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January 25, 2013

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Impact of Mobility on Cooperative Communication

Krishna Srikanth Gomadam and Syed Ali Jafar

Electrical Engineering and Computer Science

University of California, Irvine, CA 92697-2625

Email: ********@***.***, ****@***.***

A constraint on the training rate would result in severe

Abstract We investigate the performance degradation due to

performance degradation leading to an error oor. Therefore,

rapidly time varying channels in a repetition based coherent

cooperative system. We demonstrate that mobility of source noncoherent schemes are preferred although they bring in a 3

affects the performance much more than the mobility of des-

dB performance penalty compared to ideal coherent detection.

tination, for both amplify and forward (AF) and demodulate

In general, the channel can be broadly modeled as h = hc + h

and forward (DF) relays, despite the symmetry of the network.

where hc is the estimate of the channel obtained through

Exploiting the property of FSK modulation that allow us to detect

training and h denotes the estimation error. Most receivers

either coherently or noncoherently or even semi-coherently, we

develop ML detection rules for a variety of mobile scenarios. ignore h when operating coherently and similarly hc is

The detection rules that take into account the mobility of the

not considered during noncoherent detection. However there

nodes, are mostly hybrids of partially coherent detectors and

is a scope for performance improvement if both hc and the

noncoherent detectors. The performance of these detectors is

statistics of h are included in the detection process. With

better than the best of coherent and noncoherent detectors in fast

some modulation schemes like FSK, a combination of coherent

fading and a gain of about 2 dB is obtained over a wide range

of SNR and a gain of almost 3 dB is achieved at the crossing of and noncoherent detection [8], [9] can be performed utilizing

coherent and noncoherent curves. As energy ef ciency is one of

partial channel state, resulting in a signi cant energy savings.

the main objectives for pursuing cooperation and relaying, these

Partial channel state here refers to the channel information

hybrid detectors assume signi cance in fast fading scenarios.

acquired via training at a very low rate, that gets outdated due

to rapid channel variations.

I. I NTRODUCTION In a relay network, mobility of a few nodes need not make

the entire set of channels time selective. With appropriate

Despite its impressive advantages, employing multiple an-

detection strategies that utilize partial CSI, performance im-

tennas for transmission and reception is still unattractive due

provement can be obtained over a complete noncoherent detec-

to size and cost limitations of terminals in cellular, ad-hoc

tion. In Section V, we propose a variety of partially coherent

and sensor networks. For such systems, space diversity can be

detectors for a repetition based cooperative network, for both

achieved by allowing multiple users to cooperate and effec-

AF and DF relays. The detection rules obtained take account

tively share their antennas. Space diversity obtained through

of the mobility scenario and various CSI assumptions at the

this form is referred to as cooperative diversity [1] since the

relay and the destination. For cooperation with a DF relay, we

terminals share their antennas and other resources to form a

follow the framework in [10], so that the detection rules can

virtual antenna array.

be implemented using the piecewise linear approximations.

Cooperative diversity can be accomplished in a variety of

Numerical results are provided to substantiate the merits of the

ways. For example, a repetition based cooperation in [2],

detectors. As energy ef ciency is one of the main objectives

[3], a space time code based cooperation as in [4], [5] and

for pursuing cooperation and relaying, these hybrid detectors

a channel code based cooperation as in [6], can all achieve

assume signi cance in fast fading scenarios.

full diversity [7], i.e a diversity order equal to the number of

paths between the source and the destination. Repetition based

II. S YSTEM M ODEL

cooperative protocols which incur very little complexity at the

receiver are spectrally inef cient since each relay requires a Our model consists of a source-destination pair with a single

separate orthogonal channel for repeating the information [5]. relay as shown in Fig. 1. A TDMA protocol [4] based on half

Space-time coded cooperative diversity protocols improve the duplex operation, is chosen in which the source S transmits

spectral ef ciency of the system as the relays can transmit to both the relay R and destination D in the rst slot. In

simultaneously in the same sub-channel. However it increases the second slot the relay transmits to the destination, while

the decoding complexity at the terminals. the source remains idle. The set of equations given below

Wireless sensor networks where many nodes cooperate to summarize the operations taking place for the k th symbol.

detect an event and forward the information, need energy

y (k ) = h(k )x(k ) + nD1 (k )

ef cient relaying strategies, to prolong the network lifetime.

Certain applications of wireless sensor networks require the r(k ) = g (k )x(k ) + nR (k )

system to operate in a highly time selective environment. Thus

z (k) = f (k)xr (k) + nD 2 (k) (1)

a choice must be made between coherent and noncoherent

modulation/detection. For a coherent scheme to operate re- At both the relay and the destination, the received signal

liably in a fast fading environment, the channel has to be is corrupted by additive white Gaussian noise with variance

N0 . For amplify and forward (AF) relaying, xr (k ) = k rk .

estimated quite frequently. And in a pilot symbol assisted

The relay ampli cation factor, k is chosen to satisfy an

modulation, this leads to both spectral and energy inef ciency.

908

U.S. Government work not protected by U.S. copyright

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2006 proceedings.

the channel g (k ).

k = (5)

g (k) 2 Es + N0

S D

However it is hard to obtain instantaneous CSI in a rapidly

time varying channel. In this context, the channel information

obtained via training gets outdated soon and can only provide

Fig. 1. System Model

partial information. Using this partial knowledge for calculat-

ing the ampli cation factor for the k th symbol duration, we

have

average power constraint. For a demodulate and forward relay, Es

k =

xr (k ) = x(k ), where x(k ) is obtained after demodulating r(k )

E ( g (k ) 2 )Es + N0

followed by modulation for transmission to the destination.

We assume all the channels to be frequency nonselective but = . (6)

2k g 2 + (1 a2k ) 2 )E + N

(a2 0

time selective, modeled by an autoregressive (AR) process. It 0

2 s

is indicated in [11] that the rst order AR model is a good When absolutely no CSI is available,

approximation to the actual fading process.

k =,

g Es + N0

1 a2 h(k )

h(k ) = a1 h(k 1) + 1

is an optimal choice. It can be readily seen that the relay gains

1 a2 g (k )

g (k ) = a2 g (k 1) + 2

for the coherent and noncoherent case are the special forms of

(6), obtained by setting a = 1 and a = 0 respectively. As the

1 a2 f (k )

f (k ) = a3 f (k 1) + (2)

quality of the channel estimate degrades with symbol position,

where 0

Fig. 2 compares the performance of direct transmission and

This expression is accurate at high SNR and the error oor

coherent AF system with a static relay. Both the cases with

caused due to constrained channel estimation rate can be

found. source mobile and destination mobile are plotted. The relay

1 1

1 1 1 1

1 1

employs a scaling as mentioned in (6). Difference in the

a2N a2N

(a1 a2 )2N (a1 a3 )2N

3 2 3

Pe = + 1 1 +

1 1 1 1

16N

2 1 2 1

performance between the source mobility and the destination

2 2

(a1 a2 ) (a1 a3 ) a a

2 3

1 1

mobility scenarios can be observed. Consider the case where

a2N

3 1

1 1

the relay alone is mobile. As the direct path is time invari-

ant, the relay mobility case performs better than source or

destination mobility. This can also be observed in the error

B. Source Mobility versus Destination Mobility

probability expression in (10). In this case, however it should

Suppose there are two cooperative scenarios with a static be noted that the gain achieved from cooperation (over direct

relay in which either the source or the destination is mobile but transmission) is less.

not both. Naturally both the scenarios are expected to perform

identically due to the symmetry. However source mobility

IV. D EMODULATE AND F ORWARD

affects the performance slightly more than destination mobility

The relay demodulates its received symbol r(k ) and modu-

in a coherent cooperative system, regardless of whether the

relay scaling factor depends on partial channel knowledge lates it again for transmitting it with its own power constraint.

or not. When does not depend on partial knowledge of As there is a possibility of decision error at the relay, the

910

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2006 proceedings.

detector at the destination must take account of the error 10

D Mobile (a1=a3=0.999, a2=1)

propagation at the relay. The joint density of the received S Mobile (a1=a2=0.999, a3=1)

Direct (a1=0.999)

symbols y (k ) and z (k ) is

Pr(y (k), z (k) xk, a1, a2, a3, h0, f0, g0 ) = Pr(y (k) xk, a1, h0 ). 1

Pr(z (k) xk, a2, a3, g0, f0 ).

(13)

For BPSK modulation, error occurs at the relay when x(k )

is detected as x(k ). Including the decision error at the relay

BER

in the detection rule,

Pr(z (k) x(k), a2, a3, f0 ) = (1 (k))Pr(z (k) xr (k) = x(k), a3, f0 )

+ (k)Pr(z (k) xr (k) = x(k), a3, f0 ).

The average probability of error at the relay for BPSK mod- 10

ulation [8] for k th symbol position is

1 h Es

1 a2k

(k ) = (14)

2 2

2 h Es + N0 4

10 0 25

10 15

SNR in dB

Pr(z (k) x(k), a2, a3, f0 ) = .

((1 a2k )Es + N0 )

Fig. 3. BER performance of the cooperative DF schemes at N=50.

z (k) + ak f0 Es 2 z (k) ak f0 Es 2

3 3

(k) exp +(1 (k)) exp

(1 a2k )Es + N0 (1 a2k )Es + N0

3 3

brings in a 3dB loss which may not be acceptable to systems

It is quite straightforward to arrive at the following decision that are keen on saving energy. This performance penalty due

rule. k to noncoherent detection can be reduced by exploiting partial

4a1 Es Re(h0 y1 (k))

dk = +

channel knowledge.

(1 a2k )Es + N0

In a fast fading channel, the channel estimate obtained

4ak

Es Re(f0 y2 (k))

(k)

through training gets outdated so quickly that coherent detec-

+ exp

(1 a2k )Es +N0

1 (k)

ln 0

tion cannot be performed. Nevertheless the outdated channel

4ak

Es Re(f0 y2 (k))

(k) 3

1+ exp information can still be utilized in the detection process if it

(1 a2k )Es +N0

1 (k)

would result in a considerable performance improvement. The

The cutoff points, which determine the maximum contribution channel information in this context (4) has both amplitude and

of the relayed transmission in the decision rule are phase uncertainties. A detector proposed in [8] exploits this

channel information to provide performance improvements

1 ak

(k )

2 Es + N 0

Tk = ln = ln over the best of coherent and noncoherent detection. It is

(15)

1 (k ) Es

1 + ak

shown in [8] that the detector optimally uses the partial

2 Es + N 0

channel knowledge to result in a combination of coherent

As it can be seen, an increased probability of error at the relay

and noncoherent detection with weights determined according

results in a decreased weight for the relayed transmission,

to the channel variation rate and the quality of the estimate.

limiting the gain that can be achieved from cooperation. In

As nodes are distributed in a cooperative network, all the

such a situation, either the channel has to be estimated before

channels need not be rapidly varying. In such a case, the

Tk decreases below a certain threshold or the cooperative

performance improvement will be much more. We do not

mode must be halted. In a mobile source scenario, the maxi- k

mum contribution from the relayed transmission is ln( 1+ak ), consider differential modulation based cooperation because

1 a

even differential schemes succumb to an error oor in a rapidly

whereas when the destination alone is mobile, the contribution

4ak Es Re(f0 y2 (k))

time varying channel [8], [9].

is, which is not constrained as long as

(1 a2k )Es

The system model for cooperation with BFSK modulation

a = 0. Fig. 3 compares the performance of direct transmission

is given by,

and coherent DF system with a static relay. It can be seen y (k) = h(k)x(k) + nD 1 (k)

that the performance difference between the destination mobile

r(k) = g (k)x(k) + nR (k)

case and the source mobile case with a DF relay is much more

than that with an AF relay. z(k) = f (k)xr (k) + nD 2 (k), (16)

where the transmitted and received symbols are vectors with

V. PARTIALLY C OHERENT C OOPERATION WITH FSK two components representing the two orthogonal bands of

MODULATION BFSK.

xr (k ) = k r(k )

Employing purely coherent detection in a fast fading envi-

ronment in systems that have a constraint on channel estima- k is chosen to satisfy an average energy constraint per

tion rate clearly results in a serious performance degradation symbol. For DF systems, the symbol detected at the relay is

as highlighted in the previous section. Usually noncoherent transmitted with its own power constraint.

detection that obviates the need for channel estimation is

xr (k ) = xk .

preferred. However as discussed earlier, noncoherent detection

911

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2006 proceedings.

A. Demodulate and Forward 10

Coherent Detection

ML detection rule for a single relay demodulate and forward Non Coherent

Partially Coherent + Non Coherent

scheme [10] can be generalized as Partially Coherent + Partially Coherent

(k )

+ exp (q2 ) 1

1 (k) 10

dk = q1 + ln 1 0, (17)

(k )

1 + 1 (k) exp (q2 )

where q1, q2 and are obtained according to the detection

BER

strategies at the relay and the destination. Detection rule for 2

coherent detection with FSK in a time varying channel can be

directly obtained from the result in Section IV. In the rest of

the section, we provide ML detection rules for various partially

coherent detectors. 3

1) Partially Coherent Direct link and Non Coherent Decod-

ing at the relay : When it is hard to obtain partial channel

knowledge at the relay, noncoherent detection of S-R link.

In this detection strategy, the relay performs noncoherent 4

detection and the R-D link is noncoherently detected at the 0 5 10 15 20 25

SNR in dB

destination. The direct link is detected with the partial channel

knowledge and optimal combining results in the following Fig. 4. BER performance of the Demodulate and Forward cooperative

decision rule. schemes for (a1, a2, a3, N ) = (0.998, 0.998, 1, 50).

2ak Es Re[h (y1 (k) y2 (k))] + 1 a2k Es y1 (k) 2 y2 (k) 2

1 0 1

q1 =

N0 (1 a2k )Es + N0

B. Amplify and Forward

f Es z1 (k) 2 z2 (k) 2

q2 = Partially coherent detection with FSK leads to a simul-

N0 f Es + N0

taneous implementation of both coherent and noncoherent

1 detection followed by an optim

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