System and method for joint MIMO transmission and compression for interference mitigation with cooperative relay

System and method embodiments are provided for interference mitigation and signal enhancement in downlink wireless communications for MIMO systems with device-to-device communications across cooperating user terminals. In an embodiment, a network controller initializes a transmit covariance for beam-forming a transmit signal of the MIMO transmission from a base-station to a destination terminal and a relay terminal, and initializes a quantization noise covariance used for compressing a relay signal from the relay terminal to the destination. The transmit covariance and the quantization noise covariance are initialized in accordance with known channel state information and with statistics of noise and interference for transmit and relay channels. The transmit covariance and the quantization noise covariance are then jointly optimized using an iterative algorithm in accordance with a capacity constraint on a relay link between the relay terminal and the destination terminal and a transmit signal power constraint of the base-station.

TECHNICAL FIELD

The present invention relates to networking and wireless communications, and, in particular embodiments, to a system and method for joint multiple-input and multiple-output (MIMO) transmission and compression for interference mitigation with cooperative relay.

BACKGROUND

In MIMO systems, the capacity of a radio link is increased using multiple transmit and receive antennas to exploit multipath propagation in various orientations or directions. A base station or user terminal can send and/or receive more than one data signal on the same radio channel at the same time using multipath propagation. The user terminal is any user or mobile device capable of wireless communications with a network, such as a smartphone, a tablet, a laptop computer, or a sensor device. One of the challenges in current and evolving wireless communications networks, including MIMO systems, is the provisioning of high-rate downlink transmission for remote or cell-edge users. A user terminal at the edge of a cell has to account for not only the relatively weak direct signal from its own base station, but also strong interference from the neighboring base-stations. However, modern user terminals may be capable of establishing high-capacity out-of-band device-to-device links (e.g., by using WiFi, Bluetooth, or other wireless link technologies), such as when the terminals are located at sufficient proximity from each other. The physical proximity of the user terminals also suggests that the interference at the multiple terminals can be highly correlated. This opens up the possibility of utilizing device-to-device communications for interference mitigation and signal enhancement. A scheme that can take advantage of device-to-device communications to mitigate MIMO transmissions interference and enhance the signal at reception is needed.

SUMMARY OF THE INVENTION

In accordance with another embodiment, a method for receiving multiple-input and multiple-output (MIMO) transmission and relay channels using device-to-device communications includes receiving, at a destination terminal from a base-station, a transmit signal for the MIMO transmission. The transmit signal is beam-formed in accordance with a transmit covariance obtained by jointly optimizing the transmit covariance and a quantization noise covariance for compressing and relaying the transmit signal from a relay terminal to the destination terminal. The joint optimization of the transmit covariance and the quantization noise covariance is in accordance with known channel state information and with statistics of noise and interference for transmit and relay channels. The method further includes receiving, at the destination terminal from the relay terminal using the device-to-device communications, a relay signal obtained by compressing the transmit signal for the MIMO transmission. The relay signal is compressed by quantization in accordance with the quantization noise covariance. The destination node removes any interference in the received transmit signal and relay signal in accordance with correlated noise in the received transmit signal and relay signal.

In accordance with another embodiment, a method for establishing MIMO transmission and relay channels using device-to-device communications includes initializing, at a network controller, a transmit covariance for beam-forming a transmit signal of the MIMO transmission from a base-station to a destination terminal and a relay terminal, and initializing a quantization noise covariance used for compressing a relay signal from the relay terminal to the destination. The transmit covariance and the quantization noise covariance are initialized in accordance with known channel state information and with statistics of noise and interference for transmit and relay channels. The method further includes jointly optimizing the transmit covariance and the quantization noise covariance using an iterative algorithm in accordance with a capacity constraint on a relay link between the relay terminal and the destination terminal and a transmit signal power constraint of the base-station.

In accordance with another embodiment, a terminal for receiving MIMO transmission and relay channels using device-to-device communications includes a processor coupled to a memory, and a non-transitory computer readable storage medium storing programming for execution by the processor. The programming includes instructions to receive, from a base-station, a transmit signal for the MIMO transmission. The transmit signal is beam-formed in accordance with a transmit covariance obtained by jointly optimizing the transmit covariance and a quantization noise covariance for compressing and relaying the transmit signal from a relay terminal to the terminal. The joint optimization of the transmit covariance and the quantization noise covariance is in accordance with known channel state information and with statistics of noise and interference for transmit and relay channels. The programming further includes instructions to receive, from the relay terminal using the device-to-device communications, a relay signal obtained by compressing the transmit signal for the MIMO transmission. The relay signal is compressed by quantization in accordance with the quantization noise covariance. According to the programming, the terminal is also configured to remove any interference in the received transmit signal and relay signal in accordance with correlated noise in the received transmit signal and relay signal.

In accordance with yet another embodiment, a network controller for establishing MIMO transmission and relay channels using device-to-device communications includes a processor coupled to a memory, and a non-transitory computer readable storage medium storing programming for execution by the processor. The programming includes instructions to initialize a transmit covariance for beam-forming a transmit signal of the MIMO transmission from a base-station to a destination terminal and a relay terminal, and to initialize a quantization noise covariance used for compressing a relay signal from the relay terminal to the destination. The transmit covariance and the quantization noise covariance are initialized in accordance with known channel state information and with statistics of noise and interference for transmit and relay channels. The programming includes instructions to jointly optimize the transmit covariance and the quantization noise covariance using an iterative algorithm in accordance with a capacity constraint on a relay link between the relay terminal and the destination terminal and a transmit signal power constraint of the base-station.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

System and method embodiments are provided for interference mitigation and signal enhancement in downlink wireless communications for MIMO systems. A MIMO multi-antenna joint reception scheme using device-to-device communications is used to enhance the detection of the intended signal and mitigate interference such as out-of-cell interference (from multiple cells or base-stations), across cooperating user terminals. Thus, the downlink transmission of remote or cell-edge users can be significantly improved. The cooperating terminals include a destination terminal intended to receive a signal from a base-station, and a relay terminal that compresses and forwards the signal from the base-station to the destination terminal via device-to-device communications. The compression is achieved by quantizing the signal in accordance with the finite capacity of the relay link. The multi-antennas of the destination and relay terminals are used, as an antenna pooling technique, for joint reception of the transmit signal from the base-station. The relay link allows two users to effectively pool their antennas together. This can enlarge the receiver dimensions thus allowing additional transmission degree-of-freedom from the base-station. Antenna pooling also enables joint interference rejection across the multiple user terminals, thus allowing more interference-free dimensions for direct transmission.

Assuming enough proximity between two cooperating terminals, the noise at the relay terminal and at the destination terminal is expected to be highly correlated. This correlation can be exploited to improve the signal to noise ratio at the destination upon receiving the signal from the source (base-station) and the compressed signal from the relay. The correlation of noise can be exploited to remove the interference from the signal at the destination and improve signal-to-noise ratio. The transmit signal with noise and the relay quantization noise are modeled with Gaussian statistics (Gaussian noise). The transmit beam-forming at the source (base-station) and the signal quantization at the relay can be optimized to mitigate interference and improve signal reception at the destination by a joint optimization of a transmit covariance matrix (for the transmit signal) and a relay quantization noise covariance matrix (for the quantization noise at the relay.

In an embodiment, the optimization problem for the joint transmit covariance and the relay quantization noise covariance can be solved by first keeping the transmit covariance matrix fixed and solving for the relay quantization covariance matrix in closed mathematical form. The transmit covariance matrix is then solved by keeping fixed the quantization noise covariance matrix obtained at the first step fixed. The two steps can be repeated, thereby implementing an iterative optimization that alternates between the two steps until reaching an optimum solution to the transmit and quantization noise covariance matrices. As described above, the solution takes advantage of the device-to-device cooperation link assuming noise correlation between the relay and the destination terminals. The solution can optimize the relay link and lead to significant throughput improvement by enabling joint reception and interference rejection across the multi-antenna relay and destination terminals. The alternating optimization approach includes simultaneous diagonalization of two covariance matrices, considering the MIMO relay channel with correlated noises at the destination and relay terminals.

In accordance with an example of the disclosure, a method for establishing MIMO transmission and relay channels using device-to-device communications is disclosed. The method includes sending, from a base-station to a destination terminal and a relay terminal, a transmit signal for the MIMO transmission. The transmit signal is beam-formed in accordance with a transmit covariance obtained by jointly optimizing the transmit covariance and a quantization noise covariance for compressing and relaying the transmit signal from the relay terminal to the destination terminal using the device-to-device communications. The joint optimization of the transmit covariance and the quantization noise covariance is in accordance with known channel state information and with statistics of noise and interference for transmit and relay channels. The method further includes receiving the transmit covariance from a network controller configured for jointly optimizing the transmit covariance and the quantization noise covariance in accordance with known channel state information and with statistics of noise and interference for transmit and relay channels.

In accordance with another example of the disclosure, a network component for establishing MIMO transmission and relay channels using device-to-device communications is disclosed. The network component includes a processor configured to send, to a destination terminal and a relay terminal, a transmit signal for the MIMO transmission. The transmit signal is beam-formed in accordance with a transmit covariance obtained by jointly optimizing the transmit covariance and a quantization noise covariance for compressing and relaying the transmit signal from the relay terminal to the destination terminal using the device-to-device communications. The joint optimizing of the transmit covariance and the quantization noise covariance is in accordance with known channel state information and with statistics of noise and interference for transmit and relay channels. The network component is a base-station. The network component is further configured to receive the transmit covariance from a network controller configured for jointly optimizing the transmit covariance and the quantization noise covariance in accordance with known channel state information and with statistics of noise and interference for the transmit and relay channels.

In accordance with another example of the disclosure, a method for supporting MIMO transmission and relay channels using device-to-device communications is disclosed. The method includes sending, from a relay terminal to a destination terminal using the device-to-device communications, a relay signal obtained by compressing a transmit signal for the MIMO transmission from a base-station. The relay signal is compressed by quantization in accordance with a quantization noise covariance obtained by jointly optimizing a transmit covariance and the quantization noise covariance. The joint optimization of the transmit covariance and the quantization noise covariance is in accordance with known channel state information and with statistics of noise and interference for transmit and relay channels. The method further includes receiving the quantization noise covariance from a network controller configured for jointly optimizing the transmit covariance and the quantization noise covariance in accordance with known channel state information and with statistics of noise and interference for transmit and relay channels.

In accordance with another example of the disclosure, a terminal for supporting MIMO transmission and relay channels using device-to-device communications is disclosed. The terminal includes a processor configured to send, to a destination terminal using the device-to-device communications, a relay signal obtained by compressing a transmit signal for the MIMO transmission from a base-station. The relay signal is compressed by quantization in accordance with a quantization noise covariance obtained by jointly optimizing a transmit covariance and the quantization noise covariance. The joint optimizing of the transmit covariance and the quantization noise covariance is in accordance with known channel state information and with statistics of noise and interference for transmit and relay channels. The terminal is a relay terminal for forwarding compressing and relaying the transmit signal from the base-station to the destination terminal. The terminal is further configured to receive the quantization noise covariance from a network controller configured for jointly optimizing the transmit covariance and the quantization noise covariance in accordance with known channel state information and with statistics of noise and interference for the transmit and relay channels.

FIG. 1shows a wireless MIMO cellular system100according to an embodiment of the disclosure. The system100includes any number of base-stations110and user terminals120. As an example, two cell-edge user terminals120are shown. A relay user terminal120cooperates with a destination user terminal120by relaying information, from a base-station110, through a relay link between the two user terminals120. The relay link may have a different frequency band than direct links between the user terminals120and the base-stations110. The two user terminals120receive sources of interference from neighboring base-stations110, resulting in a degree of correlation of noises at the relay and the destination user terminals120.

Mathematically, the communication scenario considers a Gaussian MIMO relay channel with an out-of-band relay-to-destination link of fixed capacity C0bits per channel use. The source (base-stations110), relay (user terminal120), and destination (user terminal120) are equipped with s, r, and d antennas, respectively. Let t be the total number of antennas from all the interfering base-stations110combined together. The received signals at the relay and destination are respectively:
Yr=HsrX+Nr, and  (1)
Yd=HsdX+Nd,  (2)
where the Gaussian noises at the relay and the destination are correlated due to a common source of interference, i.e.:
Nr=HtrXt+N1, and  (3)
Nd=HtdXt+N2, respectively.  (4)

The matrices, HsrϵCr×sand HsdϵCd×sare source-relay and source-destination channel matrices, respectively. The matrices HtrϵCr×tand HtdϵCd×tare the interferers-to-relay and interferers-to-destination channel matrices, respectively. The noise functions N1˜CN(0r×1,σ2Ir) and N2˜CN(0d×1,σ2Id) are additive and independent background noises at the relay and the destination, respectively. The vector XϵCt×1is the transmit vector from the source under power constraint P. The vector XtϵCt×1is the interferer signal with Xt˜CN(0t×1,SXt), and is assumed to be Gaussian and independent of other signals.

The relay user terminal120implements a compress-and-forward strategy in which the relay quantizes its observation (i.e., the transmit signal with noise from the source) and sends the quantization index through the relay link to the destination. The quantization process may involve Wyner-Ziv coding, which accounts for the fact that the received signal at the destination is correlated with the relay observation, due to both the signal and the correlated noises. The achievable rate for compress-and-forward is:

The transmit signal with noise at the source is assumed to have a Gaussian distribution, e.g., X˜CN(0s×1,SX). The Gaussian quantization noise at the relay can be modeled as:
Ŷr=Yr+Q,(6)
where Q˜CN(0r×1,SQ). In this case, the optimization for joint transmission and compression problem becomes:
maxfo(SX,SQ)
s.t.fc(SX,SQ)≤C0, and
SX≥0,SQ≥0,tr(SX)≤P.(7)
The objective function is expressed as:

fo⁡(SX,SQ)=⁢I⁡(X;Yr,Yd)=⁢h⁡(Yr,Yd)-h⁡(Yr,Yd|X)=⁢log⁢HSX⁢H†+Sint+σ2⁢I(r+d)+[SQ0r×d0d×r0d×d]-⁢log⁢Sint+σ2⁢I(r+d)+[SQ0r×d0d×r0d×d].(8)
The constraint is expressed as:

fc⁡(SX,SQ)=⁢I⁡(Yr;Yr|Yd)=⁢h⁡(Yr,Yd)-h⁡(Yd)-h⁡(Q)=⁢log⁢⁢HSX⁢H†+Sint+σ2⁢I(r+d)+[SQ0r×d0d×r0d×d]-⁢log⁢Hsd⁢SX⁢Hsd†+Sint(2,2)+σ2⁢Id-log⁢SQ,(9)
and H=[Hsr†Hsd†]†is the overall channel matrix. The interference covariance matrix is expressed as:

The solution to the optimization problem above determines the optimized transmit beam-forming at the source (base-station) and the signal quantization at the relay to mitigate interference and improve signal reception at the destination. The optimization finds the optimal transmit signal vector for the source and the optimal quantized relay channel vector at the relay under a link capacity constraint for the relay and a transmit power constraint for the transmit signal. The optimization problem can be solved at a centralized location with knowledge of channel state information and the statistics of noise and interference. The problem is not a convex optimization problem, as the objective function and the constraint are concave in SXand convex in SQ. An iterative optimization approach is used to find an optimum of the Lagrangian of the optimization problem. To solve the problem, the Lagrangian is maximized using an iterative optimization approach. The Lagrangian of the optimization problem can be expressed as:
L(SX,SQ,μ)=fo(SX,SQ)−μ(fc(SX,SQ)−C0).  (11)

The overall optimization approach for solving the problem is to find the optimal (S*X,S*Q) that maximizes the Lagrangian for a fixed Lagrangian dual variable μ. Specifically, for fixed variable μ the following optimization problem is first solved for optimal (S*X,S*Q):

maxSXs≥0,SQ≥0,tr⁡(SXs)≤P⁢L⁡(SX,SQ,μ).(12)
Subsequently, the optimal value μ* that results in:
fc(S*X,S*Q)=C0(13)
is found in an outer loop.

In some embodiments, the optimal μ* is between 0 and 1. When μ=0 (e.g., when the objective is to maximize the overall rate without relay link capacity constraint), the optimal S*Qis a zero matrix, resulting in fc(S*X,S*Q)=∞. When μ≥1, the overall objective penalizes the relay link rate at more than a 1:1 ratio with the achievable rate, and the optimal S*Qmay be infinite, resulting in fc(S*X,S*Q)=0. The Lagrangian maximization problem

maxSXs≥0,SQ≥0,tr⁡(SXs)≤P⁢L⁡(SX,SQ,μ)
is solved with a fixed μϵ(0,1). The outer loop for searching for the optimal μ* is a one-dimensional root-finding problem that can be solved using a numerical approach such as bisection.

The Lagrangian maximization problem of equation (12) can be solved using an iterative coordinate ascent approach. The solution approach is to find the optimal SQthat maximizes L(SX,SQ,μ) for fixed SX, then to find the optimal SXthat maximizes L(SX,SQ,μ) for fixed SQ, and to iterate between the two steps. For fixed μϵ(0,1), each of the individual optimizations of SXand SQcan be solved to optimality. The iterative optimization process provides a non-decreasing sequence of the Lagrangian objective, so that the iterative process converges. The convergent point is a stationary point. This solution algorithm for achieving joint transmission and quantization is summarized in Table 1 below. The algorithm details for optimizing SQfor fixed SX, and for optimizing SXfor fixed SQare described further below.

FIG. 2is a flowchart illustrating an embodiment method200for joint transmit and quantization covariance optimization according to the algorithm above. The method200can be implemented by a network controller for optimizing jointly the transmit beam-forming signal from the source (base-station) and the compression of the signal by the relay terminal to the destination. The network controller may be located at the transmit base-station or a separate entity of the network. At step210, the transmit covariance for the source with Gaussian noise is initialized to some suitable value. The transmit covariance determines the transmit vector for beam-forming at the source. This is step 1 in the algorithm of Table 1. At step220, a suitable value for an optimization variable (Lagrangian multiplier), μ, of a Langrangian function of joint transmit covariance and relay quantization noise covariance is selected. This is step 3 in the algorithm above. The quantization noise covariance determines the quantization of the signal received at the relay and relayed to the destination. At step230, the quantization noise covariance at the relay is obtained, keeping the transmit covariance fixed. This is shown in step 5 of the algorithm. At step240, an optimal transmit covariance is obtained, keeping the resulting quantized noise covariance fixed. At decision step245, the method checks whether the transmit covariance and quantization noise covariance values have converged. If the values converged, then the method200proceeds to step250. Otherwise, the method returns to step230. This is shown in step 6 of the algorithm. At step250, the value of the optimization variable, μ, is updated using bisection and the last calculated values of the covariance matrices. At a decision step260, the method checks whether the rate on the relay link, according to the quantization, meets the fixed capacity of the relay link. If the quantization signal rate meets the capacity of the relay link, then the method200ends. Otherwise, the method returns to step220. The resulting optimized transmit covariance and quantization noise covariance are used to determine the optimal transmit signal beam-forming at the source and the quantization signal form the relay to the destination, respectively, to mitigate interference and improve signal reception at the destination for the MIMO transmission from the source.

To optimize SQfor fixed SX, a closed form solution is applied to find SQthat maximizes the Lagrangian for a givenSX, i.e., the optimum solution to

maxSQ≥0⁢L⁡(S_X,SQ,μ).(14)
The solution seeks to find a stationary point of the problem. One technique that makes a closed form solution possible is simultaneous diagonalization by congruence. For the optimization over SQwhen SXis kept fixed, the objective and constraint functions of equations (8) and (9) can be rewritten as:
fo=log|SYr|Yd+SQ|−log|SYr|Yd,X+SQ|+const, and  (15)
fc=log|SYr|Yd+SQ|−log|SQ|+const.  (16)

The Lagrangian of equation (14) can now be written as:
L(SX,SQ,μ)=(1−μ)log|SYr|Yd+SQ|+μ log|SQ|−log|SYr|Yd,X+SQ|+const.  (17)
where the conditional covariances SYr|Ydand SYr|Yd,Xare obtained using Schur's complement formula

To reduce the MIMO transmission problem to the scalar case and to solve the subsequent scalar quantization noise optimization problem, the Lagrangian of equation (17) can be written as:

Let ΣQiibe the diagonal entries of ΣQ. The following change of variable is considered:

ci=log(1+λi∑Qii),i=1,…⁢,r,(19)
where ΣQii≥0 and ci≥0. An interpretation of c; is that it is the portion of the variable C0assigned for compression of the ithelement of CYr. Using equation (19), the Lagrangian can be written as:

L=∑i=1r⁢((1-μ)⁢ci-log⁡(2ci+λi-1))+const.(20)
It can be checked that equation (20) is concave in ciwhen λi≥1. The optimal ciis given by:

∑Qii⁢={μ1-1λi-μμ<1-1λi+∞μ≥1-1λi(22)
and the optimal SQis given by S*Q=C−†Σ*QC−1.

To optimize SXfor fixed SQ, the following optimization problem:

maxSX±0,tr⁡(SX)≤P⁢L⁡(SX,S_Q,μ)(26)
can be solved using tools used in convex optimization, where for a fixedSQ, the Lagrangian in equation (11) is a concave function of SX, if μϵ(0,1). To verify the convexity, it is noted that the Lagrangian in equation (11) can be written as a function of SX(for fixedSQ) as

L⁡(SX,S_Q,μ)=fo⁡(SX,S_Q)-μ⁢⁢fc⁡(SX,S_Q)+const.=(1-μ)⁢log⁢HSX⁢H†+Sint+σ2⁢I(r+d)+[S_Q0r×d0d×r0d×d]+μ⁢⁢log⁢Hsd⁢SX⁢Hsd†+Sint(2,2)+σ2⁢Id+const.
For μϵ(0,1), the formulation is a log det optimization problem which is convex and can be solved using a numerical software package such as CVX for Matlab.

FIG. 3is a flowchart illustrating an embodiment method300for a compress-and-forward relay scheme with joint MIMO transmission using joint transmit and quantization noise covariance optimization. At step310, a transmit covariance matrix, function or value for MIMO beam-forming at a base-station to a destination terminal, and a quantization noise covariance matrix, function or value for compressing the relay signal from a relay terminal to the destination are initialized in accordance with known channel state information and the statistics of noise and interference for the transmit and relay channels. At step320, the transmit covariance and the quantization noise covariance are jointly optimized using an iterative algorithm with relay link capacity and transmit signal power constraints. The solution includes maximizing a Langrangian function of the two covariance matrices with an optimum Lagrangian variable. The optimization can be solved using the method200or the algorithm of Table 1. Steps310and320can be performed at the network controller or base-station. At step330, the transmit signal from the base-station to the destination terminal is beam-formed in accordance with the optimized transmit covariance. This step can be performed at the base-station or the network controller. For instance, the network controller can send the optimized transmit covariance to the base-station. At step340, the relay signal at the relay terminal to the destination terminal is compressed or quantized in accordance with the optimized quantization noise covariance. This step can be performed at the relay terminal. For instance, the network controller can send the optimized quantization noise covariance to the relay terminal.

FIG. 4is a flowchart illustrating another embodiment method400for a compress-and-forward relay scheme with joint MIMO transmission using joint transmit and quantization noise covariance optimization. The method can be performed by a destination terminal that receives a transmit signal from a base-station and a compressed relay signal from a relay terminal. At step410, a transmit signal for MIMO transmission is received from the base-station. The transmit signal is beam-formed in accordance with a transmit covariance matrix, function or value obtained by jointly optimizing the transmit covariance and a quantization noise covariance matrix, function or value. The quantization noise covariance is used for compressing and relaying the transmit signal from the relay terminal to the destination terminal. At step420, the compressed relay signal is received from the relay terminal. The relay signal is established by the relay terminal by receiving the transmit signal from the base-station and then quantizing the signal in accordance with the quantization noise covariance. At step430, any interference in the received transmit signal and relay signal is removed in accordance with correlated noise in the received transmit signal and transmit signal.

Simulation studies are performed to demonstrate the effectiveness of the compress-and-forward relaying scheme described above for device-to-device link to enhance cell-edge throughput in a downlink wireless cellular environment. The scheme applies the joint input and quantization covariance optimization above, such as using the method200. A pico-cell deployment is considered with a pico-base-station transmitting at a maximum power of 1 Watt over 10 Megahertz (MHz) to a user distance of 100 meter (m) away. A second user located nearby acts as a relay as shown inFIG. 1. The background noise power spectral density is assumed to be −170 Decibel-milliwatt/Hertz (dBm/Hz). A channel model with pathloss exponent of 3.76 and 8 decibel (dB) shadowing is used.

As reference, the cut-set upper bound to the capacity of a MIMO relay channel is formed as:

C≤maxp⁡(X),E⁢{X†⁢X}≤P⁢min⁢{I⁡(X;Yr,Yd),I⁡(X;Yd)+C0}..(37)
The evaluation of the cut-set bound involves solving an optimization problem. For the Gaussian MIMO relay channel, the optimal input distribution in the maximization problem of equation (37) is multivariate Gaussian. The optimization over the input covariance matrix is a convex optimization problem, which can be solved using standard optimization package such as CVX.

FIG. 5is graph that demonstrates the effect of antenna pooling for enhancing the direct communication between the base-station and the user. The graph shows the improvement in overall transmission rate using a relay link for a scenario where the transmitting base-station has two antennas (s=3), the relay and destination are each equipped with 2 antennas (r=2 and d=2), and with no intercell interference (t=0). In this scenario, the benefit of antenna pooling is in enhancing the direct signal dimension, as the overall transmission degree-of-freedom is limited by the number of antennas at the destination. Thus, pooling antennas from the relay can improve the overall throughput considerably. As shown inFIG. 5, at C0=100 Megabits/second (Mbps), the improvement in throughput by the optimized compress-and-forward relay scheme is around 95 Mbps, achieving an almost 1:1 improvement in the direct transmission rate for each relaying bit. The maximum possible improvement is around 165 Mbps which is achieved with C0=250 Mbps. For smaller values of C0, the achievable rate of the optimized compress-and-forward scheme almost meets the cut-set bound.

The graph also demonstrates the effect of optimizing the input covariance matrix on the overall achievable rates. As suboptimal choices for input covariance, the achievable rates are plotted for the cases where the transmit covariance is set to be the water-filling covariance of the source-to-destination and source-to-relay-and-destination point-to-point channels, respectively, without considering the effect of the relay. For this fixed input covariance matrix, the quantization noise covariance is optimized. Depending on the value of C0, each of these covariances can be strictly suboptimal. For small values of C0, setting the input covariance to optimize for the source-to-destination channel is close to optimal. However, as C0increases, this SXmay fail to achieve the optimal performance. For large values of C0, setting the input to optimize for the source-to-relay-and-destination channel is close to optimal, but a gap exits when C0is low.

FIG. 6is graph that demonstrates the results for a similar setup to the scenario above, except that the transmitting base-station now has two antennas, and the relay and destination are equipped with three antennas each, again with no interference (i.e., s=2, r=3, d=3, and t=0). In this scenario relaying does not increase the overall throughput notably, because the overall degree-of-freedom is constrained by the number of base-station antennas instead of number of antennas at the destination. In this case, with C0=100 Mbps, the throughput improvement is only around 17 Mbps.

FIG. 7is graph that demonstrates the results considering the same setup as the scenario ofFIG. 6. However, the scenario ofFIG. 7also considers four additional interfering single-antenna pico-base-stations, as shown inFIG. 1(i.e., s=2, r=3, d=3, and t=4). The interfering base-stations are placed on hexagonal grid 200 m away from the center base-station. Due to interference, the throughput without the relay (i.e., with C0=0) is now considerably lower, but the optimized use of the relay link is able to improve the throughput significantly. This is because, due to the common inter-cell interference, the noises at the relay and destination are highly correlated. By exploiting such noise correlation using the relay link, the destination can effectively pool the three relay antennas together with the three existing antennas of its own to create a 2×6 overall MIMO channel (i.e., s=2, r+d=6). This enables the rank-four interference (i.e., t=4) to be rejected completely, creating an effective 2×2 interference-free overall channel. As seen in the graph ofFIG. 7, at around C0=100 Mbps, the improvement in throughput brought by the optimized use of the compress-and-forward relay link is around 85 Mbps. At small C0, relaying achieves almost 1:1 improvement in the direct transmission rate for each relaying bit. It is worth noting that the overall throughput at large C0inFIG. 7is close to the achievable rate of the C0=0 scenario inFIGS. 5 and 6, illustrating the almost complete interference rejection capability of optimized compress-and-forward relaying.

FIGS. 6 and 7also demonstrate the importance of optimizing the quantization noise covariance matrix. For comparison purpose, the achievable rate for a simple suboptimal SQis also shown, where SQ=qIr, q is set to satisfy the relay rate constraint with equality, for the optimal SXobtained from the joint input and quantization algorithm in Table 1. This simple choice of SQresults in suboptimal performance as shown inFIGS. 6 and 7.

FIG. 8is a block diagram of a processing system800that can be used to implement various embodiments. For example, the system can be part of a network entity or component, such as a base-station, a user terminal, or any network controller configured to implement the optimization techniques described herein for compress-and forward relaying. Specific devices may utilize all of the components shown, or only a subset of the components, and levels of integration may vary from device to device. Furthermore, a device may contain multiple instances of a component, such as multiple processing units, processors, memories, transmitters, receivers, etc. The processing system800may comprise a processing unit801equipped with one or more input/output devices, such as a speaker, microphone, mouse, touchscreen, keypad, keyboard, printer, display, and the like. The processing unit801may include a central processing unit (CPU)810, a memory820, a mass storage device830, a video adapter840, and an I/O interface860connected to a bus. The bus may be one or more of any type of several bus architectures including a memory bus or memory controller, a peripheral bus, a video bus, or the like.

The CPU810may comprise any type of electronic data processor. The memory820may comprise any type of system memory such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous DRAM (SDRAM), read-only memory (ROM), a combination thereof, or the like. In an embodiment, the memory820may include ROM for use at boot-up, and DRAM for program and data storage for use while executing programs. In embodiments, the memory820is non-transitory. The mass storage device830may comprise any type of storage device configured to store data, programs, and other information and to make the data, programs, and other information accessible via the bus. The mass storage device830may comprise, for example, one or more of a solid state drive, hard disk drive, a magnetic disk drive, an optical disk drive, or the like.

The video adapter840and the I/O interface860provide interfaces to couple external input and output devices to the processing unit. As illustrated, examples of input and output devices include a display890coupled to the video adapter840and any combination of mouse/keyboard/printer870coupled to the I/O interface860. Other devices may be coupled to the processing unit801, and additional or fewer interface cards may be utilized. For example, a serial interface card (not shown) may be used to provide a serial interface for a printer.

The processing unit801also includes one or more network interfaces850, which may comprise wired links, such as an Ethernet cable or the like, and/or wireless links to access nodes or one or more networks880. The network interface850allows the processing unit801to communicate with remote units via the networks880. For example, the network interface850may provide wireless communication via one or more transmitters/transmit antennas and one or more receivers/receive antennas. In an embodiment, the processing unit801is coupled to a local-area network or a wide-area network for data processing and communications with remote devices, such as other processing units, the Internet, remote storage facilities, or the like.