Method and system for an improved user group selection scheme with finite-rate channel state information feedback for FDD multiuser MIMO downlink transmission

Certain embodiments of the invention may be found in a method and system for an improved user group selection scheme with finite-rate channel state information feedback for frequency division duplex (FDD) multiuser multiple-input-multiple-output (MIMO) downlink transmission. Aspects of the method may include selecting, from a plurality of users in a FDD multiuser communication system, a first user having a channel gain that is greater than a channel gain corresponding to a remaining portion of the plurality of users. A second user may be selected from the remaining portion of the plurality of users, based on a channel gain of the second user and orthogonality of the second user's channel direction with respect to the first user. The selected second user may have a channel gain that is greater than a channel gain corresponding to the remaining portion of the plurality of users.

Each of the above stated applications is hereby incorporated herein by reference in its entirety.

FIELD OF THE INVENTION

Certain embodiments of the invention relate to processing of signals in communication systems. More specifically, certain embodiments of the invention relate to a method and system for an improved user group selection scheme with finite-rate channel state information feedback for frequency division duplex (FDD) multiuser multiple-input-multiple-output (MIMO) downlink transmission.

BACKGROUND OF THE INVENTION

Mobile communications have changed the way people communicate and mobile phones have been transformed from a luxury item to an essential part of every day life. The use of mobile phones is today dictated by social situations, rather than hampered by location or technology. While voice connections fulfill the basic need to communicate, and mobile voice connections continue to filter even further into the fabric of every day life, the mobile Internet is the next step in the mobile communication revolution. The mobile Internet is poised to become a common source of everyday information, and easy, versatile mobile access to this data will be taken for granted.

Third generation (3G) cellular networks have been specifically designed to fulfill these future demands of the mobile Internet. As these services grow in popularity and usage, factors such as cost efficient optimization of network capacity and quality of service (QoS) will become even more essential to cellular operators than it is today. These factors may be achieved with careful network planning and operation, improvements in transmission methods, and advances in receiver techniques. To this end, carriers need technologies that will allow them to increase downlink throughput and, in turn, offer advanced QoS capabilities and speeds that rival those delivered by cable modem and/or DSL service providers.

In order to meet these demands, communication systems using multiple antennas at both the transmitter and the receiver have recently received increased attention due to their promise of providing significant capacity increase in a wireless fading environment. These multi-antenna configurations, also known as smart antenna techniques, may be utilized to mitigate the negative effects of multipath and/or signal interference on signal reception. It is anticipated that smart antenna techniques may be increasingly utilized both in connection with the deployment of base station infrastructure and mobile subscriber units in cellular systems to address the increasing capacity demands being placed on those systems. These demands arise, in part, from a shift underway from current voice-based services to next-generation wireless multimedia services that provide voice, video, and data communication.

The utilization of multiple transmit and/or receive antennas is designed to introduce a diversity gain and to raise the degrees of freedom to suppress interference generated within the signal reception process. Diversity gains improve system performance by increasing received signal-to-noise ratio and stabilizing the transmission link. On the other hand, more degrees of freedom allow multiple simultaneous transmissions by providing more robustness against signal interference, and/or by permitting greater frequency reuse for higher capacity. In communication systems that incorporate multi-antenna receivers, a set of M receive antennas may be utilized to null the effect of (M−1) interferers, for example. Accordingly, N signals may be simultaneously transmitted in the same bandwidth using N transmit antennas, with the transmitted signal then being separated into N respective signals by way of a set of N antennas deployed at the receiver. Systems that utilize multiple transmit and receive antennas may be referred to as multiple-input multiple-output (MIMO) systems. One attractive aspect of multi-antenna systems, in particular MIMO systems, is the significant increase in system capacity that may be achieved by utilizing these transmission configurations. For a fixed overall transmitted power, the capacity offered by a MIMO configuration may scale with the increased signal-to-noise ratio (SNR). For example, in the case of fading multipath channels, a MIMO configuration may increase system capacity by nearly M additional bits/cycle for each 3-dB increase in SNR.

The widespread deployment of multi-antenna systems in wireless communications has been limited by the increased cost that results from increased size, complexity, and power consumption. This poses problems for wireless system designs and applications. As a result, some initial work on multiple antenna systems may be focused on systems that support single user point-to-point links. However, the use of multi-antenna techniques for a multiuser environment to improve total throughput remains a challenge.

Communication systems using multiple antennas at both the transmitter and the receiver have recently received increased attention due to their promise of providing significant capacity increase in a wireless fading environment. However, most of the initial work on multiple antenna systems was focused on systems that support single user point-to-point links. More recently, various efforts have focused on utilizing multi-antenna techniques to a multiuser environment to improve total throughput.

The performance of conventional multiple antenna systems may depend on the availability of channel state information (CSI) at the transmitter (CSIT) and at the receiver (CSIR). During design and analysis stage, most of the conventional multiple-input-multiple-output (MIMO) communication systems may utilize an assumption that CSIT is complete or that there is no CSIT information available. However, in most instances, such assumptions may be impractical as only quantized CSI may be available at the transmitter. Communication systems with multiple users, such as a CDMA-based communication system or communication systems within a wireless LAN environment, may utilize user group selection algorithms and CSI feedback to achieve array gain and transmit diversity. Furthermore, multiuser diversity of the downlink channel may also be achieved by using CSI information, which may be available at the transmitter. However, most conventional user group selection algorithms, such as the optimal brute-force user group selection algorithm, may utilize complex computations to determine the CSI and may require feedback of the entire CSI from the receiving stations to the transmitting base station. Such computation complexity and full CSI feedback may increase implementation costs and reduce processing time and overall efficiency of the communication system.

BRIEF SUMMARY OF THE INVENTION

A system and/or method is provided for an improved user group selection scheme with finite-rate channel state information feedback for frequency division duplex (FDD) multiuser multiple-input-multiple-output (MIMO) downlink transmission, substantially as shown in and/or described in connection with at least one of the figures, as set forth more completely in the claims.

DETAILED DESCRIPTION OF THE INVENTION

Certain embodiments of the invention may be found in a method and system for an improved user group selection scheme with finite-rate channel state information feedback for frequency division duplex (FDD) multiuser multiple-input-multiple-output (MIMO) downlink transmission. Aspects of the method may comprise selecting, from a plurality of users in a frequency division duplex (FDD) multiuser communication system, a first user having a channel gain that is greater than a feedback channel gain corresponding to a remaining portion of the plurality of users. A second user may be selected from the remaining portion of the plurality of users, based on a feedback channel gain of the second user and feedback orthogonality of the second signal with respect to the first signal. The selected second user may have a channel gain that is greater than a feedback channel gain corresponding to the remaining portion of the plurality of users. In this regard, an improved user group selection scheme in accordance with an embodiment of the invention may significantly reduce the computational complexity and the total amount of CSI feedback information communicated from a receiver station to a base station transmitter. As used herein, the term “user” may be interpreted to refer to a mobile device.

FIG. 1Ais a diagram illustrating an exemplary signal transmission from base station to receivers within a finite-rate feedback multiuser communication environment, in accordance with an embodiment of the invention. Referring toFIG. 1A, there is shown a communication system100acomprising a base station102a, a first user (user1)104a, and a second user (user2)106a. The base station102amay comprise antennas116a, . . . ,122a. The first user104aand the second user106amay each have a single antenna. In this instance, the base station102amay transmit signals112aand114a, which are intended to be received by the first user104aand by the second user106a, respectively.

After the first user104aand the second user106aprocess signals112aand114a, respectively, the first user104aand the second user106amay communicate quantized channel state information ĥ1108aand ĥ2110a. The quantized channel state information ĥ1108aand ĥ2110amay comprise channel gain information and channel direction information for the first user104aand the second user106a, respectively. The base station102amay utilize the received quantized channel state information ĥ1108aand ĥ2110ato precode transmit information for the first user104aand the second user106a. In one embodiment of the invention, the first user104aand the second user106amay communicate limited or finite-rate channel state information108aand110ato the base station102avia the rate constraint feedback link between the base station102aand the users104aand106a, in order to maximize throughput and increase processing speed and efficiency.

In another embodiment of the invention, the base station102amay be equipped with M antennas and there may be K users within the communication system100a, where each user may comprise a single antenna. In such circumstances, the signal model may be expressed as

[y1y2⋮yk]=[h1h2⋮hk]⁢x+n,(1)
where yk(k=1, . . . , K) may be the signal received by user k, hkε1×Mmay be the channel vector to user k, x εM×1may be the transmitted symbol vector by the base station102a, and n εK×1may be the additive white Gaussian noise (AWGN) with zero mean and unit variance. The transmitted symbols may satisfy certain power constraint, for example, where E[xHX]≦P, where (•)Hmay represent complex conjugate transpose.

In this exemplary analysis, each element in hkmay be a zero-mean circularly symmetric complex Gaussian (ZMCSCG) random variable with unit variance. Moreover, the users may experience independent fading and, therefore, the channel vectors {hk}k=1Kmay be statistically independent from each other. The channel state information (CSI), hk, may be known to user k, but may not be known to other users. The base station102amay have knowledge of the CSI for all users. In one embodiment of the invention, the communication system100amay be a frequency division duplex (FDD) communication system. In this regard, the base station102amay obtain CSI108aand110afrom the first user104aand the second user106athrough a rate constraint feedback link.

Employing multiple antennas at the base station in cellular multiuser communication systems may improve the downlink system capacity. This approach may be utilized with any multiuser MIMO system, such as code division multiple access 2000 (CDMA2000), wideband CDMA (WCDMA), and Wireless LAN (WLAN), for example. The capacity improvement may be attained by communicating simultaneously to multiple users through precoding at the transmitter or base station when channel state information is available. In this regard, a transmitter or base station may refer to any device or equipment which may be adapted to communicate with multiple other devices, users, and/or receivers. Moreover, a user or a receiver may refer to user equipment or device that may be adapted for communication with a base station and/or other devices. Dirty paper coding (DPC) may be utilized as a preceding scheme that may achieve the sum capacity. However, DPC may be difficult to implement due to complexity issues. There may also exist other suboptimal but relatively low complexity schemes for multiuser MIMO downlink, such as linear preceding, Tomlinson-Harashima preceding, and vector encoding, for example.

A zero-forcing (ZF) linear precoder may achieve the sum capacity when combined with infinite-order multiuser diversity, that is, when the number of users K approaches infinity. Moreover, ZF precoders may provide near-optimal performance even with a limited number of users, when K=10 for example.

The zero-forcing precoders may be a specific type of linear precoders. When the base station, for example the base station102ainFIG. 1A, decides to transmit to a group of users D{1, . . . , K} with d=|D|≦K, a linear preceding scheme may linearly weigh the data symbols s=[s1, . . . , sd]Tbefore they are transmitted from the base station,
x=FPs(2)
where x is the transmitted signal vector as in equation (1), F=[f1, . . . , fd] may be the M×d linear precoding matrix with normalized columns (∥fk∥=1), and P=diag{P1, . . . ,Pd} with Σi=1dPi≦P may be the power control matrix that may be adapted to allocate transmit power to different users. The received signal may be given by equation

A zero-forcing precoder may use the pseudo-inverse of the overall channel matrix HD=[h1T, . . . ,hdT] as the weighting matrix when HDhas full row rank, i.e.

WD=HD†=HDH⁡(HD⁢HDH)-1,(4)FD=WD⁡[1w1⋰1wd],(5)
where {wi}i=1dare the column of WD

By defining

ξi⁢=△⁢1wi(6)
and substituting equation (5) into equation (3), the received signal for each user with zero-forcing preceding may be expressed as,
yi=ξiPisi+ni, ∀i εD.(7)

In this regard, the multiuser downlink channel may become a set of parallel channels. The maximum sum rate of the given user group D may be given by the equation:

CD=∑i∈D⁢log⁡(1+ξi⁢Pi),(8)
where the optimal Pimay be given by the water-filling solution,

Pi=(μ-1ξi)+,(9)
with the water level μ chosen to satisfy

∑i∈D⁢(μ-1ξi)+=P.
The maximum achievable sum rate for a given channel realization may be obtained by searching over all the possible user groups, that is,

An optimal or best user group selection for ZF precoding may require searching over a plurality of Σi=1M(iK) candidate user groups to find the one with the largest sum rate, which leads to a fairly high computational cost. Moreover, in an FDD system such as the communication system100a, the channel state information that may be needed at the transmitter102ato perform the optimal user group search may be obtained from the users104aand106athrough a feedback link. Because the optimal search requires CSI from each user and each user's channel is a complex vector of dimension M, that is equivalent to 2M real numbers per user, heavy burden may be placed on the feedback link to obtain this information. This may be particularly cumbersome since the feedback link tends to have very limited capacity. A user group selection scheme, such as the selection scheme described below in reference toFIG. 2B, may result in a simpler implementation and may require less feedback information. In this regard, such improved selection scheme may be utilized for finite-rate channel state information feedback within multiuser communication systems with multiple transmits antennas.

FIG. 1Bis a top-level block diagram illustrating an exemplary multiuser multiple-input-multiple-output (MIMO) downlink transmission system with finite-rate channel state information feedback, in accordance with an embodiment of the invention. Referring toFIG. 1B, there is shown a communication system100bthat may comprise a base station102band a plurality of K users150b, . . . ,152b. Within the communication system100b, the base station102bmay comprise M transmit (TX) antennas and each of the K users150b, . . . ,152bmay each have a single receive (RX) antenna. In this implementation, the total number of users or receiver antennas may be equal or higher than the number of base station antennas, that is, K≧M.

The base station102amay comprise a plurality of channel encoders104b, . . . ,106b, a user scheduler108b, a plurality of modulators (MOD)110b, . . . ,112b, a power control block114b, a beamforming or linear precoding block116b, a processor107b, and a memory109b. Each of the plurality of users150b, . . . ,152bmay each comprise one of a plurality of demodulators (DEM)118b, . . . ,119b, one of a plurality of channel decoders120b, . . . ,121b, one of a plurality of channel estimators122b,123b, one of a plurality of channel quantizers126b, . . . ,127b, and one of a plurality of feedback controllers124b, . . . ,125b.

The channel encoders104b, . . . ,106bmay comprise suitable logic, circuitry, and/or code that may be adapted to encode input binary data b1, . . . , bkfor each of the K users in the communication system100b. The beamforming or linear precoding block116bmay comprise suitable logic, circuitry, and/or code that may be adapted to processes the user data symbols to separate signals intended for different users such that each user receives little or no interference from other users. With M antennas at the base station102b, the beamforming or linear precoding block116bmay separate at most M different signals, that is, the base station102bmay transmit to at most M users at a time. Therefore, for each channel realization, the base station102bmay need to select M or less than M users among all the K users to transmit.

The user scheduler108bmay comprise suitable logic, circuitry, and/or code that may be adapted to locate a best user group from the plurality of users150b, . . . ,152bthat optimizes certain performance criterion such as the sum throughput of the system, for example. In this regard, the user scheduler108bmay be adapted to perform the steps of an improved user group selection algorithm, for example, to find the best user group. The user scheduler108bmay utilize knowledge of the channel state information (CSI) provided by the users150b, . . . ,152bvia the feedback path142bwhen determining the best user group. The user scheduler108bmay be adapted to select a first user with the strongest channel gain and a second user with the second strongest channel gain. The user scheduler108bmay be adapted to determine a first maximum system capacity based on the first user and a second maximum system capacity based on the second user. The user scheduler108bmay also be adapted to select the highest of the first maximum system capacity and the second maximum system capacity as the maximum system capacity to be supported by the communication system100b. In this regard, for a case when M=2, the user scheduler108bmay select the user group to comprise a pair of users associated with the maximum system capacity selected.

The modulators110b, . . . ,112bmay comprise suitable logic, circuitry, and/or code that may be adapted to modulate the binary data of each of the users selected by the user scheduler108b. In this regard, the modulation operation on the binary data may result in a plurality of complex symbols u1, . . . , um, for example. The power control block114bmay comprise suitable logic, circuitry, and/or code that may be adapted to allocate different users with different power levels in accordance with their respective channel quality, for example, based on CSI received via the feedback path142b.

The user scheduler108b, the power control block114b, and/or the beamforming or linear precoding block116bmay require knowledge of the state of the downlink channel. The processor107bmay comprise suitable logic, circuitry, and/or code that may be adapted to process information and/or data associated with the generation of transmission signals at the base station102b. The processor107bmay also be adapted to control at least a portion of the operations of the base station102b. The memory109bmay comprise suitable logic, circuitry, and/or code that may be adapted to store data and/or control information that may be utilized in the operation of at least a portion of the base station102b.

The demodulators118b, . . . ,119bin the users150b, . . . ,152bmay comprise suitable logic, circuitry, and/or code that may be adapted to demodulate the signals received from the base station102b, for example. The channel decoders120b,121bmay comprise suitable logic, circuitry, and/or code that may be adapted to decode the demodulated signals from the demodulators118b, . . . ,119binto received binary bit streams b′1, . . . , b′k, for example.

The channel estimators122b, . . . ,123bmay comprise suitable logic, circuitry, and/or code that may be adapted to estimate channel state information for one or more receive channels. The channel quantizers126b, . . . ,127bmay comprise suitable logic, circuitry, and/or code that may be adapted to quantize channel state information estimated by the channel estimators122b, . . . ,123b. The feedback controllers124b, . . . ,125bmay comprise suitable logic, circuitry, and/or code that may be adapted to generate channel state information output138b, . . . ,140bfor communication to the base station102bvia the feedback link142b.

In operation, input signals b1, . . . , bkmay be encoded by the channel encoders104b, . . . ,106b. Based on the knowledge of the downlink channel state information138b, . . . ,140breceived from the users150b, . . . ,152bvia the feedback link142b, the user scheduler108bmay select a determined group of users to transmit so as to optimize certain performance criterion, such as the sum throughput of the communication system100b. The binary data of each selected user may be modulated by the modulators110b, . . . ,112band may be transformed into complex symbols u1, . . . , uM. The power control block114bmay then allocate the total transmit power to different users according to their respective channel quality. The channel quality may be determined based on the downlink channel state information138b, . . . ,140breceived from the users150b, . . . ,152bvia the feedback link142b. The linear precoder116bmay then process the user data symbols in such a way that each user150b, . . . ,152bmay receive its own signal and little or no interference from other users. After the signal is transmitted from the M base station TX antennas and after it arrives at each of the users150b, . . . ,152b, it may be demodulated and decoded into received binary bit streams b′1, . . . , b′k.

In a frequency division duplex (FDD) system, such as the communication system100b, the base station102bmay obtain the downlink channel state information138b,  . . . ,140bthrough a finite-rate feedback link142bfrom the users150b, . . . ,152b. In one embodiment of the invention, each user may estimate its own channel and may quantize the channel according to the feedback rate constraint of the communication system100b. In this regard, a selection algorithm may be utilized so that the feedback controller124b, . . . ,125bat each user may determine a finite-rate channel state information to feed back on the request of the base station102bso as to optimize the user group selection by the base station102b. The selection algorithm which is described below with respect toFIGS. 2Aand/or2B, may significantly reduce the communication system complexity as well as the total amount of required feedback information, thereby effectively reducing the feedback rate.

FIG. 2Ais a high level flow diagram illustrating exemplary steps for improved user group selection with finite-rate channel state information feedback, in accordance with an embodiment of the invention. Referring toFIGS. 1B and 2A, at202a, the base station102bmay select a first user from a plurality of k users150b, . . . ,152b, based on quantized channel gain information from all users. Each of the k users150b, . . . ,152bmay measure its channel power γk=∥hk∥2and may supply the quantized channel power {circumflex over (γ)}i|i=1Kto the base station102bfor selection of the first user. At204a, after the first user is selected, a plurality of orthogonality parameters for a remaining portion of the plurality of users may be determined. The plurality of orthogonality parameters may be determined with respect to quantized channel direction of the selected first user. At206a, a second user may be selected from the remaining portion of the plurality of users, based on channel gain information and the determined orthogonality parameters for the remaining portion of the plurality of users. At208a, the first and/or the second user may be selected for receiving MIMO signals, based on a system capacity function. A precoding matrix may then be calculated by the base station102b, based on whether the first and/or the second user is selected to receive signals within the communication system100b.

FIG. 2Bis a flow diagram illustrating exemplary steps for improved user group selection with finite-rate channel state information feedback, in accordance with an embodiment of the invention. Referring toFIGS. 1B and 2B, a simplified user group selection scheme may be utilized in a multiuser downlink channel with quantized CSI feedback within the communication system100b. For simplicity, it may be assumed that M=2. Even though the algorithm is described with respect to M=2, the present invention may not be so limited and the algorithm described herein may be applicable to other FDD communication systems with a different number of transmit antennas. As demonstrated inFIG. 2B, the user group selection algorithm may be combined with a CSI feedback scheme and may comprise the following 10 steps.

It may be assumed that users have ideal CSIR in a sense that the MISO channel impulse response hkε1×2(M=2) may be known at each user. At202, each user may quantize its own channel gain, or channel power γk=∥hk∥2by a finite-rate scalar quantizer with quantization resolution Bgbits per channel update using the channel quantizers126b, . . . ,127b. The quantized channel gain γkor the equivalent quantization index may then be conveyed back to the base station102bthrough a rate constraint feedback link142b. The channel gain quantizers126b, . . . ,127bmay be optimized to match to the precoder116bused at the transmitter102b, such as zero-forcing precoder. One or more performance metric, such as capacity and bit error rate, as well channel statistical distributions may also be utilized in order to improve the system performance.

At204, based upon the feedback information

γk⁢Kk=1,
the transmitter102bmay select the user with the largest channel gain based on the following expression

Based on the selected index i, the base station may request a channel direction feedback from the ithuser asking for the unit norm vector vi(vi=hi/∥hi∥).

At206, based on the request from the base station, the ithuser may quantize its own channel direction by a vector quantizer with inner product quantization criterion. The direction vector vimay be quantized into {circumflex over (v)}iwith quantization resolution Bvbits per channel update. The quantized vector {circumflex over (v)}ior the quantization index may be fed back to the base station using the same feedback link142b.

At208, based on the feedback direction {circumflex over (v)}i, the base station102bmay form an orthonormal beam {circumflex over (v)}i⊥, which may be given by the equation
{circumflex over (v)}i⊥=[{circumflex over (v)}i,2*,−{circumflex over (v)}i,1*],  (12)
where {circumflex over (v)}i,1and {circumflex over (v)}i,2may be the first and second elements of vector {circumflex over (v)}i. The base station102bmay then broadcasts the conjugate beam {circumflex over (v)}i⊥* to all the users150b, . . . ,152b.

At210, each receiver may measure its own received signal-to-noise ratio (SNR) ηkwith respect to the broadcast beam that the base station102bsends out, which may be given by the equation
ηk=|hk,{circumflex over (v)}i⊥|2.  (13)

The inner product between the kthuser's channel directional vector vkand vector {circumflex over (v)}i⊥may, therefore, be given by the equation

ακ=〈hk,v^i⊥〉2hκ2=ηκγκ,(14)
where αkmay be an orthogonal parameter of the kthuser and may comprise a real number in the range [0, 1]. The value of αkmay be indicative of the orthogonality of the channel directions between user j and user k. For example, αk=1 may correspond to the case that hkand {circumflex over (v)}imay be ideally orthogonal to each other. Each user may quantize the parameter αkby using a scalar quantization function with quantization resolution Bαbits. In accordance with an embodiment of the invention, Bαmay equal 1. In such instance, the quantized orthogonality parameter {circumflex over (α)}kmay be communicated as a 1-bit flag to the base station102b. Further determination of the second user may be achieved based on the 1-bit flag. Such simplified user group selection algorithm is further described in U.S. patent application Ser. No. 11/232,340 filed Sep. 21, 2005, which is incorporated herein by reference in its entirety.

At212, the base station102bmay select the second user based on the orthogonality parameter feedback information {circumflex over (α)}kreceived from the k users. The base station102bmay select the second user by selecting the user with the largest projected channel power in an orthogonal direction {circumflex over (v)}i⊥. The second user j may be selected utilizing the following expression:

In this regard, the base station102bmay select the strongest user j among a plurality of semi-orthogonal groups. The strongest second user j may be identified as

max⁡(γ^i·η^i)i=1→k.
Based on the selected second user j, the base station102bmay requests a channel direction feedback from the jthuser. The jthuser may then calculate a direction vj(vj=hj/∥hj∥) as a norm vector.

At214, the jthuser may quantize its own channel direction, based on a request from the base station102b. The jthuser may quantize its own channel direction vjby a vector quantizer with inner product quantization criterion. In this regard, the direction vector vjmay be quantized into {circumflex over (v)}jwith quantization resolution Bvbits per channel update. The quantized direction vector {circumflex over (v)}jof the jthuser may be fed back to the base station102busing the feedback link142b.

In this regard, the base station102bhas obtained two candidate users, i and j, and may select between various transmission modes. In one transmission mode, transmission to only the ithuser using full power may occur. In another transmission mode, transmission to both user i and user j may occur with power being equally allocated between both user i and user j. At216, the system capacity for these transmission modes may be calculated utilizing the following expressions:

C⁡(i)≈log2⁡(1+ρ·γ^i)(16)C⁡(i,j)≈log2⁡(1+12⁢⁢ρ·γ^i·α^j)+log2⁡(1+12⁢ρ·γ^j·α^j)(17)
where ρ may be the system average SNR. The approximations “≈” may result from the fact that both {circumflex over (γ)}iand {circumflex over (γ)}jare quantized, and the two users i and j may be assumed to be perfectly orthogonal. Based on the comparison between C(i,j) and C(j), transmission mode with higher system capacity may be selected by the base station102b. In one embodiment of the invention, it may be assumed that the quantized channel direction {circumflex over (v)}jof the second user j is orthogonal to the quantized channel direction {circumflex over (v)}iof the first user i.

At220, if C(i,j)>C(j), the transmission mode that utilizes spatial multiplexing may be utilized to communicate to both users i and j at the same time. The transmitter preceding matrix F may be formed by the following equation
F=[{circumflex over (v)}j⊥H{circumflex over (v)}i⊥]/√{square root over (2)}.  (18)

At218, if C(i, j)≦C(i), a transmission mode in which the base station only communicates to the ithuser may be utilized. In this case, the preceding matrix may be selected according to the equation
F={circumflex over (v)}iH(19)

Referring toFIGS. 1B and 2B, steps202,206,210, and214may be achieved at the receiver side utilizing any of the users150b, . . . ,152b, and steps204,208,212,216,218, and220may be achieved at the transmitter or base station102bside. The approach described herein may be extended to other more sophisticated precoders that may offer better system performance such as the minimum mean square error (MMSE) precoder, the Tomlinson-Harashima preceding (THP) precoder, and/or the sphere encoding precoder, for example. When the number of users K is large enough, there may be a high probability that two users exist having close to orthogonal channel vectors. In this instance, the zero-forcing precoder may be close to an optimal precoder and most preceding techniques may have similar system performance.

A comparison in terms of both search complexity and feedback load between an optimal user group selection algorithm and the user group selection algorithm described herein may be shown in Table 1.

Complexity And Feedback Comparison

Table 1 provides a comparison between the optimal user group selection algorithm and the user group selection algorithm described herein in terms of both search complexity and feedback load. The coefficient a may represent the complexity of comparing two values, and b may represent the complexity of computing water-filling solution. In this regard, b>>a. The selection algorithm described herein may only require two searches for the maximum value determination in step202and212, respectively. The first search may be among K users, and the second search may be among the rest (K−1) users. If a represents the complexity of comparing two positive real numbers, then the complexity of the channel state information feedback scheme disclosed herein may be given by the following expression:
χ≦2Ka,  (20)
as shown in Table 1. As for the optimal group search algorithm, for each of the

(K1)+(K2)=K⁡(K+1)2
possible groups, a water-filling solution may be calculated to obtain the sum rate for each group. If b represents the complexity of computing water-filling solution, the complexity of the optimal group selection algorithm may be represented by the expression:

χopt≥K22⁢⁢b.(21)
It may be noted that a<<b, and
χ<<χopt.  (22)

The total amount of feedback of the channel state information feedback scheme disclosed herein may be represented by the expression:
B=K·Bg+K·Ba+2·Bvbits,  (23)
whereas that of the optimal group selection algorithm may be represented by the expression:
Bopt=K·Bg+K·Bvbits.  (24)
Therefore the required amount feedback may be significantly reduced in the new scheme described herein,
B<<Bopt.  (25)

FIG. 3is a graph that illustrates exemplary downlink transmission schemes in terms of sum rate, in accordance with an embodiment of the present invention. Referring toFIG. 3, there are shown the results of a numerical simulation corresponding to the sum rate of a cellular system with a single base station and K=100 users. The base station may be equipped with M=2 antennas, for example, and each user may be equipped with a single antenna. The channels are flat fading Rayleigh channels. The transmit antennas at the base station may be spaced or located so as to experience independent fading. The modulation format applied in this instance may be quadrature phase-shift keying (QPSK), for example, and the orthogonality parameter αk, as in equation (15), may be quantized by a 1 bit quantizer, Bα=1.

Referring toFIG. 3, four results are illustrated in the graph. The signal302may correspond to the rate sum of a TDMA scheme with channel state information at the transmitter (CSIT). The signal304may correspond to the rate sum of a zero-forcing (ZF), brute-force (BF) search with ideal CSIT. In accordance with an embodiment of the invention, the signal306may correspond to the rate sum of a ZF and simplified search scheme with ideal CSIT. The signal308may correspond to the rate sum of a ZF, improved search scheme with ideal CSIT. The signal310may correspond to the rate sum of a ZF, simplified search scheme with 3-bits allocated for channel gain feedback (Bg=3) and 6 bits allocated for channel directional feedback (Bv=6). The signal312may correspond to the rate sum of a ZF, improved search scheme with 3-bits allocated for channel gain feedback (Bg=3) and 6 bits allocated for channel directional feedback (Bv=6), and 1 bit allocated for orthogonality parameter αk(Bα=1).

The TDMA scheme illustrated by the signal302may pick a single user in a round robin fashion and may only transmit to one user at a time using maximum ratio transmission whereas zero-forcing precoding schemes, as described by the signals304,306, and308, may communicate to multiple users at a time. Therefore, the zero-forcing preceding schemes may achieve a higher sum rate than TDMA schemes. The zero-forcing precoding with the optimal brute-force user group selection, the signal304, may exhibit the best performance at the cost of high computational complexity and high feedback load. In accordance with an embodiment of the invention, the signal306significantly outperforms the TDMA scheme with only very limited extra CSI feedback. It may also be noted fromFIG. 3that allocating 3 bits for channel gain feedback, 6 bits for channel direction feedback, and 1 bit for orthogonality parameter feedback may be sufficient to approach the performance of ideal CSI at the transmitter (CSIT).

In one embodiment of the invention, 3 bits may be allocated for channel gain feedback, 1 bit may be allocated for the quantized orthogonality parameter {circumflex over (α)}kfeedback, and 6 bits may be allocated for the orthogonal channel direction feedback {circumflex over (v)}j. In this regard, the average feedback rate may be approximately 4.06 bits per user per channel update. It may noted from the graph inFIG. 3that the system performance of the improved user group selection scheme disclosed herein with approximately 4 bits feedback rate, may approach the performance of a communication system with an ideal CSI at the transmitter (CSIT). Furthermore, the improved user group selection scheme disclosed herein may significantly improve performance in terms of either sum rate or bit error rate (BER), while utilizing a limited CSI feedback. Such CSI feedback may be negligible when the number of users is large.

FIG. 4is a graph that illustrates exemplary downlink transmission schemes in terms of bit error rate, in accordance with an embodiment of the present invention. Referring toFIG. 4, there are shown the results of a numerical simulation corresponding to the bit error rate (BER) of a cellular system with a single base station and K=100 users. The base station may be equipped with M=2 antennas, for example, and each user may be equipped with a single antenna. The channels may be flat fading Rayleigh channels. The transmit antennas at the base station may be spaced or separated so as to experience independent fading. The modulation format applied in this instance may be QPSK, for example.

In this instance, there are four results provided. The signal402may correspond to the BER of a TDMA scheme with CSIT. The signal404may correspond to the BER of a ZF, BF search with ideal GSIT. The signal406may correspond to the BER of a ZF, simplified search scheme with ideal CSIT. The signal408may correspond to the BER of a ZF, improved search scheme with ideal CSIT. The signal410may correspond to the BER of a ZF, simplified search scheme with Bg=3, Bv=6, and Bα=1. The signal412may correspond to the BER of a ZF, improved search scheme with Bg=3 and Bv=6. The results for the BER performance between the signals402, . . . ,412are substantially the same as the results for the signals302,312shown for the rate sum inFIG. 3.

In comparison to the brute-force user selection algorithm, the channel state information feedback scheme disclosed herein may significantly reduce the computational complexity. For example, the complexity may be reduced from about K2/2 to less than 2K(K>>2), where K may represent the number of users. The various embodiments of the invention may also significantly reduce the total amount of feedback information from (K·Bg+K·Bv) bits to (K·Bg+K·Bα+2·Bv) bits with (Bv>Bα). Therefore, the new scheme may only require very limited CSI feedback rate, in an order of a few bits per user, for example.

Although with a low bitrate constrained CSI feedback channel, the channel state information feedback scheme disclosed herein may achieve multiuser diversity as well as spacial multiplexing when there are a large amount of users. In accordance with an embodiment of the invention, this simplified user group selection scheme may significantly outperform the TDMA scheme and achieve performance in terms of capacity close to systems with ideal CSIT with minimal, about 3 bits per user, feedback rate. In one embodiment of the invention, the channel state information feedback scheme disclosed herein may be utilized with more sophisticated precoders, such as a minimum mean square error (MMSE) precoder, THP precoder, sphere encoding precoder, for example.

Another embodiment of the invention may provide a machine-readable storage, having stored thereon, a computer program having at least one code section executable by a machine, thereby causing the machine to perform the steps as described above for an improved user group selection scheme with finite-rate channel state information feedback for frequency division duplex (FDD) multiuser multiple-input-multiple-output (MIMO) downlink transmission.

Referring toFIG. 1B, in one embodiment of the invention, the base station102bmay select, from a plurality of users in a frequency division duplex (FDD) multiuser communication system, a first user having a channel gain that is greater than a feedback channel gain corresponding to a remaining portion of the users. The base station102bmay select a second user from the remaining portion of the plurality of users, based on a feedback channel gain of the second user and feedback orthogonality of the second user's channel direction with respect to that of the first user. The selected second user may have a channel gain that is greater than a feedback channel gain corresponding to the remaining portion of the plurality of users. The selected second user also has a channel direction that may be approximately orthogonal to that of the first user. The feedback channel gain may comprise feedback quantized channel gain. The base station102bmay determine a quantized channel direction of the selected first user for the selecting the at least the second user.

The orthogonality of the channel direction of the second user may be based on an effective received signal-to-noise ratio (SNR) of the second user with respect to the broadcasted beam vector {circumflex over (v)}i⊥from the base station. The base station102bmay maximize a system capacity based on the selecting of the first user and the selecting of the second user. The base station102bmay generate a first preceding matrix for precoding at least one transmit signal within the communication system, if a system capacity function for the selected first user and the selected second user is greater than a system capacity function for the selected first user. The first precoding matrix may be determined from a quantized channel direction of the selected first user and a quantized channel direction of the second user. The base station102bmay generate a second preceding matrix for preceding at least one transmit signal within the communication system, if a system capacity function for the selected first user and the selected second user is not greater than a system capacity function for the selected first user. The second precoding matrix may be determined from a complex conjugate of a quantized channel direction of the selected first user.