# A High-Throughput Random Access Protocol for  Multiuser MIMO Systems

Authors: Haiyou Guo; Honglin Hu; Yan Zhang
Journal: Research Letters in Communications
 (2008)

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## Abstract

We propose a high-throughput random access protocol for2×2 multiuser multiple-input multiple-output (MIMO) systems. The cross-layer mechanism utilizes the packets combining technique to exploit the advantages of both spatial multiplexing and multipacket reception. Analytical result indicates that the proposed scheme achieves 0.669 per spatial degree of freedom in stable throughput, which is much higher than those in the existed studies.


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## Body

## 1. Introduction

Random access (RA) is a cost-efficient medium access process in next
generation wireless networks to support high-rate high-capacity multimedia
services. The traditional RA schemes, for example, slotted ALOHA, incur the
throughput penalty due to serious collision. The emerging multiple-input
multiple-output (MIMO) technology provides a new dimension of performance
enhancement for RA schemes. MIMO is able to improve the throughput in two
aspects, that is, a single-user throughput
improvement via the spatial multiplexing (SM) such as V-BLAST [1]; and the
whole system throughput improvement via the multipacket reception (MPR)
capability [2].Collision resolution (CR) has been investigated in
both MIMO systems and single-antenna systems. For
MIMO systems, a multiuser detector was developed with space-time signature
induced by the Alamouti-type space-time block code (STBC) [2]. Consequently,
the slotted ALOHA can operate over Alamouti-type STBC to achieve the MPR
capability. We will term this scheme as ALOHA-Alamouti. In the 2×2 multiuser
MIMO system, however, such MPR is at most applicable for the 2-fold collision,
and hence incurs the undesirable throughput loss for the moments of severe
collision more than 2 folds due to the ineffective
Alamouti-type coding. For the single-antenna systems, multiuser packets
combining techniques were employed in network diversity multiple access (NDMA)
[3] and successive interference cancellation tree algorithm (SICTA) [4] to
improve the throughput. It has been shown that SICTA has the highest throughput
0.693 among the splitting algorithms. However, SICTA requires unbounded amount
of memory to store the mixed packets, and NDMA may be inapplicable in multiuser
MIMO due to the assumption of the fading channel coherence time in the order of
the packet slot. This assumption may not be realistic since the channel
coefficients are usually correlated over adjacent slots.In this letter, we propose a high-throughput RA
protocol for2×2 multiuser MIMO systems. With a cross-layer design approach,
our scheme utilizes the adaptive packets combining technique to reconstruct
Alamouti-type STBC only for the 2-fold collision, and hence avoids the
undesirable throughput loss. Then, the scheme can exploit the benefits of both
V-BLAST and Alamouti-type STBC to improve the throughput. The proposed scheme
is able to achieve stable throughput as high as 0.669 per spatial degree of
freedom while maintaining the implementation simplicity like slotted ALOHA. In
addition, the scheme can operate on the block fading channel without the
constraint on the coherence time.Notations
Bold uppercase letters denote matrices and bold lowercase letters denote
vectors. Complex conjugate, transpose, and inverse operations are represented
by(⋅)*, (⋅)T,
and (⋅)−1,
respectively. [A]ij denotes the (i,j) entry of matrix A. IM is the identity matrix of size M. |⋅| represents the cardinality of a set.


## 2. Modeling Preliminaries

In a cellular
network, there is a set of users, denoted asQ={1,2,…,q,…},
communicating with the base station (BS). All transmissions initiated by a
source q are directed to a single destination d∉Q.
Each user and the BS are equipped with two antennas. The system is equally
slotted in time, and the length of one time slot is T.At each slotn,
each user q may transmit a packet consisting of 2L symbols, which can be demultiplexed into two
subpackets with the same length and fed into two transmit antennas. We denote
these subpackets as(1)xq(n)=[xn,q(1)xn,q(2)⋯xn,q(L)];yq(n)=[yn,q(1)yn,q(2)⋯yn,q(L)].The symbols xn,q(l) and yn,q(l), l=1,2,…,L,
are assumed drawn from a finite QAM constellation. We assume the symbol period
is τ such that T=Lτ.
Let I(n)⊆Q denote the set of users who are active at slot n.
If |I(n)|≥2,
we say that an  |I(n)|-fold collision occurs in the channel.In our proposed scheme as shown in Figure1, we define
three exclusive categories of time slot: remediable colliding slot (RC-Slot),
compensating slot (C-Slot), and trivial slot (T-Slot). If and only if |I(n)|=2 and |I(n−1)|≠2,
we refer to slot n and n+1 as the RC-Slot and the C-Slot, respectively.
The C-Slot immediately follows the RC-Slot; and it is reserved to retransmit
the contended packets during the RC-Slot. A slot is termed as T-Slot in case it
is neither the RC-Slot nor the C-Slot. Each slot serves as only one of the
three types. In Figure 1, slot n and n+3 are RC-Slot; slot n+1 and n+4 are C-Slot; and the other slots are T-Slot.Figure 1
Packet
scheduling of the high-throughput random access protocol for2×2 multiuser MIMO
systems.If slotn acts as a T-Slot or an RC-Slot, the active
user transmits/retransmits the packets in the original form of (1). The
received baseband discrete-time signal at the BS is(2)zn(l)=∑q∈I(n)Hn,q(l)[xn,q(l)yn,q(l)]+vn(l),l=1,2,…,L,where vn(l) is additive noise; and Hn,q(l) is the qth user's 2×2 channel matrix. On the other
hand, if slot n acts as a C-Slot, only the two users
attributed to I(n−1) are allowed to retransmit their packets in the
compensating form of xq*(n−1) and −yq*(n−1).
Specifically, the received signal at the C-Slot n can be written as(3)zn(l)=∑q∈I(n−1)Hn,q(l)[−yn−1,q*(l)xn−1,q*(l)]+vn(l),l=1,2,…,L.We assume a flat fading channel
and the channel matrices are independent across different users. The BS has the
perfect channel state information. These assumptions are reasonable in the pilot-assisted
orthogonal frequency division multiplexing (OFDM) systems. All the entries of Hn,q(l) are with zero mean, independent real, and
imaginary parts, forming an i.i.d. Gaussian collection. Note that the channel
coefficients do not change significantly during the period of (L+1)τ to meet the requirement of correct
demodulation for the reconstructed Alamouti codes, which indicates(4)Hn−1,q(l)=Hn,q(l),l=1,2,…,L.


## 3. High-Throughput RA Protocol for2×2 Multiuser Mimo Systems

In the proposed
scheme, the V-BLAST is designated as a basic mode while the Alamouti-type STBC
can be reconstructed by the packets combining for the remediable 2-fold
collision.


### 3.1. Descriptions of Proposed Protocol

The mechanism
of the proposed protocol is specified as follows.


#### 3.1.1. Immediate Feedback

At the end of each slotn,
each user obtains a 4-ary feedback from the BS with the information of |I(n)|.
Such a feedback indicates the information of |I(n)|=0, |I(n)|=1, |I(n)|=2,
and |I(n)|>2.
Based on the feedback and its own state, each user can deduce the category of
the current slot and decide the operation in the next slot. To determine the
number of the users involved in the collision, the appropriate collision
detection technique is employed at the BS similar to that of NDMA [3].


#### 3.1.2. Initial Transmission

If one packet arrives during an RC-Slot, its first
transmission is randomly scheduled in a slot except theC-Slot. Otherwise, it
is transmitted immediately at the next slot.


#### 3.1.3. Collision or Perfect Reception

If only one user sends a packet in a given slot, the
packet is correctly received. If two users send packets during an RC-Slot, then
the receiver should store the colliding packets; and the next slot is reserved
only for these two users as aC-Slot. After combining the stored packets with
the packets received during the C-Slot, the receiver can recover the desired
packets from the 2-fold collision. However, no packet information can be
extracted from a severe collision more than 2 folds,
and the irrecoverable packets are discarded.


#### 3.1.4. Retransmission of Irremediable Collisions

Each packet involved in an irremediable collision,
independent of the others, must be stochastically retransmitted in slots later
other than theC-Slot until the packet is suc-cessfully received.Figure1 shows an example of the protocol operation.
At the end of slot n,
since two consecutive feedbacks indicate |I(n−1)|≠2 and |I(n)|=2,
the active users during slot n,
that is, I(n)={q1,q2},
can deduce that slot n and the next slot n+1 are RC-Slot and C-Slot,
respectively.  Thus, the
receiver stores the mixed packets in slot n;
and {q1,q2} will retransmit packets in the compensating
form at the immediate next slot. Meanwhile, the inactive users during slot n,
that is, {q3,q4,q5},
can understand the same situation and hence keep silent in the next slot,
although {q4,q5} have new arrivals during slot n.
Thereafter, {q4,q5} will randomly schedule the new arrivals in the
future slot except the C-Slot to avoid the collision with {q1,q2} in slot n+1.
In the proposed scheme, each user decides his own operation based on the local
information. Particularly, each user behaves independently in the RC-Slot and
T-Slot analogous to the slotted ALOHA. The RC-Slot and T-Slot occur
stochastically whereas the C-Slot succeeds to the RC-Slot determinately.


### 3.2. CR through Reconstructed   Alamouti-Type STBC

In the proposed
scheme, the colliding packets can be remedied with the help of the
Alamouti-type STBC. Let us consider the case in Figure1 where two users
collide in an RC-Slot n.
Then, the receiver stores the 2-fold colliding packets during slot n,
that is, Zn=[zn(1)zn(2)⋯zn(L)],
where(5)zn(l)=[zn,1(l)zn,2(l)]=∑q∈{q1,q2}Hn,q(l)[xn,q(l)yn,q(l)]+[vn,1(l)vn,2(l)],l=1,2,…,L.Once the RC-Slot has been
detected, the system immediately enters theC-Slot. Thus, the users {q1,q2} send the compensating packet at slot n+1.
Another 2-fold colliding packets can be received at the BS, that is, Zn+1=[zn+1(1)zn+1(2)⋯zn+1(L)],
where(6)zn+1(l)=[zn+1,1(l)zn+1,2(l)]=∑q∈{q1,q2}Hn+1,q(l)[−yn,q*(l)xn,q*(l)]+[vn+1,1(l)vn+1,2(l)],l=1,2,…,L.Rearranging (5) and
(6), with the assumption of (4),
we can reconstruct the Alamouti-type STBC. Thus, we have [2](7)z˜n(l)=[Hn,q1(l,1)Hn,q2(l,1)Hn,q1(l,2)Hn,q2(l,2)][an,q1(l)an,q2(l)]+v˜n(l),l=1,2,…,L, where (8)z˜n(l)=[zn,1(l)−zn+1,1*(l)zn,2(l)−zn+1,2*(l)]T;v˜n(l)=[vn,1(l)vn+1,1(l)vn,2(l)vn+1,2(l)]T;an,q(l)=[xn,q(l)yn,q(l)]T;Hn,q(l,i)=[[Hn,q(l)]i,1[Hn,q(l)]i,2−[Hn,q(l)]i,2*[Hn,q(l)]i,1*].By applying the following block linear
filter:(9)W=[I2−Hn,q2(l,1)Hn,q2−1(l,2)−Hn,q1(l,2)Hn,q1−1(l,1)I2]we extract the original packets
from the packet mixture of (7). As a result, we obtain the interference free
packets for users q1 and q2,
shown as(10)Wz˜n(l)=[H˜n,q1(l)an,q1(l)H˜n,q2(l)an,q2(l)]+Wv˜n(l),l=1,2,…,L,where(11)H˜n,q1(l)=Hn,q1(l,1)−Hn,q2(l,1)Hn,q2−1(l,2)Hn,q1(l,2);H˜n,q2(l)=Hn,q2(l,2)−Hn,q1(l,2)Hn,q1−1(l,1)Hn,q2(l,1).SinceH˜n,q1(l) and H˜n,q2(l) keep the Alamouti structure [2], the packets
involved in the 2-fold collision are recovered with 2-fold diversity order
merely through linear processing. However, to achieve the same diversity gain
for the packet without collision, more sophisticated detection algorithm is
required other than linear processing. Thus, the multiaccess interference (MAI)
can be easily eliminated without sacrificing the space-time diversity gain.
Consequently, in the proposed scheme, the transmission reliability is mainly
impaired by the severe MAI rather than the noise. In the following throughput
analysis, we will consider the error due to packet overlapping rather than that
due to the noise.


### 3.3. Throughput Analysis

We evaluate the
throughput using the tool similar to that developed for the standard ALOHA
under the classical infinite population Poisson model [5, page 48]. Note that
for the multiantenna scenario, the throughput is defined as the fraction of
time during which the space-time channel carries useful information per spatial
degree of freedom.In the proposed scheme, each user behaves
independently during the slots except forC-Slot. Then, we can assume that the
start time of packets in the channel except for C-Slot follows a Poisson point
process with parameter γ packets/second. Let Γ denote the normalized intensity, that is, Γ=γT.
During a slot, the average number of the uncolliding subpackets is 2×Γe−Γ,
and the average number of the remediable colliding subpackets is 4×0.5Γ2e−Γ.
Taking into account the extra cost of the C-Slot spent on the collision
remediation, the average number of the required C-Slots is 0.5Γ2e−Γ.
Therefore, the throughput, S,
is given by(12)S=2Γe−Γ+2Γ2e−Γ2(1+0.5Γ2e−Γ)=2(Γ+Γ2)e−Γ2+Γ2e−Γ.Figure2 compares the highest throughput of different
RA schemes under the same scenario. Here G is the normalized offered load [5] for
ALOHA-Alamouti and ALOHA with V-BLAST. Since the highest throughput is
unrelated to the scale of abscissa, we can derive that our proposed scheme,
ALOHA-Alamouti, and ALOHA with V-BLAST can reach their own maximal throughput
at 0.669, 0.420, and 0.36 per spatial degree of freedom, respectively. The
latter two schemes improve the throughput only via MPR or SM, respectively.
However, our strategy can permeate the flexibility of Alamouti codes to the MAC
layer so as to employ the advantages of both MPR and SM. For the T-Slot without
collision, the packet can be exactly received achieving the SM gain. For the
RC-Slot and C-Slot, the packets of two active users
can be resolved via the MPR capability of the reconstructed Alamouti-type STBC.
Consequently, the proposed protocol achieves much higher throughput than the
conventional ones. In addition, the achieved throughput approaches to the known
highest throughput 0.693 in SICTA whereas the proposed protocol can behave as
simple as slotted ALOHA.Figure 2
Highest throughput per spatial degree of freedom achieved by different random
access protocols for2×2 MIMO systems.We also make the network simulation for the proposed
scheme used by a group ofK (K=20,40,60) users each with single buffer. At each slot
of the simulating system, if the user has no packet in his buffer, he
independently generates a packet with probability σ.
If a packet transmission is unsuccessful, the packet is backlogged in the
buffer and its retransmission is independently scheduled with probability ν except C-Slot, where ν=σ.
Figure 3 shows the throughput versus generation probability with different
number of users. In Figure 3, the highest values of each throughput curve are
closed to 0.669, and hence corroborate the theoretical analysis.Figure 3
Throughput versus generation probability in the proposed scheme withK users.


## 3.1. Descriptions of Proposed Protocol

The mechanism
of the proposed protocol is specified as follows.


### 3.1.1. Immediate Feedback

At the end of each slotn,
each user obtains a 4-ary feedback from the BS with the information of |I(n)|.
Such a feedback indicates the information of |I(n)|=0, |I(n)|=1, |I(n)|=2,
and |I(n)|>2.
Based on the feedback and its own state, each user can deduce the category of
the current slot and decide the operation in the next slot. To determine the
number of the users involved in the collision, the appropriate collision
detection technique is employed at the BS similar to that of NDMA [3].


### 3.1.2. Initial Transmission

If one packet arrives during an RC-Slot, its first
transmission is randomly scheduled in a slot except theC-Slot. Otherwise, it
is transmitted immediately at the next slot.


### 3.1.3. Collision or Perfect Reception

If only one user sends a packet in a given slot, the
packet is correctly received. If two users send packets during an RC-Slot, then
the receiver should store the colliding packets; and the next slot is reserved
only for these two users as aC-Slot. After combining the stored packets with
the packets received during the C-Slot, the receiver can recover the desired
packets from the 2-fold collision. However, no packet information can be
extracted from a severe collision more than 2 folds,
and the irrecoverable packets are discarded.


### 3.1.4. Retransmission of Irremediable Collisions

Each packet involved in an irremediable collision,
independent of the others, must be stochastically retransmitted in slots later
other than theC-Slot until the packet is suc-cessfully received.Figure1 shows an example of the protocol operation.
At the end of slot n,
since two consecutive feedbacks indicate |I(n−1)|≠2 and |I(n)|=2,
the active users during slot n,
that is, I(n)={q1,q2},
can deduce that slot n and the next slot n+1 are RC-Slot and C-Slot,
respectively.  Thus, the
receiver stores the mixed packets in slot n;
and {q1,q2} will retransmit packets in the compensating
form at the immediate next slot. Meanwhile, the inactive users during slot n,
that is, {q3,q4,q5},
can understand the same situation and hence keep silent in the next slot,
although {q4,q5} have new arrivals during slot n.
Thereafter, {q4,q5} will randomly schedule the new arrivals in the
future slot except the C-Slot to avoid the collision with {q1,q2} in slot n+1.
In the proposed scheme, each user decides his own operation based on the local
information. Particularly, each user behaves independently in the RC-Slot and
T-Slot analogous to the slotted ALOHA. The RC-Slot and T-Slot occur
stochastically whereas the C-Slot succeeds to the RC-Slot determinately.


## 3.1.1. Immediate Feedback

At the end of each slotn,
each user obtains a 4-ary feedback from the BS with the information of |I(n)|.
Such a feedback indicates the information of |I(n)|=0, |I(n)|=1, |I(n)|=2,
and |I(n)|>2.
Based on the feedback and its own state, each user can deduce the category of
the current slot and decide the operation in the next slot. To determine the
number of the users involved in the collision, the appropriate collision
detection technique is employed at the BS similar to that of NDMA [3].


## 3.1.2. Initial Transmission

If one packet arrives during an RC-Slot, its first
transmission is randomly scheduled in a slot except theC-Slot. Otherwise, it
is transmitted immediately at the next slot.


## 3.1.3. Collision or Perfect Reception

If only one user sends a packet in a given slot, the
packet is correctly received. If two users send packets during an RC-Slot, then
the receiver should store the colliding packets; and the next slot is reserved
only for these two users as aC-Slot. After combining the stored packets with
the packets received during the C-Slot, the receiver can recover the desired
packets from the 2-fold collision. However, no packet information can be
extracted from a severe collision more than 2 folds,
and the irrecoverable packets are discarded.


## 3.1.4. Retransmission of Irremediable Collisions

Each packet involved in an irremediable collision,
independent of the others, must be stochastically retransmitted in slots later
other than theC-Slot until the packet is suc-cessfully received.Figure1 shows an example of the protocol operation.
At the end of slot n,
since two consecutive feedbacks indicate |I(n−1)|≠2 and |I(n)|=2,
the active users during slot n,
that is, I(n)={q1,q2},
can deduce that slot n and the next slot n+1 are RC-Slot and C-Slot,
respectively.  Thus, the
receiver stores the mixed packets in slot n;
and {q1,q2} will retransmit packets in the compensating
form at the immediate next slot. Meanwhile, the inactive users during slot n,
that is, {q3,q4,q5},
can understand the same situation and hence keep silent in the next slot,
although {q4,q5} have new arrivals during slot n.
Thereafter, {q4,q5} will randomly schedule the new arrivals in the
future slot except the C-Slot to avoid the collision with {q1,q2} in slot n+1.
In the proposed scheme, each user decides his own operation based on the local
information. Particularly, each user behaves independently in the RC-Slot and
T-Slot analogous to the slotted ALOHA. The RC-Slot and T-Slot occur
stochastically whereas the C-Slot succeeds to the RC-Slot determinately.


## 3.2. CR through Reconstructed   Alamouti-Type STBC

In the proposed
scheme, the colliding packets can be remedied with the help of the
Alamouti-type STBC. Let us consider the case in Figure1 where two users
collide in an RC-Slot n.
Then, the receiver stores the 2-fold colliding packets during slot n,
that is, Zn=[zn(1)zn(2)⋯zn(L)],
where(5)zn(l)=[zn,1(l)zn,2(l)]=∑q∈{q1,q2}Hn,q(l)[xn,q(l)yn,q(l)]+[vn,1(l)vn,2(l)],l=1,2,…,L.Once the RC-Slot has been
detected, the system immediately enters theC-Slot. Thus, the users {q1,q2} send the compensating packet at slot n+1.
Another 2-fold colliding packets can be received at the BS, that is, Zn+1=[zn+1(1)zn+1(2)⋯zn+1(L)],
where(6)zn+1(l)=[zn+1,1(l)zn+1,2(l)]=∑q∈{q1,q2}Hn+1,q(l)[−yn,q*(l)xn,q*(l)]+[vn+1,1(l)vn+1,2(l)],l=1,2,…,L.Rearranging (5) and
(6), with the assumption of (4),
we can reconstruct the Alamouti-type STBC. Thus, we have [2](7)z˜n(l)=[Hn,q1(l,1)Hn,q2(l,1)Hn,q1(l,2)Hn,q2(l,2)][an,q1(l)an,q2(l)]+v˜n(l),l=1,2,…,L, where (8)z˜n(l)=[zn,1(l)−zn+1,1*(l)zn,2(l)−zn+1,2*(l)]T;v˜n(l)=[vn,1(l)vn+1,1(l)vn,2(l)vn+1,2(l)]T;an,q(l)=[xn,q(l)yn,q(l)]T;Hn,q(l,i)=[[Hn,q(l)]i,1[Hn,q(l)]i,2−[Hn,q(l)]i,2*[Hn,q(l)]i,1*].By applying the following block linear
filter:(9)W=[I2−Hn,q2(l,1)Hn,q2−1(l,2)−Hn,q1(l,2)Hn,q1−1(l,1)I2]we extract the original packets
from the packet mixture of (7). As a result, we obtain the interference free
packets for users q1 and q2,
shown as(10)Wz˜n(l)=[H˜n,q1(l)an,q1(l)H˜n,q2(l)an,q2(l)]+Wv˜n(l),l=1,2,…,L,where(11)H˜n,q1(l)=Hn,q1(l,1)−Hn,q2(l,1)Hn,q2−1(l,2)Hn,q1(l,2);H˜n,q2(l)=Hn,q2(l,2)−Hn,q1(l,2)Hn,q1−1(l,1)Hn,q2(l,1).SinceH˜n,q1(l) and H˜n,q2(l) keep the Alamouti structure [2], the packets
involved in the 2-fold collision are recovered with 2-fold diversity order
merely through linear processing. However, to achieve the same diversity gain
for the packet without collision, more sophisticated detection algorithm is
required other than linear processing. Thus, the multiaccess interference (MAI)
can be easily eliminated without sacrificing the space-time diversity gain.
Consequently, in the proposed scheme, the transmission reliability is mainly
impaired by the severe MAI rather than the noise. In the following throughput
analysis, we will consider the error due to packet overlapping rather than that
due to the noise.


## 3.3. Throughput Analysis

We evaluate the
throughput using the tool similar to that developed for the standard ALOHA
under the classical infinite population Poisson model [5, page 48]. Note that
for the multiantenna scenario, the throughput is defined as the fraction of
time during which the space-time channel carries useful information per spatial
degree of freedom.In the proposed scheme, each user behaves
independently during the slots except forC-Slot. Then, we can assume that the
start time of packets in the channel except for C-Slot follows a Poisson point
process with parameter γ packets/second. Let Γ denote the normalized intensity, that is, Γ=γT.
During a slot, the average number of the uncolliding subpackets is 2×Γe−Γ,
and the average number of the remediable colliding subpackets is 4×0.5Γ2e−Γ.
Taking into account the extra cost of the C-Slot spent on the collision
remediation, the average number of the required C-Slots is 0.5Γ2e−Γ.
Therefore, the throughput, S,
is given by(12)S=2Γe−Γ+2Γ2e−Γ2(1+0.5Γ2e−Γ)=2(Γ+Γ2)e−Γ2+Γ2e−Γ.Figure2 compares the highest throughput of different
RA schemes under the same scenario. Here G is the normalized offered load [5] for
ALOHA-Alamouti and ALOHA with V-BLAST. Since the highest throughput is
unrelated to the scale of abscissa, we can derive that our proposed scheme,
ALOHA-Alamouti, and ALOHA with V-BLAST can reach their own maximal throughput
at 0.669, 0.420, and 0.36 per spatial degree of freedom, respectively. The
latter two schemes improve the throughput only via MPR or SM, respectively.
However, our strategy can permeate the flexibility of Alamouti codes to the MAC
layer so as to employ the advantages of both MPR and SM. For the T-Slot without
collision, the packet can be exactly received achieving the SM gain. For the
RC-Slot and C-Slot, the packets of two active users
can be resolved via the MPR capability of the reconstructed Alamouti-type STBC.
Consequently, the proposed protocol achieves much higher throughput than the
conventional ones. In addition, the achieved throughput approaches to the known
highest throughput 0.693 in SICTA whereas the proposed protocol can behave as
simple as slotted ALOHA.Figure 2
Highest throughput per spatial degree of freedom achieved by different random
access protocols for2×2 MIMO systems.We also make the network simulation for the proposed
scheme used by a group ofK (K=20,40,60) users each with single buffer. At each slot
of the simulating system, if the user has no packet in his buffer, he
independently generates a packet with probability σ.
If a packet transmission is unsuccessful, the packet is backlogged in the
buffer and its retransmission is independently scheduled with probability ν except C-Slot, where ν=σ.
Figure 3 shows the throughput versus generation probability with different
number of users. In Figure 3, the highest values of each throughput curve are
closed to 0.669, and hence corroborate the theoretical analysis.Figure 3
Throughput versus generation probability in the proposed scheme withK users.


## 4. Conclusion

We have
proposed a high-throughput random access protocol for the2×2 multiuser MIMO
systems. The throughput can be as high as 0.669 per spatial degree of freedom.
Our scheme can be readily extended to the 2×M (M>2) multiuser MIMO systems to accommodate M-fold
collision [2].



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*Source: 730610-2008-05-15.xml*