A Distributed System for Cooperative MIMOTransmissions

Hsin-Yi Shen, Haiming Yang, Biplab Sikdar, Shivkumar KalyanaramanDepartment of ECSE, Rensselaer Polytechnic Institute, Troy, NY 12180 USA

Abstract— In this paper we propose a distributed systemfor facilitating cooperative MIMO transmissions in networkswithout multiple antenna devices. MIMO diversity is achievedby employing groups of nodes in the vicinity of the sourceand destination to help with the transmission. The distributedsending nodes are assumed to have different carrier frequencyoffsets (CFO). Space-time block codes (STBC) and code com-bining are used to utilize spatial diversity. The estimationof multiple CFO and detector for STBC-coded data undermultiple CFO are provided. The BER of the proposed system isshown and discussed. We also consider the energy consumptionand compare it with other cooperative designs.

I. INTRODUCTION

Various schemes in previous research have shown thatspatial diversity can be leveraged at the network, link orphysical layers to provide energy efficient transmissions. Atthe physical layer, MIMO systems use multiple antennas toachieve spatial diversity. However, MIMO systems requiremulti-antennas devices, which may not be feasible in somedevices due to cost and size limitations. Thus the concept ofcooperative diversity has been proposed to provide spatial di-versity with single antenna devices. In cooperative networks,the source uses idle nearby nodes to provide spatial diversity.Most of existing research considers the transmission betweentwo senders and one receiver [1]–[4] or multiple relaysbetween source and destination [5]. Also, most of previousschemes can be viewed as an extension of relay models anddo not allow arbitrary numbers of cooperating nodes.

The key challenges faced with distributed implementationof cooperative MIMO system are: (1) node coordinationin sending and receiving groups, (2) distributed space-timecoding and carrier frequency offsets in senders, and (3) datacombining in the destination. Compared to the centralizedcoding scheme in traditional MIMO systems, a distributedcoding scheme is expected for cooperative MIMO transmis-sions. In this paper we propose to use space-time block codes(STBC) and combine it with a distributed MAC protocol toachieve a distributed implementation that allows for flexiblenumber of cooperating nodes. A solution is also proposedto solve the problem of multiple carrier frequency offsets(CFO) arising from the fact that each sending node hasits own individual electronic circuits to generate the carriersignal.

To facilitate cooperative MIMO transmissions, this paperproposes a distributed system architecture. The system isbased on the source and destination nodes recruiting nearbynodes to cooperate with the transmission. STBC are usedat each transmitting nodes and code combining is used atthe destination to complete the detection. While the use ofmultiple nodes provides spatial diversity, the use of STBC

Fig. 1. Proposed cooperative MIMO system: (a) Recruitment, (b) MIMOtransmission, (c) Data Collection and Combining

and code combining provides MIMO diversity even underimperfect carriers. The proposed system therefore providesa viable alternative for reliable low-power transmissions.

The rest of this paper is organized as follows: the proposedsystem is described in Section II. The iterative estimation formultiple CFOs and the MMSE detector for received signalsare also discussed in section II, followed by the simulationresults for BER and energy consumption in Section III.Finally, we conclude the paper in Section IV.

II. SYSTEM DESIGN

To facilitate cooperative, virtual MIMO communicationin networks without multiple-antenna devices, the sourceand destination nodes require the help of surrounding nodesto help with the transmissions and receptions. This sectiondescribes the design of such a system and is based on athree step process with the source and destination nodesforming clusters to aid in the transmission and reception. Anoverview of the proposed scheme is shown in Figure 1 andconsistes of the following steps: Step 1: Cluster Formation:At the beginning of each transmission, the source node sendsa recruiting RTS (RRTS) message to its neighbors to solicithelp form them for transmitting the data packet. The RRTSmessage is transmitted at a power level lower than that usedfor normal transmissions (at least by a factor of two) in orderto reduce the interference and power consumption, and alsoto ensure that only nearby nodes are recruited. Neighboringnodes that are available, reply with a sequential CTS (SCTS)packet in order to eliminate collisions. The sequence isexplicitly mentioned in the RRTS packet which lists the

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order in which the neighbors of the source are expected toreply (neighbor discovery is assumed to have been done).After recruiting the sending group, the source node sendsa MIMO RTS control message (MRTS) to the destinationnode to reserve the channel for the transmission. If thedestination node is able to receive the MRTS message, itfirst recruits receiving group nodes, using the same procedureas the source node (using RRTS and SCTS messages). Thedestination node then replies with a MIMO CTS (MCTS)message to the source node to confirm the transmission.The size of the receiving group is included in the MCTSpacket. If no RCTS is received, the source node times outand follows an exponential backoff mechanism similar toIEEE 802.11.

Step 2: STBC MIMO Transmissions: Once the MCTSmessage is received, the source node encodes the informationbits of the data packet using error correction codes. Thenthe source node broadcasts the data and synchronizationinformation with low power to the selected neighbor nodes.The source node also specifies to each helper node whichrow in the STBC matrix it is supposed to use. Since thedistance between the source and the helping nodes is quiteshort, members of the sending group are not required to sendan ACK back to the source node. All nodes in the sendingcluster then transmit their data to the destination cluster.

Step 3: Data Collection and Combining: After receivingthe data from the sending group, each node in the receivinggroup uses the channel state information and estimated car-rier frequency offsets to decode the space-time block codeddata. After decoding for STBC, each node in the receivinggroup relays its copy of the data to the destination node. Thedestination receives signal copies from the helper nodes anddetects them as soft symbols. Then the destination uses codecombining and chooses the most probable codeword basedon the received soft symbols. If the original data is decodedcorrectly, the destination node sends an ACK to the sourcenode. Otherwise, no ACK is sent and the source node willtimeout and initiate a backoff mechanism before attemptinga retransmission (where the whole procedure is repeated).

A. Carrier Frequency Offset Estimation

A key challenge in the design of the system proposedabove is that since the cooperative transmissions will bemade at different nodes, a frequency offset is expected intheir carrier frequencies. This in turn may lead to unaccept-ably high levels of bit errors at the receiving nodes. In thissection we propose a mechanism for enabling each receiverto estimate the multiple carrier frequency offset (CFO) usinguncorrelated pilot symbols. Note that existing schemes like[6] either require independent data streams (not possible withSTBC) or are not accurate when the number of sendersincreases [7] in addition to not specifying how to designuncorrelated pilot symbols.

To design pilot symbols for distributed senders, we usepseudo-random noise (PN) sequences because the receiveronly needs information on the shift register length and initialstate in each sender to obtain pilot symbols. To send pilotsymbols, the source node first decides the length of the shiftregister and assigns the initial state of the shift register for

each sending node. PN-sequences use primitive polynomialsto generate sequences and each specific value of shift registerlength L has only one corresponding primitive polynomial.Thus a receiver only needs to know the length L and canfind the corresponding primitive polynomial. Besides, thePN sequence only has high autocorrelation R(t1 − t2) whent1 = t2. If the initial state is different (i.e, t1 �= t2),the autocorrelation function is almost 0. Thus the sendingnodes can use the same length of shift register as PN-sequence generator and choose different initial states togenerate uncorrelated pilots. The receiving node only needsto know the length L of the shift register and the initialstates of the sending nodes, instead of the whole pilot symbolsequence. This information can be obtained by the receivingnodes through MIMO RTS control messages.

Next, the sending group starts pilot symbol transmissionand all receiving nodes use the received mixed signal of pilotsymbols to estimate the multiple carrier frequency offset. Weassume that there are M sending nodes and N receivingnodes and denote the pilot symbols and carrier frequencyoffset in sending node i as pi and fi, respectively, and thecomplex channel gain between sending node i and receivingnode r as αir. The received signal at receiving node r canbe denoted by

yr[n] =∑

i

αirpi[n]ej2πfin, n = 1, 2, · · ·

where n represents the symbol index. The discrete-timeFourier Transform (DTFT) of the received signal is

Yr(w) =∑

n

yr[n]e−jwn =∑

i

αirPi(w − 2πfi)

where Pi(w) is the DTFT of pi and Pi(w) =∑n pi[n]e−jwn. Next, we compute the cross-correlation

between Yr(w) and the DTFT of the pilot symbol, Pi(w) =Σnpi[n]e−jwn. This cross-correlation is given by [7]

Rr(w, θ) =∫

Yr(w)P∗i (w + θ)dw

= αir

∫Pi(w − 2πfi)P∗

i (w + θ)dw (1)

since the pilots are uncorrelated and Pi(w) is uncorrelatedto Pk(w) for k �= w. From above, Rr(w, θ) becomes theauto-correlation of Pi(w). The autocorrelation function willhave its maxima at lag 0 and receiving node r can estimatethe CFO fi as [7]:

fi = − 12π

maxθ

Rr(w, θ) (2)

However, the channel gain αir is complex, i.e., αir =|αir|ejφir . Thus it distorts the signal phase and affects theestimation in Equation (2), which also uses signal phasefor the carrier frequency offset estimation. To improveestimation precision, we use iterative updating to update fi.The iterative updating algorithm is shown in Algorithm 9.The channel is assumed to be quasi-static fading and thechannel state information (CSI) is known at the receivers.The iterative updating can be viewed as a digital phaselock loop (PLL) for multiple carrier drift signals. Throughiterative updating, the estimation is more precise and themultiple carrier frequency offsets are locked.

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Algorithm 1 Iterative CFO estimation.while

∑n |yr[n] − yr[n]| < ε or iteration < 100 do

for k=1 to M doxkr[n] = yr[n] − ∑

i,i �=k αirpi[n]ej2πfin

Xkr(w) =∑

n xkr[n]e−jwn

Rkr(w, θ) =∫

Xkr(w)P∗k(w + θ)dw

fk = − 12π maxθ Rkr(w, θ)

end foryr[n] =

∑i αirpi[n]ej2πfin

end while

B. STBC decoding under Multiple Carrier Frequency Offset

In the cooperative MIMO transmission described earlierin this section, the receiving nodes decode the space-timeblock coded data and relay their decoded signal copies tothe destination code. With STBC-coded data x, the receivedsignal at receiving node r, yr, is given by

yr = Hrx + N (3)

where N is Gaussian noise and Hr is the matrix of pathgains at receiving node r. Let τt denote the permutation ofsymbols from [x1, x2, · · · , xc] to the tth column in the STBCencoding matrix. The row position of xi in the tth column isrepresented by τt(i). The element in position (t, τt(i)) of thematrix Hr, hr

t,τt(i), is the path gain for symbol xi transmitted

at time t by sending node τt(i). hrt,τt(i)

can be expressed ashr

t,τt(i)= ατt(i),r

dλ/2τt(i),r

, where λ is the path-loss exponent and

αi,r is the fading gain. If the size of the sending group isodd, symbol xi may not be transmitted at time t and hr

t,τt(i)

is 0.If the coded data bits are transmitted without carrier

frequency offsets and we assume quasi-static channels, thematrix Hr is an orthogonal matrix, i.e, Hr = [h1h2 · · ·hc]and h1,h2, · · · ,hc are orthogonal to each other. Thus thesymbols x can be easily decoded. However, for cooperativeMIMO transmissions without perfect carriers, the matrixHr is not orthogonal and becomes time-variant. This timevarying matrix is denoted by Hr,k and the element atposition (t, τt(i)) of matrix Hr,k is given by

hr,kt,τt(i)

= hrt,τt(i)

ej2πfτt(i)t, k =⌊

t

c

⌋(4)

where c is the coding length. Thus hr,kt,τt(i)

is a function oftime t and thus Hr,k is time-variant and nonorthogonal.

Receiving node r can estimate the matrix Hr,n through thechannel gain ατt(i),r and the estimated CFOs fτt(i). How-ever, the receiving node j still needs to detect the symbolsx through the nonorthogonal matrix Hr,n. Considering thecomputation complexity, in this paper we propose to usea linear MMSE detector to detect the STBC-coded dataunder multiple carrier frequency offsets. We now describethe detector design.

At time kc, the signal received at receiving node r is

yr,k = Hr,kx + N, k = 1, 2, · · · , κ (5)

where c is the coding length and is the size of the squarematrix Hr,k and κ = (packet length)/c. We assume that

symbols x are transmitted using BPSK and a linear detectorDi is used. Di is a vector with length c × 1. For the lineardetector Di, the BPSK symbol xi is detected by the phaseof the term (Di

T · y). If the phase is between −π/2 andπ/2, xi is detected as 1. Otherwise it is detected as −1. Tosimplify the computational complexity in receiving node r,we use y instead of y [8]:

y = Hr,kH ·y = Hr,k

HHr,kx+Hr,kH ·N = Rx+N (6)

where R = Hr,kHHr,k and N is Gaussian noise N(0, σ2R)

and σ2 is the noise power. R is a Hermitian matrix, i.e,RH = R. The mean square value of detection error (xi −Di

H · y) is given by

MSE = E[(xi − DiH · y)∗(xi − Di

H · y)]= E[(x∗

i − DiT · y∗)(xi − yT · Di

∗)]= E[x∗

i xi − xi · (DiT · y∗) − x∗

i · (yT · Di∗)

+DiT · y∗yT · Di

∗] (7)

The linear detector Di minimizes the mean square error ifthe gradient

∇Di= E[−xiy∗ + y∗yT Di

∗] = 0 (8)

Thus the linear MMSE detector for xi is

Di = ((E[y∗yT ])−1E[xiy∗])∗ (9)

with E[y∗yT ] and E[xiy∗] defined as

E[y∗yT ] = E[(R∗x∗ + N∗)(xT RT + NT )] (10)

= R∗RT + σ2R∗ (11)

E[xiy∗] = E[xi(R∗x∗ + N∗)] (12)

= R∗ · ei (13)

where ei is a c× 1 vector that only has 1 in the ith elementand 0 otherwise. Thus the linear MMSE detector Di is

Di = (R∗RT + σ2R∗)−1R∗ · ei∗ (14)

= (RT + σ2I)−1 · ei∗ (15)

The matrix (RT + σ2I)−1 does not have a high com-putational complexity since the matrix R is a Hermitianmatrix and I is the identify matrix. The inverse is thuseasy to compute. Also, Di is the ith column in the matrix(RT +σ2I)−1. Thus the linear MMSE detector Di is appliedto the received signal y

DiH y = (RT + σ2I)−1 · ei)T y (16)

= [(RT + σ2I)−1)T y]i (17)

and the ith element in the output vector above is detectedas xi.

III. SIMULATION RESULT

This section presents simulation results to evaluate theperformance of the proposed cooperative MIMO system withmultiple CFO and compare it against other system designs.BPSK modulation is applied to the signal and the channelis assumed to be quasi-static Rayleigh fading. The distancebetween source and destination nodes is 125 meters. The

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5 10 15 20 25 30

10−4

10−3

10−2

10−1

100

SNR (dB)

BE

R

Comparison for BPSK signals over Rayleigh Fading Channel (3×3)

point to pointSTBC with FEC combiningFEC combining without STBCSTBC without FEC combining

Fig. 2. Comparison of Bit error rate (BER) in different systems when thesize of sending/receiving group is 3.

locations of the sending and receiving group nodes arerandomly generated and assumed to be within a circle ofradius 25 meters around the source and destination nodes,respectively. The length of the shift registers is set as 5and the length of pilot symbol sequences is 32 bits. Thetotal transmission power used in step 1 and step 3 of theproposed scheme is assumed to the 10dB lower than the totaltransmission power used in the MIMO transmission in step 2.Also, the total transmission power is divided equally amongall transmission nodes. The transmission power used in theMIMO transmission in step 2 is set to achieve equivalentreceiving SNR in a point-to-point transmission. Thus, thetransmission power in step 2 is defined as SNR·dλ

SD·N0/M ,where dSD is the distance between the source node anddestination node, λ is the path-loss exponent, M is thenumber of nodes in the sending group (including sourcenode), and N0 is the noise power.

To evaluate the proposed cooperative STBC system, wecompare it with two other schemes: (i) cooperative codecombining without STBC and (ii) cooperative MIMO sys-tems without code combining. The performance of the threesystems in terms of the BER for sending and receiving groupsizes of 3×3 is shown in Figure 2. The figure also showthe performance of a traditional point-to-point transmissionwith the same total power consumption as the cooperativeschemes. The system with STBC but no code combining hasthe worst performance among the three schemes because thedestination node only detects symbols based on the majorityin multiple receiving signal copies. The performance of thesystem with code combining but no STBC and the proposedsystem with both STBC and code combing are close sincethe path gain matrix Hr,k is not orthogonal due to multiplecarrier frequency offsets and no full transmitter diversity isguaranteed. However, the performance of proposed systemis a little better than that of the system with only code com-bining. Although no full transmitter diversity is guaranteeddue to multiple CFO and nonorthogonal Hr,k, space-timeblock coding and the proposed linear MMSE detector stillimproves BER performance.

In Figure 3 we evaluate the proposed system (with code

5 10 15 20 25 30

10−4

10−3

10−2

10−1

100

SNR (dB)

BE

R

Comparison for BPSK signals over Rayleigh Fading Channel (3×3)

With itertive estimationNo iterative estimationno CFO estimation

Fig. 3. Comparison of Bit error rate (BER) with different CFO estimationmethod while the size of sending/receiving group is 3.

combining and STBC) under different carrier estimationmethods and discuss the effect of inaccurate CFO estimation.The figure corresponds to group sizes of 3×3. We evalu-ate the system in three scenarios: (1) no CFO estimationschemes are used, (2) CFO estimation without the proposediterative technique, and (3) CFO estimation with the pro-posed iterative estimation technique. The BER of the systemwithout any CFO estimation is around 0.4-0.5 and doesnot decrease as the SNR increases. For BPSK signals, theperformance is near the performance of random guessing forbinary data bits. For systems without the iterative estimationmethod, the performance degrades as the size of the sendinggroup increases and the BER is almost constant when theSNR is greater than 10dB. The performance of the proposediterative scheme is significantly better.

Next, we consider the energy consumption of the pro-posed system. We only consider the energy spent duringa transmission and compare the proposed scheme with (1)cooperative relay systems and (2) cooperative FEC system,which both have one sending node (i.e. the source node)and the receiving group including the destination node. Thesource nodes transmits information bits to the receivinggroup and the receiving nodes relay the received signal to thedestination node. In cooperative FEC system the destinationnode uses code combining to combine the signal copies. Inthe cooperative relay system, the destination node detects theinformation bits only based on the majority.

For the calculation of energy consumption, we considerthe possibility of retransmissions and the power consumptionin control messages. We assume that the MAC protocolsfor cooperative FEC and cooperative relay systems are thesame as the proposed system, except that the recruitingcontrol messages (RRTS and SCTS) are only required inthe receiving group. In the proposed system, the energyconsumption for an unsuccessful transmission attempt is

Eucoopmimo = Emrts + Emcts + 2Errts

+(M − 1)Escts + (N − 1)Escts

+Ebr + Edata + (N − 1)Ecol (18)

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and that for a successful attempt is

Escoopmimo = Emrts + Emcts + 2Errts

+(M−1)Escts + (N−1)Escts

+Ebr + Edata + (N−1)Ecol + Eack (19)

where Emrts, Emcts, Eack, Errts and Escts are the energyspent on sending MRTS, MCTS, ACK, RRTS and SCTSpackets. Ecol is the energy spent by each receiving nodeduring the data collection in the third phase. M and N arethe number of nodes in the source and destination clusters,respectively (including the source and destination nodes).Ebr is the energy spent on broadcasting data to the helpingnodes in the sending group. Edata is the energy spent on thedata transmission between the sending and receiving groups.

We assume that the length of all control messages is Lc

and the size of a data packet is L. The data rate is R anda convolutional code with rate Rc is applied on the datapacket to enable code combining in the receiving group.Thus, the energy spent on transmitting data is Edata =PtL/R/Rc and that on transmitting control messages isEmrts = PmrtsLc/R where Pt is the power level fortransmissions in step 2 and Pmrts is the power level fortransmissions in step 1 and step 3. Thus, Equations (18) and(19) can be rewritten as

Eucoopmimo =Lc

R(Pmrts + Pmcts + 2Prrts

+ (M − 1)Pscts + (N − 1)Pscts)

+L

RRc(Pbr + Ptx + (N − 1)Pcol)(20)

Escoopmimo =Lc

R(Pmrts + Pmcts + 2Prrts

+ (M − 1)Pscts + (N − 1)Pscts + Pack)

+L

RRc(Pbr + Ptx + (N − 1)Pcol) (21)

Combining the two terms above, the total energy for atransmission in the cooperative MIMO system is

E =Pe

1 − PeEucoopmimo + Escoopmimo (22)

where Pe is the packet error probability. The energy con-sumption of the cooperative relay and cooperative FECsystems is similar to Equation (22), except that there is onlyone RRTS and N −1 SCTS control messages in the systemsand Pbr = 0.

In Figure 4 we compare the energy consumption of thethree systems when 3 nodes are used in the receiving groupor for relaying. The following parameters were used forthese figures: R = 2 Mbps, Rc = 1/2, Lc = 64 bytes,and L = 256 bytes. The control messages between thesource and destination nodes (MRTS, MCTS and ACK)are transmitted at 15 dBm while control messages insideeach group (RRTS and SCTS), are transmitted at 1/4 ofthe transmission power of MRTS and MCTS packets. Tomake the comparison reasonable, we assume the total powerconsumption for a transmission attempt is the same in allthree systems. However, the power consumed per successfultransmission is different in each case, because of the different

5 10 15 20 25 3010

−5

100

105

1010

SNR

Tot

al E

nerg

y co

nsum

ptio

n (J

)

Energy Consumption for Systems with 3 receiving nodes

3×3 Cooperative MIMO1×3 Cooperative FEC1×3 Cooperative relay

Fig. 4. Energy Consumption for 3 × 3 cooperative system

BERs in each system. Among the three schemes, the energyconsumption in the proposed system is the smallest. This isbecause the proposed system provides transmitter diversityby forming the sending group. Also, the energy consumptionof cooperative FEC is smaller than that of cooperative relaysystems because code combining improves the decoding.For all schemes, the BER increases at low SNR, which inturn results in multiple retransmissions, thereby resulting inhigh power consumption. As SNR increases, reduction inthe BER decreases the power consumption. However, thisdecrease does not continue unboundedly since higher poweris required for transmitting at high SNRs.

IV. CONCLUSION

This paper proposed a distributed system for cooperativeMIMO transmissions that utilizes space-time block codingand code combining in the sending and receiving groups,respectively. A PN sequence based uncorrelated pilot symbolgeneration with iterative updates is proposed to estimate themultiple carrier frequency offsets from received mixed pilotsignals. For the data transmission, we proposed a MMSEdetector for receiving STBC-coded data under multiple CFO.Simulation results are used to demonstrate the performanceimprovements resulting from the proposed system.

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