IET Communications

Research Article

New SRRC receiver filter design with reducednumber of filter taps for wirelesscommunication systems

ISSN 1751-8628Received on 26th July 2017Revised 23rd January 2018Accepted on 18th February 2018E-First on 3rd May 2018doi: 10.1049/iet-com.2017.0858www.ietdl.org

Hoon Kang1, Jong-Seon No1 1Department of Electrical and Computer Engineering, INMC, Seoul National University, Seoul 08826, Republic of Korea

E-mail: jsno@snu.ac.kr

Abstract: In wireless communication systems, it is well known that inter-symbol interference (ISI) can be avoided by using apair of matched square-root-raised-cosine (SRRC) filters in the transmitter and receiver. In an effort to find methods whichminimise the number of filter taps in the matched filter, numerous studies have been done. However, in practise, when thecommunication specification is fixed by the standard, it is not possible to change the coefficients of the transmit filter. In thisstudy, the authors propose a new SRRC filter design with the reduced number of filter taps for a receiver of a wirelesscommunication system. The proposed design utilises a recursive steepest-descent algorithm when the filter coefficients of thetransmitter are fixed. That is, relaxing the ISI criterion while maintaining the stopband attenuation, the proposed receiver filterhas fewer filter taps than that in the conventional case without undergoing bit error rate performance degradation. The proposedreceiver filter design with the reduced number of filter taps reduces the computational complexity and the detection delay in thereceiver.

1 IntroductionIn wireless communication systems, the received signal is oftendistorted by the inter-symbol interference (ISI) due to the narrow-band bandpass signalling. In order to realise an ISI-free system, thereceiver must have a square-root-raised-cosine (SRRC) filteridentical to that of the transmitter known as the matched filterdesign [1]. In wireless communication systems, it is also importantto ensure that the magnitude response of the SRRC receiver filter isdesirable in the frequency domain because one of the mainpurposes of the SRRC filter in the receiver is to remove adjacentchannel interference (ACI). That is, most of receiver filter designalgorithms attempt to minimise the ISI and meet the targetmagnitude response under the matched-filter constraint. There arethree different design methods for the SRRC filters as follows:

(i) Optimise the magnitude response of the SRRC filter with zeroISI [2–8].(ii) Optimise the magnitude response of the SRRC filter withminimum ISI [9–14].(iii) Optimise the SRRC filter through a joint cost function of theISI and the magnitude response [15–19].

In fact, when the communication specification is fixed by astandard, there is no way to modify the receiver filter in theconventional systems because the matched-filter constraint shouldalso be satisfied by the receiver. However, several studies modifiedthe receiver filter by relaxing the matched-filter constraint with no

degradation of the ISI, which shows high potential for new receiverfilter designs [20–22].

A simplified system model of a wireless communication systemis illustrated in Fig. 1. Modulated data passes through thenarrowband SRRC transmitter filter and digital-to-analogueconverter (DAC) to make a band-limited analogue signal. Theconverted analogue signal is transmitted through the narrowbandchannel, which is typically a multi-path fading channel in wirelessmobile communication systems. In the receiver side, ACI andadditive white Gaussian noise (AWGN) are added to the receivedsignal. After converting the received analogue signal to a digitalsignal by an analogue-to-digital converter (ADC), the digitisedreceived signal is filtered by the SRRC receiver filter anddemodulated. Even though the multi-path fading and ACI are themost important channel distortions in the wireless communicationsystems, we will focus on ISI and ACI for the design of the SRRCreceiver filter in the AWGN channel.

In this paper, we propose a new design of an SRRC filter for thereceiver in a wireless communication system which uses arecursive steepest-descent algorithm while the SRRC filter of thetransmitter is fixed. By relaxing the ISI criterion while maintainingthe stopband attenuation, the proposed SRRC filter of the receiverhas fewer filter taps than the conventional SRRC matched filterwithout any degradation of the bit error rate (BER) performance ina wireless communication system. The reduced number of filtertaps of the modified SRRC filter of the receiver results in lowcomputational complexity and the low detection delay in thereceiver, both of which are important factors for the mobile stationsin the cellular communication systems.

The remaining of the paper is organised as follows. In Section2, ISI and stopband attenuation are briefly reviewed as the filterdesign criteria and these are derived in the matrix form for theproposed SRRC filter design algorithm. In Section 3, theconventional SRRC filter design algorithm is introduced and a newSRRC receiver filter design algorithm based on the steepest-descent method is proposed. In Section 4, the performanceassessment of the proposed SRRC filter in various environments isprovided through a numerical analysis. Finally, conclusions aregiven in Section 5.

Fig. 1  Simplified system model of wireless communication system

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2 Receiver filter design criteriaThere are three filter design criteria to be considered: the impulseresponse, magnitude response, and phase response. In this paper,the design of a finite impulse response (FIR) SRRC filter isconsidered, where the phase response is ignored because asymmetric FIR filter has a linear phase characteristics [23]. Thus,we concentrate only on the impulse response and magnituderesponse for the design of the receiver filter. ISI is the mostimportant channel distortion when estimating the performance ofthe impulse response, because ISI is directly related to the receivedsignal quality. The magnitude response of the receiver filter is alsoused to estimate the stopband attenuation, where removing the ACIis required in the mobile communication systems. Matrix forms ofISI and the stopband attenuation are derived for the proposedSRRC filter design algorithm.

2.1 Inter-symbol interference

The sample of the desired symbol at the sampling time should belocated at the zero crossing point of the adjacent symbols. ISIoccurs from the adjacent symbols in the time domain, where zerocrossings of the adjacent symbols at the sampling time of thedesired symbols are broken; that is, the sampled symbols containthe non-zero meaningful interferences from the adjacent symbols.Suppose that the received signal is oversampled by V times. If thesamples of the adjacent symbols are non-zero at each samplingpoint, these will work as additive noise to the desired sampledsymbol. Let M and N denote the number of transmitter and receiverfilter taps, respectively. Then the squared power ratio of the ISI tothe desired signal is then expressed as

RISI =∑m ≠ 0 ∣ ∑k = 0

N − 1 hr k htM2 + N

2 + mV − k ∣2

∣ ∑k = 0N − 1 hr k ht

M2 + N

2 − k ∣2 (1)

where ht k and hr k are the kth filter coefficients of the transmitterand the receiver filters, respectively. Letht = ht(M − 1), ht(M − 2), …, ht(0) T and hr = hr(0), hr(1), …,hr(N − 1) T, where ⋅ T denotes the transpose, and let H be anN × N matrix whose k, n element is expressed as

hk, n = ∑m = − M + N

2 V , m ≠ 0

M + N2 V

htM2 + N

2 + mV − k

× htM2 + N

2 + mV − n .

Then, the matrix form of (1) is expressed as

RISI = hrTHhr

∣ ∑k = 0N − 1 hr k ht

M2 + N

2 − k ∣2 .

If we normalise the filter coefficients ht k and hr k such that

∣ ∑k = 0

N − 1hr k ht

M2 + N

2 − k ∣2

= 1,

RISI can be rewritten as

RISI = hrTHhr . (2)

2.2 Stopband attenuation

The stopband attenuation of the low-pass filter is determined by themagnitude response of the higher frequency band above the signalbandwidth. The receiver filter removes the ACI depending on itsstopband attenuation. As depicted in Fig. 2, we can calculate thestopband attenuation according to the discrete Fourier transform(DFT) output of the receiver filter, where the frequency index k isthe index of the DFT output.

The stopband attenuation ASB can be expressed as

ASB = 1N2 − N ⋅ 1 + α

2V∑

k = N ⋅ 1 + α2V

N2 − 1

∣ Hr k ∣2 (3)

where Hr k is the kth frequency component of the receiver filter inDFT output and α is the roll-off factor of the original SRRC filterwith 0 ≤ α ≤ 1. Clearly, N /2 is the last frequency index andN ⋅ ((1 + α)/2V) is the first frequency index of the stopband.N /2 − N ⋅ ((1 + α)/2V) in the right-hand side of (3) represents

the number of frequency indices in the stopband, which is used forthe normalisation of (3). The kth component power ∣ Hr(k) ∣2 in thesummation is computed as

∣ Hr k ∣2 = ∣ ∑n = 0

N − 1hr n e(− j2πnk)/N ∣

2

= ∑n = 0

N − 1hr n e(j2πnk)/N ∑

m = 0

N − 1hr m e((− j2πmk)/N)

= ∑n = 0

N − 1∑

m = 0

N − 1hr n e((− j2π m − n k)/N)hr m .

Similar to the ISI case, the stopband attenuation is also changedto the matrix form as

ASB = hrTWhr

where the N × N matrix W is the DFT operator and its (m, n)element Wm, n is given as

Wm, n = 1N2 − N ⋅ 1 + α

2V∑

k = N ⋅ 1 + α2V

N2 − 1

e((− j2π m − n k)/N) .

Let W be an N × N matrix whose element Wm, n is expressed as

Wm, n = 1N2 − N ⋅ 1 + α

2V∑

k = N ⋅ 1 + α2V

N2 − 1

cos 2π m − n kN .

Since W is a Hermitian matrix, ASB can be rewritten as

ASB = hrTWhr . (4)

3 Proposed SRRC receiver filter designIn this section, the conventional SRRC filter design is reviewedand the SRRC receiver filter is modified by reducing the number ofthe receiver filter taps based on joint optimisation by using a

Fig. 2  Magnitude response and its stopband attenuation of the receiverfilter

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steepest-descent method with no degradation of the BERperformance at the receiver.

3.1 Conventional SRRC filter design

In the wireless communication systems, the specification of theSRRC transmitter filter is given as a standard [1]. When we use thesame filter in the receiver side, it makes a matched filter, which isknown to have the best BER performance. This is the most populardesign rule for the SRRC filters of the receivers in the wirelesscommunication systems.

The conventional design method for the SRRC transmitter filteris to generate its filter coefficients by the inverse DFT (IDFT) ofthe following frequency response:

Ht f =

1, ∣ f ∣ < 1 − α2V

1 + cos πVα ∣ f ∣ − 1 − α

2V2 , 1 − α

2V ≤ ∣ f ∣ ≤ 1 + α2V

0, 1 + α2V < ∣ f ∣ < 1

V .

The time-domain response of the SRRC filter is given as

ht t =sin π t

V 1 − α + 4α tV cos π t

V (1 + α)

π tV 1 − 4a t

V2 , (5)

which is also used as the receiver filter response as noted earlier[24].

3.2 New design algorithm of the SRRC receiver filter

The proposed SRRC receiver filter design algorithm reduces thenumber of FIR receiver filter taps by relaxing the restriction of the

ISI criterion while maintaining the stopband attenuation withoutdegrading the BER performance. By reducing the number ofreceiver filter taps, the computational complexity and the detectiondelay of the receiver can be reduced. In this subsection, we willcombine the ISI RISI and the stopband attenuation ASB to make onecost function as

Chr = γ ⋅ RISI + 1 − γ ⋅ ASB

where γ, 0 < γ < 1 is the weighting factor for the linearcombination of the ISI and the stopband attenuation. The gradientof the linearly combined Chr is given as

∇hrChr = γ ⋅ 2Hhr + 1 − γ ⋅ 2Whr . (6)

Subsequently, we can determine the optimum filter coefficientsby applying the steepest-descent algorithm to (6) as follows:

Step 1: We set the initial filter coefficient vector hr0 of the receiver

by choosing coefficients identical to those of the transmitter, whichis generated by (5). The error vector hr

0 is set to 0.

We calculate receiver filter coefficients by iterating thefollowing three steps from Step 2 to Step 4 for i = 1, 2, . . . , Niter,where Niter is the number of allowed iterations.Step 2: Calculate hr

i at the ith iteration as

hri = hr

i − 1 ⋅ 1 − htThr

i − 1

∣ ht ∣2 .

Step 3: Calculate the gradient ∇hrChri at the ith iteration as

∇hrChri = γ ⋅ 2Hhr

i + (1 − γ) ⋅ 2Whri ,

which is derived from (6).Step 4: Calculate the error vector hr

i for next iteration as

hri = hr

i − μ ⋅ ∇hrChri

where μ is the step size of the steepest-descent algorithm foroptimisation.

Many researches have been done to find the optimal step sizefor fast acquisition and to minimise the jitter after the acquisitionstep [12, 25, 26]. Because optimisation can be done in thepreprocessing stage to find the filter coefficients, we set the stepsize to a very small number such as 0.0001 with a very largeiteration number of 10,000. Thus, we can find the globally optimalsolution because it is a quadratic problem.

3.3 Design example

In this subsection, an example of the proposed SRRC receiver filterdesign is given. We set the parameters as follows. Theoversampling rate is V = 4, the weighting factor γ = 0.9, and theroll-off factor α = 0.22, all of which are sourced from the third-generation partnership project wideband code division multipleaccess standard [24], where a conventional FIR SRRC receiverfilter with 49 filter taps was used. Then the proposed SRRC filtercoefficients with number of 17, 25, 33, 41, and 49 taps aredesigned in Table 1. The BER performance of the receiver will beevaluated by a numerical analysis for the proposed number of theSRRC receiver filter taps in the following section.

4 Performance evaluationIn this section, we will show the performance of the proposedSRRC receiver filter with the reduced number of filter taps. First,the performances of ISI and stopband attenuation for the proposedSRRC receiver filter are evaluated. The BER performance of the

Table 1 Proposed SRRC receiver filter design examples49 taps 41 taps 33 taps 25 taps 17 taps

hr(0), hr(N − 1) −0.00327 −0.00836 0.03115 −0.06776 0.15007hr(1), hr(N − 2) 0.00427 −0.00853 0.01142 −0.00880 −0.01736hr(2), hr(N − 3) 0.00364 0.00459 −0.02389 0.06243 −0.16666hr(3), hr(N − 4) −0.00411 0.02051 −0.04896 0.09660 −0.20824hr(4), hr(N − 5) −0.01078 0.02314 −0.03861 0.05648 −0.07913hr(5), hr(N − 6) −0.00755 0.00388 0.01060 −0.05058 0.21383hr(6), hr(N − 7) 0.00664 −0.02835 0.07075 −0.16297 0.58173hr(7), hr(N − 8) 0.02182 −0.04940 0.09503 −0.18989 0.88557hr(8), hr(N − 9) 0.02301 −0.03595 0.04883 −0.06142 1.00000hr(9), hr(N − 10) 0.00274 0.01424 −0.05913 0.22378hr(10), hr(N − 11) −0.02954 0.07320 −0.16790 0.58359hr(11), hr(N − 12) −0.04984 0.09519 −0.18911 0.88346hr(12), hr(N − 13) −0.03546 0.04702 −0.05599 1.00000hr(13), hr(N − 14) 0.01519 −0.06154 0.23065hr(14), hr(N − 15) 0.07392 −0.16943 0.58859hr(15), hr(N − 16) 0.09522 −0.18903 0.88525hr(16), hr(N − 17) 0.04643 −0.05460 1.00000hr(17), hr(N − 18) −0.06227 0.23239hr(18), hr(N − 19) −0.16978 0.58978hr(19), hr(N − 20) −0.18879 0.88562hr(20), hr(N − 21) −0.05400 1.00000hr(21), hr(N − 22) 0.23293hr(22), hr(N − 23) 0.58996hr(23), hr(N − 24) 0.88552hr(24) 1.00000

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receiver with the proposed SRRC receiver filter is also numericallyanalysed in the AWGN channel, high ISI environment, and highACI environment, respectively, which is then compared with theconventional SRRC receiver filter with the reduced number offilter taps.

In the wireless mobile channel, the transmitted signal isdistorted in phase, amplitude, and delay by multi-path fading. The

original SRRC filter and the proposed filter do not affect the phase,amplitude, and delay. This means that those filters have almost thesame BER performance in the wireless mobile channel if they havethe same performance in the AWGN channel.

4.1 Performance of ISI and stopband attenuation

In order to derive the relationships between γ and ISI and betweenγ and the stopband attenuation for the proposed receiver filter andcompare these results with those for the conventional SRRC filter,various numerical analyses are conducted as shown in Fig. 3,which shows that the ISI is reduced as γ and the number of filtertaps increase. There exists a floor of the ISI for γ = 0.9 and largerthan 41 filter taps. The ISI of the proposed SRRC receiver filter islower than that of the conventional SRRC receiver filter whenγ ≤ 0.5.

The stopband attenuations for the proposed SRRC receiverfilter and the conventional SRRC filter are presented in Fig. 4,which shows that the stopband attenuation decreases as γ decreasesor as the number of filter taps increases. Note that the stopbandattenuation of the proposed receiver filter is better than that of theconventional SRRC filter.

4.2 BER performance in the AWGN channel

The BER performance of the receiver with the proposed SRRCreceiver filter is numerically analysed for QPSK, 16QAM, and64QAM with γ = 0.1, 0.9 and with 17, 25, 33, 41, and 49 filtertaps, as given in Fig. 5, which shows that the BER performance ofthe proposed SRRC receiver filter with 25 filter taps when γ = 0.9is nearly identical to that of the conventional SRRC filters with 49filter taps, even though the ISI and stopband attenuation of theproposed SRRC receiver filters are deteriorated compared to theconventional case. The computational complexity of the proposedSRRC receiver filter is reduced compared to the conventionalreceiver filter, which reduces the computational complexity and thedetection delay.

4.3 BER performance in high ISI environment

In order to check the effect of ISI, the BER performance of theproposed SRRC receiver filter is evaluated with phase offset 1

10V ,2

10V , 310V , 4

10V , and 510V for QPSK, 16QAM, and 64QAM, which is

compared with the conventional SRRC receiver filter, as presentedin Fig. 6. To evaluate the BER performance, 25 filter taps SRRCreceiver filter is used which comes from the previous subsection. InFig. 6, ‘Conv.’ means the conventional SRRC filter, ‘Prop.’ meansthe proposed SRRC filter, and ‘PO’ means phase offset. As the ISIincreases, the BER performance of the conventional SRRC filterand the proposed SRRC filter deteriorates in the same manner.From the simulation results, the conventional SRRC filter and theproposed SRRC filter have almost the same BER performanceunder ISI.

4.4 BER performance with ACI

When fewer filter taps are chosen, the proposed receiver filter haslower stopband attenuation performance as shown in Fig. 4.However, it is challenging to find an ACI tolerance gap betweencases with small and large numbers of filter taps, which causes thestopband attenuation performance difference between these cases.For example, when γ = 0.5, the stopband attenuation gap betweenthe cases with 17 and 49 filter taps is approximately 20 dB, whichdoes not mean that there is a 20 dB BER performance gap betweenthem.

The BER performance of the proposed SRRC receiver filter isevaluated for QPSK, 16QAM, and 64QAM with γ = 0.9 and 17,25, 33, 41, and 49 filter taps, as shown in Fig. 7, which shows thatthe BER performance of the receiver of the proposed SRRCreceiver filter with 25 filter taps for γ = 0.9 is almost the same asthat of the conventional SRRC filters with 49 filter taps and theproposed receiver filter with 33 filter taps has better performancethan that of the conventional SRRC filters with 49 filter taps.

Fig. 3  ISI of the proposed SRRC receiver filter and the conventional SRRCfilter

Fig. 4  Stopband attenuation of the proposed SRRC receiver filter and theconventional SRRC filter

Fig. 5  BER performance of the proposed and the conventional SRRCreceiver filters with QPSK, 16QAM, and 64QAM in AWGN channel(a) γ = 0.1, (b) γ = 0.9

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5 ConclusionIn this paper, a new receiver filter design algorithm for the wirelesscommunication systems is proposed by reducing the number offilter taps, which is based on the steepest-descent method with ajoint cost function of ISI and stopband attenuation. Reduction ofthe receiver filter taps reduces the computational complexity andthe detection delay in the receiver. The ISI and stopbandattenuation were modified into the matrix forms to make the jointcost function for the steepest-descent method.

From the numerical analysis, it is shown that ISI and stopbandattenuation are degraded by reducing the number of filter taps. The

proposed SRRC receiver filter design algorithm efficiently reducesthe number of filter taps without BER performance degradation inthe AWGN channel, where the proposed receiver filter designalgorithm can reduce the number of filter taps to 17 for QPSK and16QAM and 25 for 64QAM without BER performance degradationcompared to the conventional SRRC filter with 49 filter taps. Inhigh ISI environment, the proposed SRRC receiver filter with 25filter taps for QPSK, 16QAM and 64QAM have almost the sameBER performance as the conventional SRRC receiver filter with 49filter taps. In high ACI environment, the proposed receiver filterwith 25 filter taps has almost the same BER performance as theconventional SRRC filter with 49 filter taps.

6 References[1] Proakis, J.G., Salehi, M.: ‘Communication systems engineering’ (Prentice-

Hall, New Jersey, 2002, 2nd edn. 2002)[2] Chevillat, P.R., Ungerboeck, G.: ‘Optimum FIR transmitter and receiver

filters for data transmission over band-limited channels’, IEEE Trans.Commun., 1982, COM-30, pp. 1909–1915

[3] Salazar, A.C., Lawrence, V.B.: ‘Design and implementation of transmitter andreceiver filters with periodic coefficient nulls for digital systems’. Proc. IEEEInt. Conf. Acoustics, Speech, and Signal Processing (ICASSP 1982), Paris,France, 3–5 May 1982, (7), pp. 306–310

[4] Samueli, H.: ‘On the design of optimal equiripple FIR digital filters for datatransmission applications’, IEEE Trans. Circuits Syst., 1988, 35, pp. 1542–1546

[5] Tuqan, J., Vaidyanathan, P.P.: ‘A state space approach to the design ofglobally optimal FIR energy compaction filters’, IEEE Trans. Signal Process.,2000, 48, pp. 2822–2838

[6] Balaji, B., Yeap, T.H.: ‘Minimal length multirate zero ISI filters’. CanadianConf. on Electrical and Computer Engineering World Trade and ConventionCentre (CCECE 2000), Halifax, NS, Canada, 7–10 May 2000, (1), pp. 113–117

[7] Sood, R., Xiao, H.: ‘Root Nyquist pulses with an energy criterion’. Int. Conf.Communications (ICC 2007), Glasgow, Scotland, 24–28 June 2007, 2711–2716

[8] Eghbali, A., Saramaki, T., Johansson, H.: ‘On two-stage Nyquist pulseshaping filters’, IEEE Trans. Signal Process., 2012, 60, pp. 483–488

[9] Ramachandran, R.P., Kabal, P.: ‘Minimax design of factorable Nyquist filtersfor data transmission systems’, IEEE Trans. Signal Process., 1989, 18, pp.327–339

[10] Vandamme, P.: ‘On the synthesis of digital transmit filters’, IEEE Trans.Commun., 1991, 39, pp. 485–487

[11] Chen, C.L., Willson, A.N.: ‘A trellis search algorithm for the design of FIRfilters with signed-powers-of-two coefficients’, IEEE Trans. Circuits Syst. II,1999, 46 pp. 29–39

[12] Yao, A.C., Chien, C.: ‘Design of a square-root-raised-cosine FIR filter by arecursive method’. IEEE ISCAS 2005, Kobe, Japan, 23–26 May 2005, (1),pp. 512–515

[13] Farhang-Boroujeny, B.: ‘A square-root Nyquist (M) filter design for digitalcommunication systems’, IEEE Trans. Signal Process., 2008, 56, pp. 2127–2132

[14] Hua, J., Wen, J., Lu, W., et al.: ‘Design and application of nearly Nyquist andSR-Nyquist FIR filter based on linear programming and spectrumfactorization’. IEEE Conf. on Industrial Electronics and Applications (ICIEA2014), Hangzhou, China, 9–11 June 2014, pp. 64–67

[15] Yardim, A., Laakso, T.I., Sabel, L.P., et al.: ‘Design of efficient receive FIRfilters for joint minimization of channel noise, ISI, and adjacent channelinterference’. The Global Communications Conf. (GLOBECOM 1996),London, UK, 18–28 November 1996, (2), pp. 948–952

[16] Campbell, W.M., Parks, T.W.: ‘Optimal design of transmitter and receiverfilters with mixed performance objectives’. Proc. Int. Conf. Acoustics,Speech, and Signal Processing (ICASSP 1996), Atlanta, GA, USA, 9 May1996, (3), pp. 1527–1529

[17] Sevillano, J.F., Velez, I., Irizar, A.: ‘On the design of receiver root-raisedcosine FIR filters in high interference scenarios’, IEEE Trans. ConsumerElectron., 2005, 51, pp. 1104–1109

[18] Yao, C.Y., Willson, A.N.Jr.: ‘The design of symmetric square-root pulse-shaping filters for transmitters and receivers’. IEEE Int. Symp. Circuits andSystems (ISCAS 2007), New Orleans, LA, USA, 27–30 May 2007, pp. 2056–2059

[19] Wilson, S.G., Lo, H.H.J.: ‘Optimum digital pulse shaping filters’. MilitaryCommunications Conf. (MILCOM 2016), Baltimore, MD, USA, 1–3November 2016, pp. 660–665

[20] Xia, X.G.: ‘A family of pulse-shaping filters with ISI-free matched andunmatched filter properties’, IEEE Trans. Commun., 1997, 45, pp. 1157–1158

[21] Demeechai, T.: ‘Pulse-shaping filters with ISI-free matched and unmatchedfilter properties’, IEEE Trans. Commun., 1998, 46, p. 992

[22] Siohan, P., de Saint-Martin, F.M.: ‘New designs of linear-phase transmitterand receiver filters for digital transmission systems’, IEEE Trans. Circuits.Syst. II, 1999, 46, pp. 428–433

[23] Oppenheim, A.V., Schafer, R.W.: ‘Discret-time signal processing’ (Pearson,New Jersey, 2010, 3rd edn. 2010)

[24] 3GPP: ‘Technical Specification Group Radio Access Network; UserEquipment (UE) radio transmission and reception (FDD), V8.h.0’. 2016

[25] Hong, S., Stark, W.E.: ‘Performance driven coefficient optimization for highthroughput energy efficient digital matched filter design’. Pacific rim Conf.

Fig. 6  BER performance of the proposed and the conventional SRRCreceiver filters with QPSK, 16QAM, and 64QAM in high ISI environment

Fig. 7  BER performance of the proposed and the conventional SRRCreceiver filters with QPSK, 16QAM, and 64QAM in ACI environment(a) 25 tap filter, (b) 33 tap filter

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on Communications, Computers and Signal Processing (PACRIM 1999),Victoria, BC, Canada, 22–24 August 1999, pp. 321–324

[26] Xing, T., Zhan, Y., Lu, J.: ‘A performance-optimized design of receiving filterfor non-ideally shaped modulated signals’. Int. Conf. Communications (ICC2008), Beijing, China, 19–23 May 2008, pp. 914–919

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