the considered case 3gL .

Sets of the direct and the adjacent subchannels cross-talk impulse responses for 100 flat fading realizations could be seen in [8].

Deinter.- MF Decoderr

L_app

'r

σ2

f L_extr

d̂

L_api

Inter.

h

P(r|d=+1/sqrt(2)) P(r|d=-1/sqrt(2))

SIC Detector

Fig. 1. SISO SIC Detector

Detection process in [4] comprises the estimation of the individual impulse responses, successive interference cancellation, matched filtering and FEC decoding, as shown in Fig. 1. The very iterative procedure relies on the SIC block Extrinsic probability in form of the conditional probability

)22/(2)(exp| kksE

knd

knf

knd

knrP . (5)

where the knf is the matched filter (MF) output, calculated (in

simplified form [8]) as

1

1' '

','

''

ˆˆ'k

L

Ln

ks

kn

kkn

kknn

kn Edhrf . (6)

In (6) the term ''' kknnr

represents the residual of the received

signal sample(s) after subtracting influence of all previously

estimated symbols, knd̂ , on the current bin, including itself:

1

1" "

",'"

"'"'

''

''

ˆˆ'

k

L

Ln

kkkn

kkknnn

kknn

kknn hdrr . (7a)

while k

nd̂ is the “soft” estimate from the previous iteration

}{

)(}|{ˆkn

kn

kn

d

k

n

api

d

k

n

k

n

k

n dPdrdEd

(7b)

and ksE represents the symbol energy per subchannel,

calculated in the following manner:

21

1' '

','

ˆ

k

L

Ln

kkn

ks hE . (7c)

The a priory probabilities used for for data samples estimates in (7b) are produced, in presence of the FEC decoder, through

)()()( 111

1111

k

n

ext

dcod

k

n

ext

d

k

n

api

ddPdPdP k

nkn

kn

kn

kn

(8)

where the right most term represents the Extrisnic probability provided by FEC decoder, being used as the apriory probability of the particular data symbol. Similarly, the probability informations on paricular values of data bits are passed to the FEC decoder from the SIC detector. If FEC decoder is not included, this second multiplicand is omitted.

B. SISO to MIMO Extension

In the following we consider 2T2R configuration in the SDM (space-division multiplexing) mode illustrated in Fig. 2.

Tx Rx

Tx1

Tx2

Rx1

Rx2

h1,1

h2,2

h2,1

h1,2

Fig. 2. 2x2 MIMO configuration.

Starting from (4), by simple extension, the received signal into one of received antennas has the form

k

ni

k

L

Ln

kk

ni

kk

nnk

L

Ln

kk

ni

kk

nn

k

nibhdhdr

h

h

h

h

1

1' '

',

'2,

'

'2

1

1' '

',

'1,

'

'1. (9)

where the first and the second index of h correspond to

receive and transmit antenna, respectively, while indices 1 and

2 of d differentiate between data symbols sent from the

antennas 1 and 2, respectively.

The first two summands in (9) represent the (real-valued)

signals, k

njir , , received from different transmit antennas after

passing through independent channels and k

nib is the noise

term for the i-th receive antenna chain.

Before proceeding with detection, the impulse responses ',

'j,kk

nih pertinent to the four MIMO sub-channels are estimated

sequentially by the same procedure as for the SISO case [4][8].

For the considered 2x2 MIMO system we have to calculate four different expressions for conditional probability, inside each of the “SIC detector” block, see Fig. 3. As in (5) the conditional probabilities are calculated as:

22

2)(exp|

,

,,

,

k

ks

Ekn

dkn

fkn

dkn

rP

ji

jijji

jji

. (10)

where ks

E ji, represents the symbol energy and along the

adequate impulse response, ',

'j,ˆ kk

nih is calculated as:

21

1' '

',

',,ˆ

k

L

Ln

kk

njik

sjihE . (11)

Calculation of the individual MF outputs, kn

f ji, , to be used in

(10), will be described in the next section along with description and explanation of the proposed receiver structure.

III. PROPOSED DETECTOR STRUCTURE

By previously estimated real-valued impulse responses

pertaining to direct and cross-antenna transmission channels,

the iterative interference cancellation framework becomes

rather straightforwardly applicable, with involvement of

certain “strategic” and “tactical” measures in terms of signals

ordering and overcoming of non-Gaussian statistics of the

residual interference during the iterations.

The iterative procedure starts with the signal that has the

highest energy and temporarily treating the weaker signal as a

‟noise‟. By using the LLR (log-likelihood ratio) formulation,

the soft symbols corresponding to the stronger signal, denoted

with аpid jˆ in Fig. 3, are determined for each receive antenna

according to expression, in lieu of (7b)

2

2/)(tanhˆ ,

k

njapp

k

njiextrk

nj

LLapid

. (12)

The division by two is used to adjust the saturation level of

tanh function (1) to the transmitted constellation

2/1* jd in MIMO subchannels2. The proposed strategy

uses two different log-likelihood ratios (LLRs): extrinsic

jiextrL , and a posteriori jappL . The extrinsic LLR is

determined at output of each „SIC detector‟ block, starting from (10), as

)2/1(

)2/1(ln

,

,

, k

nj

k

nji

k

nj

k

njik

njiextrdrP

drPL . (13)

The term k

njappL is calculated as average of two LLR values:

the first one is obtained after „weighting‟ block,jextrL , and the

second one at the output of decoder, japiL . In initial iteration

when output of decoder is still not available, k

njappL is set to

zero. Then, in accordance with Fig. 3, which describes the

iterative cancellation of MIMO inter-stream and SISO self-

interference, the residuals

1

1" "

',

'i,

"'

"'

'

'

'

',ˆˆˆ

k

L

Ln

kk

nm

kkk

nnnm

kk

nni

kk

nnmihapidrr . (14)

are interchangeably sent to the „SIC detector‟ blocks. Here,

m designates opposite antenna or signal from the set 2,1m .

Now, four jiextrL

, values corresponding to „SIC detector‟

outputs, are combined by MRC-like weighting to get

jextrL values:

jj

jextrjjextrj

jextrEE

LELEL

,2,1

,2,2,1,1

. (15)

2 In this way total power of MIMO signal remains the same as in SISO case.

jextrL are then passed through deinterleaver and sent to

decoder. The outputs from decoder are interleaved to get

adequately orderedjapiL values for use within SIC detectors.

The soft a posteriori estimates of data symbols are obtained as

2

2/)(tanhˆ

k

njextr

k

njapik

nj

LLappd

. (16)

and their impact is subtracted from received signal, in the

same manner as аpid jˆ is applied in (14):

1

1" "

",'

'1

"'

"'1

'

'

'

',ˆˆˆ

k

L

Ln

kkk

nm,

kkk

nnn

kk

nni

kk

nnmihappdrr . (17)

In Fig. 3 the dashed (blue and red) lines are feeding the

estimates of the symbolsk

nd1 , and the solid lines carry the

estimates of the symbolsk

nd 2 .In Fig. 3 solid green line

represents column vector of estimates of the symbols k

nd1 and

knd2 . From resulting estimates

'

',ˆ kk

nnjir

, the residuals are

produced as:

1

1" "

",'

"2,

"'

"'2

'

',

'

',ˆˆˆ'

k

L

Ln

kkk

nm

kkk

nnn

kk

nnmi

kk

nnmihappdrr .(18)

Under assumption that all symbols are properly estimated the residuals from (18) correspond to noise term, the effect of which is partially suppressed by the MF. The output of MF is added to properly scaled symbol estimation to form a new decision variable:

1

1' ',

',

','

',,ˆˆ'

k

L

Ln

k

sjik

njkk

njikk

nnjik

njiappEdhrf . (19)

Fig. 3. Receiver structure for MIMO 2x2 system.

The remaining term from (10), variance 2, kji

is calculated as

P

k

L

Ln

kk

nji

kk

nnjiji hrPk 1

21

' '

',

',

'

',,ˆ'

12 . (20)

where P represents number of T/2 instants during the transmission block of data samples.

The newly estimated quantities in (19) and (20) enable a new estimation of conditional probability in (10) and LLR value in (13). In this way, we are getting the novel information about reliability of the estimated soft symbols and repeating the process iteratively. The message passing within SIC and FEC decoder, as well as within the two, proceeds similarly to the SISO case.

The described detector structure is obtained as extension of our approach to develop the 2x1 MUD system. In that system we still have the problem to overcame the similar or too different levels of interfering and signal of interest. In proposed detector this problem is overcome by including the second antenna at receiver side.

A. Simulation results

As most challenging for the MUD setup, the primarily

simulated channel model was Rayleigh flat fading where, due

to absence of time-frequency bins independence on signal

block level, there is no contribution from interleaving and

FEC decoding. The channel parameters are estimated with a

training period long enough (60 T intervals) to ensure a

reasonably well LS-type channel estimation. The system uses

R=1/2 (133,171) convolutional code followed by an

interleaver of length 56. For this purpose we used system with

six out of eight active subchannels. The results presented in

Fig. 4 are produced after seven iterations.

Fig. 4. BER comparasion: MIMO vs. SISO. As shown on Fig. 4, the increase of signal-to-noise ratio

(SNR) brings additional reduction of overall BER for MIMO

transmission. The receiver diversity effect is achieved through

the appropriate (MRC) combining of the soft data symbols

pertaining to signals received from the two receive antennas

for each of the two transmitted data streams, without

noticeable effect of their generally disparate received energy

levels and effects of residual inter-stream cross-talk.

IV. ADVANCED SISO PROCESSING - I/Q DIVERSITY AND/OR

NOISE PREDICTION AND CANCELLATION

Rather than considering the “intrinsic interference” as a problem, its constructive use appears to be possible, primarily through independence of the noise components present on the in-phase and quadrature branches, with likely further benefitting from at least certain independence among the in-phase and quadrature branches of fading channels impulse responses. As in (3), the quadrature branch system model then becomes

dt)t2/nT()t2/nT(yImimagr

TL

TL

k

n

g

g

. (21)

The block diagram of such a configuration, with incorporation of the prediction and cancellation of the noise part colored by the receiver-end filter-bank is shown in Fig. 5.

Fig. 5. Block diagram of noise prediction and cancellation in SIC framework. The vertical dashed line shows demarcation between the complex- and real-domain processing.

It might be worth nothing that while the utilization of redundancy contained within the I/Q staggered formats had been something normal for offset QAM (OQAM) in satellite communications [5], for FBMC application - with the essentially same modulation in subchannels - it has only recently been made the related proposal in [6]. The preliminary simulation results shown in Fig. 6 have indicated the 3dB of SNR gain in the AWGN case, but some more work is to be done to produce a comprehensive set of compelling enough simulation results, in particular regarding the absence of the gain in the coded case. While difference between the real- and complex-domain MAP, that is SIC framework in terms of implementation complexity might be practically non-existent due to the longer impulse responses in the former case, its advantage can actually be sought in the context of the I and Q redundancy based gain.

Fig. 6. BER in function of SNR for the case with and without exploation of imaginary branch

Since the joint (bivariate) distribution of two independent Gaussian processes, is equivalent to product of individual distributions, the effective extrinsic probability would be a product of extrinsic probabilities of Re{} and Im{} branches,

2

k

2k

s

k

n

k

n

2k

s

k

n

k

n

2

k

][Im

ext

[Re]

ext

eff

ext

2

)[Im]Ed[Im]f()Re][Ed[Re]f(exp

2

1

PPP

(22) The superscripts are added to differentiate between the two branches that have the same form as probability in (5). This becomes conceptually quite appealing, in that the product of the two probability density functions (with the same average values and the same variances) reveals narrowed shape compared with any one of them, implying (by the product of two numbers smaller than 1 is smaller than either one of them) the reduction of the overall variance, that is the effective SNR, which lies in the essence of the maximal-ratio combining of the two (diversity) branches. The given simulation results are, however, related to the equivalently performing configuration that is based on averaging the residuals of real and imaginary branches:

2

'''

imagrrealravrr

k

n

k

nk

n

. (23)

(The calculation of the term imagr kn' requires the previous

estimation of impulse responses for imaginary branch, which is performed using the same procedure as for the real branch.)

Another possibility of making the FBMC performance to even be exceeding those of the CP-OFDM ones, rather than just striving to attain them, is based on reduction and cancellation of the noise part which has been colored by passage of the AWGN through the receiver-end filter-bank subchannels. Namely, the subchannel noise in complex-domain becomes quite strongly correlated with T/2 lag, by about factor 0.5 in case of 100% subchannels‟ roll-off factor. In order to produce the candidate noise samples for prediction, the complex received signal has to be reconstructed, whereby the SIC framework applied at the signal-block (frame) level eliminates the problem of causality present in conventional noise prediction configurations.

The complex-domain FBMC signal reconstruction, in line

with (1), is based on soft data samples estimates and has the

form

)(~2

1

12

0

tdjy k

n

k

kk

M

m

k

n

mkk

n

. (24)

The predicted noise samples in complex-domain, )~{ k

n

k

n yy ,

are produced based on the difference between the actual and

interpolated complex receive samples, k

ny and k

ny~

.

For the FBMC referent impulse response

0] 0.0008 0.0259- 0.0243 0.9992 0.9996 0.0245 0.0260- 0.0008 [0g

that is designed by the procedure proposed in [10], the prediction coefficients are calculated by the spectral decomposition, e.g. using the Levinson-Durbin algorithm:

] 0.1268 0.2650- 0.3750 0.5250- 0.6716 0.8383- 0.8869 [-0.9691p .

Simulation results for noise prediction and cancellation for an AWGN channel (without fading) are shown below in Fig. 7.

Fig.7. Simulation results for the cases without and with noise suppression for

the AWGN channel.

While in the both cases the effect of noise suppression and gain of utilization of imaginary branch are clearly visible, when realistically estimated noise samples are used in prediction only the uncoded BER performance becomes significantly improved, for even more that 3dB, while the coded performance remains unchanged with respect to the case without noise suppression. This behavior needs to be

further explored and a remedy be possibly be found in introducing more inertness in the iterating process.

V. CONCLUSION AND FUTURE WORKS

In this work the novel MIMO 2x2 scheme for successive iterative interference cancellation is proposed. The SNR gain is observed as result of the described iterative procedure. Future contribution based on proposed receiver structure will be extended to multi-tap channels, where the strategy for estimation of soft symbols should be devised separately for each subchannel.

Performance enhancements based on redundant in-phase and quadrature components and cancellation of the predictable noise power spectral density, although partly demonstrated, need further elaboration. Also, the 2x1 MISO multi-access configuration remains to be tackled based on insights gained from the 2x2 MIMO, where 2x1 MISO is contained as sub-set.

ACKNOWLEDGMENT

This work has been supported by the FP7 project 318362

“ICT-EMPhAtiC”

References

[1] M. El Tabach, et al., “Spatial data multiplexing over OFDM/OQAM modulations,” ICC 2007.

[2] R. Zakaria, and D. Le Ruyet, “Partial ISI cancellation with Viterbi detection in MIMO filter-bank multicarrier modulation,” ISWCS), 2011.

[3] Hesham El Gamal, Bassel Beidas: Combined interference cancellation with FEC decoding for high spectral efficiency satellite communications. Hughes Electronics Corporation, December 30, 2003: US06671338

[4] M. Aoude, at al., “Interference cancellation in coded OFDM/OQAM,“ ISWCS 2012.

[5] Lifang Li and Simon, Marvin K., "Performance of coded OQPSK and MIL-STD SOQPSK with iterative decoding," Communications, IEEE Transactions on , vol.52, no.11, pp.1890,1900, Nov. 2004

[6] G. Ndo, et al., “FBMC/OQAM equalization – exploiting the imaginary interference,” PIMRC 2012.

[7] ICT-Emphatic public deliverable D4.2 “MIMO channel estimation and data detection”, march 2014, http://ict-emphatic.eu/

[8] ICT-Emphatic public deliverable D3.2 “Adaptive equalization and Successive self-Interference Cancellation (SIC) methods”, march 2014, http://ict-emphatic.eu/

[9] ICT-Emphatic public deliverable D4.1 “MIMO techniques end reception strategies”, September 2013, http://ict-emphatic.eu/

[10] A. Vahlin and N. Holte, “Optimal finite duration pulses for OFDM,” Communications, IEEE Transactions on, vol. 44, no. 1, pp. 10–14, 1996. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=476088