Assessment of potentiality of Adjacent Channel Interference Mitigation ...

Assessment of potentiality of Adjacent Channel Interference Mitigation in a low-rate TDMA system Gennaro Gallinaro Space Engineering S.p.A. Rome, Italy [email protected] Abstract— In this paper an assessment of the effectiveness of Turbo-Interference Cancellation (Turbo-IC) for improving the spectral efficiency of a TDMA based satellite Return Link channel will be addressed. Interference mitigation algorithms have been widely studied and implemented in terrestrial wireless CDMA systems. In the present paper Turbo-IC is instead adopted for reducing the carrier spacing on the satellite return channel, thus allowing to increase the system throughput for a given system bandwidth. Performance results show that throughput improvements are possible notwithstanding the higher criticality of carrier synchronization at reduced carrier spacing. It shall be noted that such an improvement in system capacity is achieved without any complexity increase at the Satellite Terminal (ST), as the additional signal processing required is entirely located at the Gateway. Moreover, the proposed technique is fully compatible with DVB-RCS standard, which allows for applicability in current RCS VSAT systems. In the paper, extensive simulation results obtained in a realistic broadband satellite system scenario are shown and discussed.

I.

INTRODUCTION

In order to increase the competitiveness of the satellite as transport media for next generation multimedia networks it is imperative to improve the spectral efficiency of satellite transmission whilst reducing bit delivery cost. In a previous paper [1], an effective solution for increasing the RL throughput of a satellite system adopting an enhanced-version of the DVB-RCS standard was presented. The proposed approach was specifically devised for a multi-beam system scenario, where the multi-beam satellite antenna pattern generates a MIMO channel that can be exploited through appropriate spatial processing. Although granting a remarkable capacity increase (exceeding 100%), this solution is however not suited to current single-beam satellites. A new approach has recently been conceived for increasing RL capacity without exploiting spatial processing, which makes it therefore also applicable to single-beam systems. Moreover, the investigated technique appears less critical than the one based on spatial processing in terms of channel estimation requirements, as the same algorithms used in conventional systems (i.e. without interference mitigation) can be utilized. The proposed solution is based on reducing the carrier channel spacing, intended as the distance between the central frequencies of two RL adjacent carriers, and mitigating the

Rita Rinaldo European Space Agency, Kepleerlann 2201-AG Noordwijk, Holland [email protected] higher interference level with an Iterative Interference Cancellation (IIC) scheme. In particular, a scheme based on Soft-IC has been selected and investigated in detail in the present paper. The performances of the proposed technique have been derived through an extensive simulation campaign, where a sensitivity analysis to a number of key algorithm and physical layer channel parameters has been carried out. Both QPSK and 8PSK modulations were considered. Moreover each carrier was assumed to be turbo-coded with a duo-binary code similar to the one used in the DVB-RCS standard, but slightly more powerful due to the doubling of the code states (16 instead of 8) [7]. The potential performance of the above ACI mitigation scheme was already addressed in a previous paper [2]. The present paper extends the results of the previous paper. In particular, some new optimization of the interference cancellation algorithm were introduced aimed mainly at simplifying the hardware complexity (uses of max metrics in the SISO decoders instead of the max*). Furthermore, the effects of imperfect signal frequency knowledge were neglected in the previous paper. Frequency estimation actually resulted to be very critical in the present context. Operation in presence of even modest frequency errors requires the use of a distributed preamble instead of the conventional preamble generally used in TDMA systems (e.g. DVB-RCS). An optimization of the distributed preamble composition was attempted for various combinations of modulation/coding rates and frequency spacing. Such an optimization hopefully results in the best compromise between the added overhead and the capability of the scheme to manage reduced carrier frequency spacing. Such an optimal compromise is the one resulting in the best effective spectral efficiency. The effective spectral efficiency is here defined as the one corresponding to the useful channel throughput per Hz. Such a useful channel throughput is decreased by the overheads (preambles and pilots) which have to be added for synchronization purposes. Given the overhead typically required to achieve good synchronization performances (particularly as far as the frequency estimation is concerned), achieved performances, when measured in terms of effective spectral efficiency, can be reduced with respect to what was claimed in [2]. A further criticality which has emerged once minimization of the overhead has been attempted is the fact that also timing estimation may become critical. Non-data aided timing

estimator (like the Oerder & Meyr scheme) are, in fact affected by the interfering signals and their performance is reduced. Further, a bias in the timing estimator may also result. Obtained results anyway proved that the proposed interference mitigation scheme makes operation with a very narrow carrier spacing feasible and may improve the effective spectral efficiency. It is worth noting that, as it is usually the case in current satellite systems, the performance comparison here done assumes that the on-board power allocated for the RL channel is not the limiting factor. Hence, system performances are only dependent on the up-link. The proposed paper, after a review of the proposed IIC approach presents some of the results of the simulation campaign which was carried out to comparatively evaluate its performances. The subject paper is based on the results of a study contract awarded to Space Engineering by the European Space Agency. II.

Shaping Filter

SISO Decoder

Soft Demodulator

SISO Decoder

MUD Front-End Shaping Filter

Figure 1 General Iterative Parallel Interference Cancellation scheme



ITERATIVE INTERFERENCE CANCELLATION

Different iterative interference cancellation schemes have been described in the literature. These schemes can be applied in a variety of situations, e.g. for mitigating interference from adjacent co-channel beams or from adjacent carriers in case adjacent carrier spacing is lower than the carrier bandwidth. Iterative Interference Mitigation techniques for copying with these two different scenarios are similar. The general block diagram for copying with the two mentioned scenarios is similar and is shown in Figure 1 where for simplicity we assumed a two carrier input (either coming from different co-channel beams or corresponding to two adjacent carriers of the same beam) Different MUD front-ends have been proposed in literature with different complexity/performance trade-off. In particular, the following MUD front-ends, in order of decreasing complexity, are often considered in the literature (see [4], [5] and [6]):  Full Belief Propagation. This is the optimal approach at least when the factor graph representing the channel/codes are cycle free. Cycle free factor graphs are never achieved in practice but still the approach is the best performing amongst the one here considered. Anyway the absence of a cycle free factor graph makes the performance sensitive to the scheduling of operations. This is true for all of the following schemes also. For simplicity, if not otherwise stated we will always consider parallel interference cancellation although a serial approach is probably the best compromise between complexity and performance. The complexity of this

Soft Demodulator







approach is exponential in the modulation alphabet as well as channel memory. Hence this approach is impractical for the present application and was not further considered. Iterative Interference Cancellation through a LMMSE filter (MMSE-IC). In this approach the MUD front end deliver at its output a refined estimation of the input signal through LMMSE filtering of the original input signal partially cleaned from interference as estimated through the extrinsic information. Complexity of the scheme is still high as the optimal LMMSE filter is in general different for each symbol being the covariance matrix of extrinsic info generally different from symbol to symbol. The complexity of this approach is still quite high and in practice a simplified approach as discussed in the next bullet is used instead. Unconditional Iterative Interference Cancellation through a LMMSE filter (U-LMMSE-IC). This approach is a simplification of the above where the LMMSE filter is computed only once for each iteration (and per each channel). The LMMSE filter is then computed based on the mean vector and mean covariance matrix computed on the overall frame. Single User Matched Filter Interference Cancellation (SUMF-IC). In this case no LMMSE filter is computed. This approach, being a good compromise between complexity and performance is the one actually used in our work and will be discussed more in depth in next sections. Hard Interference cancellation (Hard IC) where at the decoder output hard decisions are taken and the corresponding signal is then regenerated for cancellation from the input signal at next iteration. This approach is the simplest one but also the less performing. It was thus not further considered in our work. III.

SIGNAL MODEL AND TURBO-IC

Given our system scenario where ACI is the predominant signal impairment, partly following [2], we may write the received signal as:

y (t ) 

M /2



 Aa

l   M / 2 k  

l l ,k

p(t  kTs )e j ( 2 l ft l )  n(t )

where for notational simplicity we have assumed all signals to be time synchronous. M represents the number of carriers with spacing f; Al represent the amplitude of carrier l; am,k is the modulation, p(t) is the pulse shape and n(t) the thermal noise. A set of sufficient statistics, {xm,i}, may be obtained at the receiver through a bank of matched filter with each filter tuned to one of the channel and sampled at a rate Ts=1/Rs. It is:

xm (iTs )   h( ) y (iTs   )e  j 2 m f ( iTs  ) j m d where h (t) = p*(-t) is the matched filter to the pulse shape and the wanted signal has been translated to zero frequency before matched filtering. Hence:

xm (iTs )   p * ( ) y (iTs   )e  j 2 m f (iTs  ) j m d Introducing the cross-correlation:

Cl , m (kTs , iTs )  Al e j 2 ( l  m ) f iTs  j ( l  m )

 p * ( ) p(  iT

s

 kTs )e j 2 ( l  m ) f d

Then we may write: 

M /2

 a

xm (iTs ) 

l   M / 2 k  

l ,k

Cl ,m (kTs , iTs )  nm (iTs )

Assuming pulse length is equal to L and that only the two adjacent channels contribute to ACI we may simplify the above expression as:

xm (iTs ) 

iL

C

k i  L



m,m

iL

a

k i  L



( kTs , iTs )am , k 

m 1, k

Cm 1, m ( kTs , iTs ) 

m 1, k

Cm 1, m ( kTs , iTs )  nm (iTs )

iL

a

k i  L

The second and third addend in the above expression represent the interference Im(iTs) which affects channel m at decision instant i. With the change of summation variable h=k-i we have:

I m (iTs ) 

L

a

hL



m 1, h  i

Cm 1, m (hTs  iTs , iTs ) 

L

a

hL

m 1, h  i

Cm 1, m (hTs  iTs , iTs )

To introduce the possible turbo interference cancellation methods, let us rewrite in matrix form the received signal equation. Let it be x a vector of samples representing all the matched filters output from time index i-2L to i+2L. For sake of reference we will assume that the ordering of x is such that we

have first all the samples of the first frequency channel, then all the samples of the second frequency channel and so on. We may then write: x = Zm,k am,k + R a + n where a is the vector of information symbols ordered at the same way as x with the exception of the symbol am,k; Z,m,k is the vector :

[Cm, -M,(kTs ,(k-2L)Ts) , Cm, -M,(kTs ,(k-2L+1)Ts) , ….. Cm,+M,(kTs ,(k+2L)Ts)]T R is the matrix representing the interference contribution (i.e. due to terms different from the symbols we want to estimate). The columns of R are actually representing the interfering effect of the corresponding symbol at the output of the various channels. Each column of R is actually a sequence of different impulse response to the pulse of the corresponding channel/time index. The form (1) in which we wrote the signal model is suitable for deriving an estimate of the symbol am,k according to MMSE-IC, SUMF-IC, or Hard-IC methods. After each iteration of the SISO decoders an estimate of the vector a in (1) can be obtained by computing its expected value given the extrinsic info. In the SUMF-IC scheme an estimation of the symbol am,k, is obtained through:

aˆ m,k 

Z m. k H

H

Z m,k Z m,k

x  REa | λ

Assuming that distribution of vector a conditioned to the extrinsic information is Gaussian, its covariance matrix a can readily be computed. Matrix R could be, in principle, precomputed if perfect knowledge of pulse shapes and carrier frequency is available. In practice, frequency errors, phase noise and the fact that pulse shape used at the transmitter may not be fully controllable would make preferable that R is estimated through the received data. The following shall be observed:  R is different for every symbol to be estimated. Actually, if the channel is perfectly stable (e.g. no frequency error variation or phase noise), R is the same for all symbols of a given channel (apart edge effects) although different for symbols of different channels.  Estimating R completely from data would require to measure separate impulse response representing the crosscoupling between channels. This would require the transmission of a preamble for each channel in absence of transmission in other channels. As this is impractical, we assume that the pulse shaping at Tx side and Rx side are known (square root raised cosine truncated to a given length). Hence, channel estimation is only responsible of providing exact amplitude, frequency and phase tracking of the various channels. Similar considerations can be done for Zm,k. A further simplification of the SUMF-IC is possible recognizing that for

each am,k to decode, the vector Zm,k contains one dominant term (the one corresponding to the m-carrier matched filter). So simulation results which are reported in this paper actually assume that all elements of the vector Zm,k are zero apart the dominant one. In practice, this is equivalent to consider in eq. (1), the use of a single channel observation (i.e. of just channel m) for estimation of am,k. The observation vector x becomes a scalar thus reducing the scheme complexity. IV.

SIMULATION SCENARIOS

A simulation program has been set-up to evaluate performance of soft-IC interference mitigation. A previous paper [2] reports results in presence of negligible frequency error. In the present paper a frequency error of 2.5 % of the symbol rate was instead assumed. In order to allow good frequency recovery at low SNIR, a distributed preamble was considered when operating at carrier frequency spacing lower than the symbol rate for all tested modulation and coding rate. A distributed preamble was also considered for test cases not using ACI mitigation if the operating SNR is very low (e.g. QPSK ½) or if 8PSK modulation is considered. In particular the distributed preamble was actually constituted of a preamble, a postamble, and pilot symbols periodically inserted within the burst. In all simulation results here reported the periodicity of the pilots was 9 symbols, i.e. a pilot symbol is inserted after each group of 8 data symbols. The preamble and postamble may have different lengths in our simulations. In particular, in most of the simulations a very short postamble (from 3 to 7 seven symbols) were used. The role of the postamble, in those cases, was that of improving the carrier phase estimation at the end of the burst (see later section on demodulator algorithms). The simulation scenario assumes a DVB-RCS-like scenario. An improved turbo code with respect to DVB-RCS, the so-called turbo- code [7], was, however, used. This code is slightly more efficient than the standard RCS turbo code thanks to the doubling of the number of states (from 8 to 16). All adjacent carriers were assumed to be frame synchronous but not symbols synchronous. In particular a small random timing error (lower than the frame guard time, here assumed equal to 6 symbols) was added to each user bursts. A. Demodulator Algorithms The incoming signal corresponding to the group of adjacent carriers which is intended to be processed is down-converted to a suitably low IF and then AD converted. Once in the digital domain the stream of samples is replicated into several paths (one path for each of the carriers) where a separate demodulator will take care of the processing. The following functions have to be done by each of the demodulators:  Frequency conversion to a nominal zero frequency.  Matched filtering with a square root raised cosine filter having the selected roll-off.



Burst detection with coarse frequency and timing recovery. This was done in our implementation through coherent integration over the preamble and the postamble with non coherent combining of the two results. Three or five frequency hypotheses were considered spanning the uncertainty range of ±Rs (the symbol rate). The maximum correlation measured on a time window spanning the burst guard time thus provides both a coarse carrier frequency and symbol timing estimations.  Fine Timing Estimation and Correction. The estimation is done using one of the two approaches below: - Oerder & Meyr (O&M algorithm [8]). This algorithm generates a sequence with a clock component by computing the square norm of the burst symbols. The phase of the clock component is then extracted using a DFT and used to estimate the fine timing error. - Dicotomic search with linear interpolation. A dicotomic search is performed computing the correlations over preamble and postamble with fractional sample offsets. In our implementation we actually iterate this search up to 1/16 of the symbol period. This accuracy is actually not very high and introduces some performance degradation. We will later refer to this method as the data aided timing estimator as it operates on the known symbols of preamble and postamble. The subsequent timing correction was done with a Farrow interpolator.  Fine Frequency correction. This is done through the Mengali-Morelli algorithm [9] operating on the pilot symbols. In the cases where a compact preamble without distributed pilots was used, fine frequency recovery still uses the Mengali-Morelli algorithm operating however on modulated data suitably non-linearly transformed to eliminate modulation.  Phase Correction. This is done by estimating the phase of the average phasor obtained by the sum of a number of adjacent pilot symbols. A sliding window approach is used for minimizing the bias due to the residual frequency error. For the case where a compact preamble is used the same approach is used but operating on the modulated data suitably non-linearly transformed to eliminate the modulation  AGC. Carrier level estimation is needed not only for computing metrics for the decoder but also for interference cancellation. Such an estimation can be done either by the burst detector (i.e. as a by product of the correlations done on preamble / postamble for the scope of burst detection) or by exploiting the carrier phase estimator. In this last case the carrier level can be extracted by the modulus of the average phasor computed by the phase estimator (see previous bullet). The following shall be further noted. The reason why an alternative to the Oerder & Meyr timing estimator was considered is that, in presence of strong ACI, the performance of the Oerder & Meyr estimator may significantly degrade. Also bias can appear as the timing of the

2.E-05

Std. Dev. / Rs

4.E-04

STD Average

3.E-04

1.E-05

3.E-04 2.E-04

0.E+00

2.E-04 1.E-04

-1.E-05

Average value / Rs

4.E-04

5.E-05 0.E+00

-2.E-05 0.5

0.7

0.9

1.1

1.3

1.5

Delta Freq / Rs

Figure 3 Std. Deviation and bias of Mengali Morelli frequency estimator of central channel vs. carrier spacing. Es/N0 =3 dB. Other carriers are @ 3dB higher level. Pilot Periodicity 9 symbols. Short burst case. Timing recovery based on Oerder & Meyr method.

adjacent carriers may influence the estimator result. The dataaided timing estimator approach may in principle be less influenced by the timing of adjacent carriers as uncorrelated preamble / postamble can be used. As a matter of fact however, with short preamble and / or postamble it is difficult to control the cross-correlation between adjacent carriers. Such cross-correlation is in fact also function of the frequency separation of the carriers and not only of the preamble and postamble patterns. No optimization of such patterns was done in our work. Fine frequency recovery was also found to be sensitive to the carrier spacing (see example performance in Figure 2). It shall be observed that in our simulator we may refine the frequency estimation after each cancellation iteration. Similarly, the carrier phase estimation and the carrier level estimation can also be refined at every iteration. For the timing estimator however we decided to not exploit iterations for refining the estimation as this have a quite significant impact on the hardware complexity as it implies to process at least 3 samples per symbol also during the iterative process of cancellation. Hence, fine timing correction is only done before interference cancellation and only one sample per symbol is subsequently processed. This has the consequence that the quality of timing correction can be not very good in presence of strong adjacent channel interference as it could happen with very close spacing of the carriers. From results in Figure 3 it is evident that the timing jitter

rapidly increases below 0.7 Rs carrier spacing (at least when 3 dB higher level adjacent carriers are considered). The strong bias for carrier spacing equal to Rs for the data aided algorithm is due to the fact that the preamble and postamble patterns were the same for all the carriers. From Figure 2 it is apparent that also frequency estimation rapidly deteriorates below 0.75 Rs carrier spacing (still assuming 3 dB higher level adjacent carriers) due to the increase in outlier probability. B. ACI Mitigation performances. As already mentioned in the introduction, the max algorithm has been used in the decoder instead of the optimal max*. Suitable weights on the extrinsic information which is passed between the SISO decoders in the various iterations are used in order to minimize the losses with respect to the max* strategy. A different set of weights is also used on the extrinsic information before soft remodulation of data for interference cancellation purposes. Actually no real optimization of such weights has been done due to lack of time. Example performances are given in following Figure 4 to Figure 7. In particular Figure 6 shows the case of 8PSK rate 2/3 at spacing 0.9 Rs. Adjacent carriers are assumed at 3 dB higher level. In the same figure, as reference, the performance with ideal timing are also shown as well as the reference performance without ACI with spacing 1.12 Rs. In Figure 7 the same 8PSK rate 2/3 case is shown at spacing 0.75 Rs.but using ideal timing. Investigation of better techniques to cope with criticality of frequency and timing recovery at closer carrier spacing may be required to achieve the full potentiality of ACI mitigation. It shall however be observed that low rate TDMA carriers may well be designed to operate in a symbol synchronous way, thus making the criticality of timing recovery less problematic. In such a case, in fact, it can be assumed that timing error measurement is done on ad-hoc specialized bursts where a longer known pattern is available to reduce criticality of timing estimation at lower carrier spacing. Table 1, finally, shows a performance comparison between 8PSK rate 2/3 with ACI mitigation and of 8PSK rate 4/5 without ACI mitigation. It appears that using a carrier spacing of 0.9 Rs for the case with ACI mitigation the same spectral

0.3

Stad Dev / Ts

Average Value /Ts

O&M Data Aided

0.25 0.2 0.15 0.1 0.05 0 0.5

0.7

0.9

1.1

Delta Freq / Rs

1.3

1.5

0.16 0.14 0.12 0.1 0.08

O&M Data Aided

0.06 0.04 0.02 0 -0.02 -0.04 0.5

0.7

0.9

1.1

1.3

1.5

Delta Freq / Rs

Figure 2 Standard Deviation and bias of the data aided and Oerder & Meyr timing estimators versus the carrier spacing. Es/N0 =3 dB. Other carriers are @3dB higher level. The preamble (41 symbols) and postamble (3 symbols) were the same for all carriers. Short burst (478 payload symbols).

efficiency is approximately achieved as with 8PSK rate 4/5 without ACI but at an Eb/N0 lower than 1.4 dB. As an extra Eb/N0 margin is still available for the 8PSK 2/3 to further reduce the carrier spacing, a better spectral efficiency may in the end be achievable with interference mitigation. V.

[3]

[4]

[5]

CONCLUSIONS

ACI interference mitigation can improve the spectral efficiency of return-link TDMA carriers. The gain in spectral efficiency is somewhat limited by the higher criticality of synchronization (timing and frequency) at narrow carrier spacing. Further investigations are required to minimize the performance losses due to synchronization errors.

[6]

REFERENCES

[8] [9]

1.E+00

Error probability

FER 1.E-01

BER Seri es3 Seri es4 Seri es5

1.E-02 1.E-03

5QPSK 1/2 Ch Roll-off =0.5 DF=0.75 Rs Equilevel Carriers Preamble: 41 symbols Postamble: 3 symbols Pilot Periodicity 9 symbols

1.E-04 1.E-05

1.E-02 1.E-03 1.E-04 1.E-05 Single Channel

Single Carriers

1.E-06 2

1.E-06 0

0.5

1

1.5

2 Eb/No (dB)

2.5

3

3.5

Figure 4 Performance of ACI mitigation with 5 equilevel QPSK ½ carriers at spacing 0.75 Rs. Roll-off=0.5. Pilot period 9 symbols. Asymmetric length for preamble and postamble used (41+3 symbols). Data aided timing recovery.

1.E+00

Adj. Carriers @+3 dB level

1.E-01

5 Ch QPSK 2/3 central QPSK 3/4 adj @+3 dB F=0.75 Rs Roll-off=0.6

FER BER

1.E-01

1.E+00

Error Probability

[2]

M. Debbah, G. Gallinaro, R. Muller, R. Rinaldo, A. Vernucci “Interference Mitigation for the Reverse-Link of Interactive Satellite Networks”, 9th International Workshop on Signal Processing for Space Communications - SPSC 2006, 11-13 September 2006 at ESTEC. G. Gallinaro, A.Vernucci, R.Rinaldo, “Increasing Throughput of Wideband Satellite Systems Reverse-Link through Adjacent Channel Interference Mitigation”, 25th AIAA International Communications Satellite Systems Conference 2007

2.5

3

3.5

4

4.5

1.E-03

Figure 5 Performance of ACI mitigation with 5 carriers at spacing 0.75 Rs. Roll-off=0.6. Outer carriers (QPSK r=3/4) @+ 3 dB with respect to central one wich is QPSK 2/3. Pilot Periodicity 17 symbols. Symmetric Preamble/Postamble. Data Aided Timing Recovery.

1.E-04 Central Channel Central Ch. Ideal Timing No Mitig., DF=1.12

1.E-05 1.E-06 4

4.5

5

5.5

6

6.5

Eb/No (dB)

Figure 6 Performance of ACI mitigation with 5 8PSK carriers at spacing 0.9 Rs. Roll-off=0.35. Adjacent carriers @+3 dB

5

Eb/No (dB)

8PSK 2/3 (k=928, n=1392) DF=0.9 Rs Roll=0.35 Pilot Period:9 symb.

1.E-02 FER

[1]

[7]

B. F. Beidas, H. El Gamal, S. Kay, Iterative Interference Cancellation for High Spectral Efficiency Satellite Communication, IEEE Trans. On Comm., January 2002 J. Boutros, G. Caire, Iterative Multiuser Joint Decoding: Unified Framework and Asymptotic Analysis, IEEE Trans. On Information theory, July 2002. M. Moher, An Iterative Multiuser Decoder for Near--Capacity Communications, IEEE Trans. On Comm., July 1998. G. Caire, R. Müller, T. Tanaka, Iterative Multiuser Joint Decoding: Optimal Power Allocation and Low complexity implementation, IEEE Trans. On Information Theory, Sept. 2004 C. Berrou, R. De Gaudenzi, C. Douillard, G. Gallinaro, R. Garello, D. Giancristofaro, A. Ginesi, M. Luise, G. Montorsi, R. Novello, A. Vernucci, "High Speed Modem Concepts and Demonstrator for Adaptive Coding and Modulation with High Order in Satellite Applications". M. Oerder and H. Meyr, “Digital filter and square timing recovery” IEEE Trans. Commun., vol. 35, May 1988. M. Morelli and U. Mengali, “Data-aided frequency estimation for burst digital transmission,” IEEE Trans. Commun., vol. COM-45, pp. 23-25, Jan. 1997

Figure 7 Performance of ACI mitigation with 5 8PSK carriers at spacing 0.75 Rs and ideal timing. Roll-off=0.5. Outer carriers (8PSK r=3/4) @+ 3 dB with respect to central one.

8-PSK 2/3 with Mitig. N. Of Carriers Carrier Spacing/Rs Overall band /Rs Info_bits , coded bits Payload Symbols

8PSK 4/5 – No Mitig.

5 0.9

5 1.12

4.95 (roll-off 0.35)

5.68 (roll-off 0.2)

928 , 1392

928 , 1164

464

388

start UW + end UW

20 + 20

29 +7

N. of pilots / Period

57 / 9

48 / 9

Total slot

565

476

Eff. Spectral Effic

1.66

1.72

Asymptotic Spectral Eff.

1.82

1.74

Required Eb/No (dB) 5.8 7.2 Table 1 Comparison of 8PSK 2/3 (short burst) with ACI Mitigation with 8PSK 4/5 without ACI mitigation. Worst case conditions with adjacent channels @+3dBwith respect to wanted is considered. The total slot length also includes 4 symbols guard .time. The asymptotic spectral efficiency is that achievable by processing an infinite number of carriers instead of 5 (assuming the same performance still applies for the central channel).