Performance Improvement of DPSK System Using a Reconfigurable Multiple Bit Differential Detection

Algorithm in the Presence of Frequency Offset Bojan DIMITRIJEVI , Nenad MILOŠEVI , Zorica NIKOLI

Dept. of Telecommunications, Faculty of Electronic Engineering, Aleksandra Medvedeva 14, 18000 Niš, Serbia

bojan.dimitrijevic@elfak.ni.ac.rs, nenad.milosevic@elfak.ni.ac.rs, zorica.nikolic@elfak.ni.ac.rs

Abstract. In this paper we propose a reconfigurable multiple bit differential detection algorithm that can be used for the DPSK signal reception in the presence of significant frequency offsets. The analysis shows that the bit error probability of the proposed algorithm is nearly constant in a wide frequency offsets range and equal to the error probability for zero frequency offset. Also, the proposed receiver has better performance than the ordinary differential detection receiver for any frequency offset.

Keywords Differential phase shift keying, Frequency offset, Multiple bit differential detection.

1. Introduction Real transmission channels introduce, among other

effects, a unknown phase offset. In order do mitigate the performance degradation due to phase offset, the noncoherent detection of phase shift keying (PSK) signals is often used strategy. When the phase offset is unknown but time–invariant, the constellation rotation due to the phase offset can be removed using a differential PSK (DPSK) modulation scheme [1]. This approach, however, needs higher signal–to–noise power ratios (SNRs) than coherent detection to achieve the same average bit error rate (BER) [1]. An attractive approach to mitigate this SNR loss is called multiple–symbol differential detection (MSDD) [2]–[6]. This detection technique is, in fact, a general case of conventional differential detection that uses more than two consecutive received samples to detect the information symbols. In [3], it is shown that by increasing the number of received samples in a MSDD receiver, the receiver’s performance can approach that of a coherent receiver at a cost of additional complexity. Multiple symbol differential detection is used in different communication systems, and MSDD for UWB communications is proposed in [5]. UWB impulse radios entail distinct signaling structures and stringent performance-complexity requirements, giving rise to the

need for a new MSDD scheme capable of coping with dense multipath UWB channels and detecting a large block of symbols at practical complexity. Paper [5] developed a novel MSDD-based UWB receiver that attains the desired performance advantages by jointly detecting blocks of received symbols based on the autocorrelation principle. The MSDD receiver proposed in [3], assumes that the frequency offset equals zero. In the case of nonzero frequency offset, the conventional MSDD technique must take the frequency offset into account; otherwise, when increasing the number of received samples which contribute in the receiver’s metric, the performance of the receiver degrades very quickly [7,8]. In order to overcome this difficulty a double DPSK (DDPSK) modulation scheme has been proposed [8]–[11]. However, even under the most optimistic conditions, i.e. infinite number of received samples and SNR , the proposed receiver in [8] still needs 3 dB more SNR to achieve the same BER as an optimum coherent detector with DPSK modulation [8].

Modern software and cognitive radio system are often based on reconfigurable structures [12] . Reconfigurable structures may for many purposes at mentioned systems, such as for interference rejection [13].

In this paper we modify the multiple bit differential detection (MBDD) algorithm and make it reconfigurable, so that it can be used for the DPSK signal reception in the presence of significant frequency offsets. The proposed receiver has better performance than the ordinary differential detection receiver for any frequency offset. The analysis will show that the bit error probability of the proposed reconfigurable MBDD (R-MBDD) algorithm is nearly constant in a wide frequency offsets range of practical importance. The proposed algorithm may be used in mobile communication systems in the presence of large Doppler due to relative movement of mobile unit and base station.

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2. System Model Block diagram of the DPSK signal receiver used in

this paper is shown in Fig. 1.

Signal at the input of the receiver is:

)()()( tntstr += (1)

where s(t) is the useful DPSK signal:

tjtj ceets ωθ ˆ)()( = (2)

)()()( tdTtt ⋅+−= πθθ (3)

where symbol d(t) has one of the following two values:

{ } ...2,1,)1(,1,0)( ±±=+<≤∈ pTptpTtd ss (4)

T is the bit interval.

ωωω Δ+= ccˆ is the carrier frequency at the input of the receiver, ωc is the locally generated fixed reference carrier frequency, ωΔ is the frequency offset, and n(t) is white Gaussian noise with variance N0 / 2.

+

⋅s

s

Tk

kTdt

)1(

)(

)cos( tcω

)sin( tcω

r(t)

+

⋅s

s

Tk

kTdt

)1(

)(

Signal processing

)(ˆ kd

xI(k)

xQ(k)

Fig. 1. Block diagram of the proposed M-DPSK signal receiver

The input signal is multiplied by the fixed frequency reference carrier and passed through the integrate and dump circuit. The complex baseband signal at the input of the Signal processing block can be expressed as

)()()( kjxkxkX QI += (5)

Signals at in-phase and quadrature branches are

+

+

=

=

s

s

s

s

Tk

kT

cQ

Tk

kT

cI

dtttrkx

dtttrkx

)1(

)1(

)sin()()(

)cos()()(

ω

ω

(6)

where k is discrete time corresponding the output of the integrate and dump circuit.

The estimated bit )(ˆ kd is determined in the signal processing block by the proposed algorithm that will be described in the following text.

As in [11, Eq. (9)], we set 1−= BNH MN hypothesis

using variable Ri(k,c) as

1,...,1,0

),()()(exp

)()(Re),(

1

2

0

1

1

−=

+−−×

×−−=

−

=

−

=

−

+=

∗

H

n

mli

N

m

N

mni

Ni

lkcnmj

nkXmkXckRB B

θϕ (7)

where NB is the number of bits in multiple bit detection,

M

MMilk li

πθ 2mod),( = (8)

1,...,0,2

)1()( −=−−= csc

s NcN

ccϕϕϕ (9)

where Nc is the number of channels that R-MBDD algorithm is operating with, and sϕ is the algorithm parameter that represents a phase step. The idea is to try to detect symbol with the assumption that the frequency offset is equal to TN sc 2/)1( ϕ−− , TN sc 2/)3( ϕ−− , …,

TN sc 2/)3( ϕ− , TN sc 2/)1( ϕ− . The best assumption (out of given Nc) will give the estimated frequency offset.

In ordinary MBDD algorithm, Nc would be equal to 1, and 0)( =cϕ .

Now, we first find the maximum value of Ri(k,c) with the respect to i

),(max),(max ckRckR ii= (10)

To mitigate the effect of noise, S(k,c) keeps low pass filtered Rmax(k,c) values:

),()1)(,1(),( max ckRAAckSckS ⋅+−−= (11)

where A is the filter parameter. The next step is to find c that maximizes S(k,c):

),(maxarg)(max ckSkcc

= (12)

Using cmax(k) it is possible to find i that maximizes Ri(k,c)

))(,(maxarg)( maxmax kckRki ii

= (13)

The detected symbol is equal to

MM

kikd

BN mod)()(ˆ2

1max

−= (14)

3. Numerical Results The results presented in this section are obtained by

Monte-Carlo simulation with 20 million simulation steps. System parameters are energy per bit to noise power spectral density ratio Eb / N0 = 6 dB, carrier frequency fc = ωc / 2π = 1.6 GHz, bitrate 1 / T = 100 kHz, phase step

01.0=sϕ .

Fig. 2. shows the bit error probability as a function of frequency offset for ordinary differential detection (DD), multiple bit differential detection with NB = 5 bits (5BDD), and proposed reconfigurable MBDD (R-MBDD) with Nc = 10 and Nc = 20.

-20 -15 -10 -5 0 5 10 15 20

10-2

10-1

DD 5BDD R-5BDD, N

c = 10

R-5BDD, Nc = 20

Pb

Δf [kHz] Fig. 2. Bit error probability as a function of frequency offset

It can be seen that DD has worse performance for zero frequency offset than the other considered receivers. Both MBDD and R-MBDD have the same performance for zero and small frequency offset. However, the proposed R-MBDD receiver can operate in much wider frequency offsets range than the conventional MBDD receiver. Also, the higher Nc, the wider performance curve for R-MBDD is.

4. Conclusion In this paper we proposed a reconfigurable multiple

bit differential detector. The analysis has shown that the proposed receiver has bit error probability equal to that of MBDD receiver for zero frequency offset, but has much wider frequency offsets range than can operate with.

Acknowledgements The authors thank the anonymous reviewers for their

valuable suggestions and comments.

Research described in the paper was financially supported by the Ministry of Science and Technological Development of Serbia within the Project "Development and implementation of next-generation systems, devices and software based on software radio for radio and radar networks" (TR-32051).

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