Friday, August 28, 2009

How to Broadcast Multimedia Contents? IV Hierarchical Modulation

[How to Broadcast Multimedia Contents? I Introduction]
[How to Broadcast Multimedia Contents? II Lessons from The Channel]
[How to Broadcast Multimedia Contents? V Overloaded Tx and IC]
[How to Broadcast Multimedia Contents? VI Open-Loop MIMO for BCMCS]
[How to Broadcast Multimedia Contents? VII Network Layer or Steam Layer Design]
[Contribution to 3GPP2 Next Generation Technologies Ad Hoc Group (NTAH) 2007]
[On Enhancing Hierarchical Modulations, 2008 IEEE Int. Sym. on BMSB ]

As shown in Figure 1, hierarchical modulation, also called layered modulation, is one of the techniques for multiplexing and modulating multiple data streams into one single symbol stream, where the base-layer symbols and enhancement-layer symbols are synchronously overlapped together before being transmitted. When hierarchical modulation is employed, users with good reception and advanced receiver can demodulate more than one layer of data streams. For a user with conventional receiver or poor reception, it may be able to demodulate the data streams embedded in low layer(s), e.g, the base layer only. From an information-theoretical perspective, hierarchical modulation is taken as one of the practical implementations of superposition precoding, which can help achieve the maximum sum rate of Gaussian broadcast channel with employing interference cancellation by receivers. From a network operation perspective, a network operator can seamlessly target users with different services or QoS’s with this technique. However, traditional hierarchical modulation suffers from inter-layer interference (ILI) so that the achievable rates by low-layer data streams, e.g. the base-layer data stream, can be dented by the interference from high-layer signal(s). For example, for the hierarchically modulated two-layer symbols with a 16QAM base layer and a QPSK enhancement layer, the base layer throughput loss can be up to about 1.5bits/symbol with the total receive signal-to-noise ratio (SNR) of about 23 dB. This means, due to ILI, there is about 1.5/4 = 37.5% loss of the base-layer achievable throughput with 23dB SNR. And the demodulation error rate of either the base-layer and enhancement-layer symbols increases too. From a practical implementation point-view, it is also known that the severe amplitude and phase fluctuations of wireless channels can significantly degrade the receiver demodulation performance since the demodulator must scale the received signal so that the result signals is within the dynamic range of the followed analog-to-digital convertor (ADC) or, more generally, the receiver processing region, mostly with automatic gain control (AGC). Even though pilots may be available for assisting the receiver channel estimation and equalization, there are channel estimation errors, especially when the channel coherent time is short. If the channel is estimated in errors, it can lead to improperly compensated signals and incorrect demodulation even in the absence of noise. On the other hand, multicarrier transmission, e.g. orthogonal frequency-division multiplexing (OFDM), is widely used for broadcast multicast services (BCMCS) as well as next generation wireless systems, due to its high diversity gain and high spectral efficiency with simple receiver design. However, the advantages of OFDM, specially when it is modulated by high-order signal constellations, are counter-balanced by the high peak-to-average-power ratio (PAPR) issue. High PAPR of modulated signals can significantly reduce the average output power of the high-power amplifier (HPA) at the transmitter due to more back-offs. It also increases the receiver demodulation and decoding errors and therefore limits the throughput of whole transceiver chain. Therefore it is important to understand and optimize regular hierarchical modulations for the best achievable performance.

Figure 1. Enhanced hierarchical modulation example: QPSK/QPSK

In this contribution, the regular hierarchical modulation is firstly extended by allowing additional rotation on the enhancement layer signal constellation. The generalized hierarchical modulations are then studied and analyzed from four different perspectives, such as achievable capacity [Figure 2], modulation efficiency [Figure 4], demodulation robustness and peak-to-average-power ration (PAPR) when it is combined with the popular OFDM. At first, the achievable capacities of hierarchical modulations over Gaussian broadcast channel are studied from an information-theoretical perspective. As an example, the capacity of a regular 16QAM is tore down into the equivalent capacities of a base layer and enhancement layer. It is shown that there is a capacity loss on the base layer due to the inter-layer interference (ILI) from the enhancement layer [Figure 2]. And this capacity loss can be mitigated by properly rotating the enhancement signal constellation. From a signal-processing perspective, it is known that the capacity loss is also related to the Euclidean distance profile of the hierarchical modulation signal constellation. For example, in high signal-to-noise ration (SNR) region, the symbol error rate usually is dominated by the minimum Euclidean distance. Obviously, with properly rotating the enhancement layer signal constellation and maximizing the minimum Euclidean distance, the resulted symbol error rate will decrease. Additionally, for tracking Euclidean distance profile changes, several parameters like effective signal power, effective SNR and modulation efficiency are discussed too. After this, hierarchical modulations are analyzed from an implementation perspective with considering channel estimation errors, which includes both channel amplitude estimation errors and channel phase estimation errors. It is shown that the demodulation robustness of hierarchical modulations can also be controlled by changing the Euclidean distance profile. Finally hierarchical modulations are discussed from a transmit power efficiency perspective when it is combined with multicarrier transmission. With avoiding high back-offs and maximizing average output power, it shows that high RF transmitter power efficiency is achievable by properly rotating the enhancement layer signals. With the analyses from different aspects of hierarchical modulation, a in-depth understanding of it can be achieved.

Figure 2. Capacity tear-down of 16QAM, a hierarchical modulation perspective

Figure 3. Bit error rates of hierarchical modulation and inter-layer interference
Figure 4. Modulation efficiencies of hierarchical modulations


Wednesday, August 12, 2009

How to Broadcast Multimedia Contents? III Scalable Video Coding

H.264 Network Abstract Layer Header
[How to Broadcast Multimedia Contents? I Introduction]
[How to Broadcast Multimedia Contents? II Lessons from The Channel]
[How to Broadcast Multimedia Contents? IV Hierarchical Modulation]
[How to Broadcast Multimedia Contents? V Overloaded Transmission and IC]
[How to Broadcast Multimedia Contents? VI Open-Loop MIMO for Broadcast Multicast Services]
It is very challenging to deliver multimedia contents through wireless links. Diverse receivers may request the same video with different bandwidths, spatial resolutions, frame rates, computational capabilities. Heterogeneous networks with unknown network conditions. Wired and wireless links, time-varying bandwidths. One Example is when you originally code the video you don’t know which client or network situation will exist in the future. Probably have multiple different situations, each requiring a different compressed bit stream. It needs a different compressed video matched to each situation. Possible solutions include 1) compress and store MANY different versions of the same video, 2) real-time transcoding (e.g. decode/re-encode), and 3) scalable video coding.

The procedure of scalable coding includes decomposing video into multiple layers of prioritized importance, coding layers into base and enhancement bit streams, and progressively combining one or more bit streams to produce different levels of video quality. Examples of scalable coding with base and two enhancement layers, such as 1) Base layer, 2) Base + Enh1 layers, 3) Base + Enh1 + Enh2 layers. Three basic types of scalability (refine video quality along three different dimensions).
Temporal scalability → Temporal resolution
Spatial scalability → Spatial resolution
SNR (quality) scalability → Amplitude resolution
Multiple types of scalability can be combined to provide scalability along multiple dimensions

Saturday, July 11, 2009

How Wide A Wideband Channel Should Be?

[Frequency Selectivity of A 1.2288MHz, 3GPP2, TSG-C, Working Group 3, C30-20090511-028]

How wide should a channel be before it is called wideband? Dictionary.com says it is "responding to or operating at a wide band of frequencies". I guess this is pretty much the one in most people's mind. Wikipedia.org gives us a more technical definition,"a system is typically described as wideband if the message bandwidth significantly exceeds the channel's coherence bandwidth". Basically it says whether a channel can be called wideband channel or not largely depends on the multiple of coherence bandwidth it has. The question then becomes what is coherence bandwidth and how wide a typical coherence bandwidth can be. For example, should a CDMA2000 channel, which has a bandwidth of 1.22288MHz, be called wideband or not?  Why can a 5.0MHz WCDMA channel usually be called wideband? Let's find out here.

Coherence Bandwidth

Coherence bandwidth is a statistical parameter indicating how fast a channel changes in frequency and the frequency range over which the channel can be considered "flat". Narrower a channel's coherence bandwidth is, more frequency selectivity it has and more frequency diversity gain the communication system can achieve. In general, the channel's "flatness" depends on both the cell size and operating environment. The factors includes, macro-cell or micro-cell, urban or suburban, indoor or outdoor, line-of-sight or no-line-of-sight detection, and detection threshold in a typical receiver design. Fundamentally, the coherence bandwidth of a multi-path channel is an inverse to its delay spread. And the delay spread of a channel can be quantified through the measuring of root mean squared (RMS) delay spread or maximum excess delay spread. Maximum excess delay spread can be taken as an upper bound reference.

As we know, RMS delay spread is known to follow a log-normal distribution, which is similar to that of log-normal shadowing (LNS). In fact, RMS delay spread is correlated to log normal shadowing and its median grows as some power of distance. RMS delay spread has been modeled and simply quantified in the form:

Δ rms = E1/2{ (d - d0)2 } ≈ Δ0 · dε · y


where d is the distance in km, ε is an exponent between 0.5 and 1.0, and y is a log-normal variant. The correlation coefficient value for suburban and urban data was shown to be about -0.75, which indicates that for a strong signal ( positive LNS ), the delay spread is reduced, and for a weak signal condition ( negative LNS ), the delay spread is increased. In [1], Sousa, et. al., reported the 90th percent rms delay spread to be 1.2 μs in suburban Toronto. In [2], Ling, et. al. observed that the 90th percent rms delay spread was 1.7 μs in Lakehurst NAES, New Jesey. In [3],  Baum reported the 77th percent rms delay spread was 1 μs, the 94th percent rms delay spread was 2 μs in Rolling Meadows, Chicago.
Figure 1. The statistic model of delay spread

Now, considering the fundamental chip rate of 1.2288Mcps of CDMA2000 mobile communication standards, a 70%-90% RMS delay spread is between 1-2 chips, which is about a 3dB-coherence bandwidth of 25 – 60 subcarriers with the assumption of 180 subcarriers per 1.2288MHz. Therefore, a CDMA2000 1x channel statistically has 3 ~ 7 coherence bandwidths and it should be called narrowband instead.  For a 5MHz WCDMA channel, 12 ~ 28 coherence bandwidths should be observed.  It can be called wideband. 

Impact of Cyclic Delay Diversity (CCD)

The impact of multiple Tx antennas on channel delay spread also depends on the employed multi-antenna techniques. CCD is one of the most open-loop multi-antenna techniques.  When CCD is employed by the transmitter, the total delay spread will increase. This usually results in more fluctuations in the frequency domain of channel response.




Example: Coherence Bandwidth of OFDM Channels

Figure 2. OFDM Coherence Bandwith

[1] E. Sousa, V. Jovanovic, C. Daigneault, “Delay spread measurements for the digital cellular channel in Toronto”, IEEE Trans. on Vehicular Technology, Nov 1994
[2] J. Ling, D. Chizhik, D. Samardzija, R. Valenzuela, “Wideband and MIMO measurements in wooded and open areas”, Lucent Bell Laboratories,
[3] K. Baum, “Frequency-Domain-Oriented Approaches for MBWA: Overview and Field Experiments”, Motorola Labs, IEEE C802.20-03/19, March 2003
[4] L. Greenstein, V. Erceg, Y. S. Yeh, M. V. Clark, “A New Path-Gain/Delay-Spread Propagation Model for Digital Cellular Channels,” IEEE Transactions on Vehicular Technology, VOL. 46, NO.2, May 1997, pp.477-485.
[5] A. Algans, K. I. Pedersen, P. Mogensen, “Experimental Analysis of the Joint Statistical Properties of Azimuth Spread, Delay Spread, and Shadow Fading,” IEEE Journal on Selected Areas in Communications, Vol. 20, No. 3, April 2002, pp. 523-531.
[6] Spatial Channel Model AHG (Combined ad-hoc from 3GPP & 3GPP2), “Spatial Channel Model Text Description ”, 3GPP, 2003
[7] H. Arslan and T. Yucek, Estimation of Frequency Selectivity for OFDM based New Generation Wireless Communication System, WWC 2004.

Friday, March 20, 2009

How Much Feedback Is Enough for MIMO? VI Rank Deficiency

[How Much Feedback Is Enough for MIMO? I Introduction]
[How Much Feedback Is Enough for MIMO? II Channel Estimation]
[How Much Feedback Is Enough for MIMO? III Codebook Design]
[How Much Feedback Is Enough for MIMO? IV Channel Quantization]
[How Much Feedback Is Enough for MIMO? V Feedback Reliabilities]
[3GPP2 TSG-C WG3 C30-20090511-030]
[3GPP2 TSG-C WG3 C30-20090511-032]

The adoption of multi-antenna techniques is believed to be able to provide additional antenna gain, diversity gain, multiplexing gain and interference cancellation gain. They can help improve link quality and increase link throughput. Multi-antenna techniques are believed to be critical in meeting the demand of high data rate and high link quality and can be employed for both forward link and reverse link transmission. However, there are many issues which should be carefully considered when multi-antenna techniques are implemented. These issues include the rank deficiency of actual MIMO channels, the limitations of mobile terminal's RF design and the impact of multi-antenna techniques on other services in bandwidth-limited situations.

In theory, the achievable capacity of a MIMO channel grows linearly with the minimum of transmit and receive antenna sizes. In reality, the achievable spatial multiplexing gain depends on both channel scattering of underlying and antenna configurations of both sides instead of the geometric limitation, min{ Ntx, Nrx }. The scattering statistics of a MIMO channel is usually quantified with angular intervals. The antenna array configuration is characterized by the area or size limitation in the unit of wavelength λ and the shape. Without considering AT size, the achievable spatial multiplexing gain is limited by spatial scattering. For example, in the case of a typical 4x4 MIMO mobile communication scenario and without the limitation of access terminal's size, it is observed that less than 1% of the users are able to use rank 4 and around 90% users have either rank 1 or 2. However, it is non-trivial to “squeeze” multiple antennas and RF circuits into a mobile phone in actual commercial mobile terminal design, especially when you need additional planning on the power consumption, mechanical limitation, antenna spacing and supported frequency bands of the mobile terminal. Currently, there are many radio interfaces already enabled in most mobile phones, such as GPS, bluetooth, WiFi, etc. However, from a RF engineering perspective, there is an antenna spacing requirement that the separation between antenna elements should be larger than 0.5λ in order to maximize spatial diversity gain. This can be translated into about 7.5 cm or 3.0 inches for a 2GHz operating band, as an example. Therefore, there usually is a tradeoff between the physical size and achievable performance in each mobile terminal design. For an AT with the physical size of a few times of wavelength, e.g., about 0.5~3λ, the achievable spatial multiplexing gain is limited by the angle spread, AT size and C/I ratio. This means for practical multi-antenna mobile devices, the expected spatial multiplexing gain mostly is less than 3.


Expected Spatial Degree of Freedom. 6 spatial cluser, angle spread = 35o, dual-polarized antenna array, f = 2GHz

Sunday, March 8, 2009

How Much Feedback Is Enough for MIMO? V Feedback Reliabilities

[How Much Feedback Is Enough for MIMO? I Introduction]
[How Much Feedback Is Enough for MIMO? II Channel Estimation]
[How Much Feedback Is Enough for MIMO? III Codebook Design]
[How Much Feedback Is Enough for MIMO? IV Channel Quantization]
[How Much Feedback Is Enough for MIMO? VI Rank Deficiency]


Figure 1. A Noisy Feedback Channel Model
The reverselink channel model is a concatenation of a Gaussian channel and binary erasure channel, which are independent to each other. In generally, the reliability of reverselink is controlled by both channel fading and received SNR. When the erasure rate εr is high, it means the amount of fading of reverselink is very high. Higher erasure rate also means it takes the forwardlink transmitter longer time to accurately filter out a proper forwardlink precoding word and it usually yields higher MIMO precoding mismatch given a certain channel coherent time. Since the unreliable symbols are erased based on their received SNR, the left symbols are more reliable and their reliability is mostly decided by γRL. In this case, the well-known sphere-packing upper bound of Gaussian channel reliability function is

Figure 2. The rate-reliability region with γRL = 7dB

Wednesday, February 25, 2009

How Much Feedback Is Enough for MIMO? IV Channel Quantization

[How Much Feedback Is Enough for MIMO? I Introduction]
[How Much Feedback Is Enough for MIMO? II Channel Estimation]
[How Much Feedback Is Enough for MIMO? III Codebook Design]
[How Much Feedback Is Enough for MIMO? V Feedback Reliabilities]
[How Much Feedback Is Enough for MIMO? VI Rank Deficiency]

Generally, MIMO channel quantizer or CQI generation, maps the input channel estimation vector to the index of a codeword in the codebook. The decode will do the reverse. It is similar to the vector coding in EVRC, AMR, MPEG-4, etc. The designing a best codebook as well as finding the general boundary of Voronoi cell is NP-hard.

Figure 1. MIMO Precoding Mismatching

With Figure 1, it is shown that there are multiple issues involving MIMO precoding mismatching. In most existing MIMO beamforming systems, the receiver tracks the channel norm information for link adaptation purpose and the phase information for beamforming precoding. In this case, Dh can be rewritten by

Dh = 2M σh2 [ 1 - ( 1- Dθ )1/2 ]

with Dθ denoting the phase quantization deviation. A lower bound for distortion rate of channel quantization for MIMO beamforming is

R( Dθ )   ≥ max{ - M log2[ 2 - 2( 1- Dθ )1/2 + σh2h2 ], 0 }

for each beam. With the feedback rate of R, it also tells us that the minimum precoding mismatch for forwardlink MIMO beamforming is

Dθ ≤ 1-[1-2-R/M-1 + σh2/(2σh2)]2

Figure 2. The rate-distortion region with M = 4

Tuesday, February 17, 2009

How Much Feedback Is Enough for MIMO? III Codebook Design

[How Much Feedback Is Enough for MIMO? I Introduction]
[How Much Feedback Is Enough for MIMO? II Channel Estimation]
[How Much Feedback Is Enough for MIMO? IV Channel Quantization]
[How Much Feedback Is Enough for MIMO? V Feedback Reliabilities]
[How Much Feedback Is Enough for MIMO? VI Rank Deficiency]

Figure 2. Voronoi cell and various bounds

MIMO beamforming mismatch upper bound depends on the codebook design. The maximum MIMO beamforming mismatch can be determined by the largest radius of the codebook’s Voronoi cellVi : 1   ≤ i ≤ 2R }, which in general is the solution to the disk-covering problem that still is open. Instead of finding the exact boundary for the Voronoi cell Vi, a heuristic approach using sphere-packing bound and sphere cap to approximate the actual polytope boundary can be used. The result is an approximate of the sphere packing solution, in which all spheres are supposed to be non-overlappedly placed. With this approach, sphere caps are overlapped with each other in space but the interior of them has the same area as the Voronoi cell. The border of this sphere cap is named sphere-packing boundary. The relationship between sphere-packing boundary and Voronoi cell is shown in Fig. 2. For an uniform random codebook of size 2R in M-dimensional Euclid space, the area of a Voronoi cell is given by

A( V) = 2πM / [ 2R Γ(M) ]

where Γ(*)denotes the gamma function. A heuristic upper bound of MIMO beamforming mismatch is given by

Dθ ≥ { (M-1)/M [ 1 - ( 1 - 2-R )1/(M-1) ] }1/2

Saturday, January 24, 2009

How Much Feedback Is Enough for MIMO? II Channel Estimation

[How Much Feedback Is Enough for MIMO? I Introduction]
[How Much Feedback Is Enough for MIMO? III Codebook Design]
[How Much Feedback Is Enough for MIMO? IV Channel Quantization]
[How Much Feedback Is Enough for MIMO? V Feedback Reliabilities]
[How Much Feedback Is Enough for MIMO? VI Rank Deficiency]

MIMO beamforming with finite-rate feedback is modelled as a noisy Gaussian binary erasure feedback channel depicted. In reality, the receivers estimate channels with the pilots sent by transmitter. Accuracy of the channel estimation depends on both forwardlink design and receiver design. The pilot transmission is important for receiver to efficiently estimate CSI. antenna. An overview of pilot-assisted transmission (PAT) including pilot placement and channel estimation can be found in [Tong 04]. There are two popular pilot patterns, time multiplexed pilots (TMP)  and superimposed pilots (SIP), receiving much attention for MIMO CSI estimation. They are shown in Fig. 1. Optimal pilot placement was investigated in [Dong 02]. TMP is a typical example of orthogonal pilot design where pilot symbols and data symbols are separated in time and/or frequency domain, which makes them orthogonal to each other. With orthogonal pilots, the CSI estimation and data demodulation can be done separately which may lead to simple receiver design [Dong 02]. SIP does the opposite. In SIP design, pilots and data nonorthogonally share the same time period and frequency band. In this case, joint channel estimation/demodulation and the demodulation with pilot interference cancellation are among the most popular receiver design techniques [Coldrey 06]. After channel estimation, the receiver chooses a beamforming vector from a shared MIMO precoding codebook. This is called channel quantization. It means the receiver actually feeds back the chosen precoding index(es) to transmitter(s) instead of channel response for MIMO precoding.

Figure 1. Pilot patterns for channel estimation

In general, the channel quantization distortion is decided by channel quality, channel estimation and codebook design. Given σh2, the channel estimation mean squared error (MSE), the minimum rate at the channel quantization mean squared distortion Dh is given by

R( Dh )   ≥ M log2[ σh2 / ( Dh/M + σh2 ) ]

Meanwhile, the lower bound to the unbiased MSE σh2 is given by Cramer-Rao lower bound (CRLB), which is defined as the inverse of the Fisher Information Matrix (FIM).

Monday, January 5, 2009

How Much Feedback Is Enough for MIMO? I Introduction

[How Much Feedback Is Enough for MIMO? II Channel Estimation]
[How Much Feedback Is Enough for MIMO? III Codebook Design]
[How Much Feedback Is Enough for MIMO? IV Channel Quantization]
[How Much Feedback Is Enough for MIMO? V Feedback Reliabilities]
[How Much Feedback Is Enough for MIMO? VI Rank Deficiency]

Figure 1. MIMO model with feedback

Multi-antenna systems have received much attention over the last decades, due to their promise of higher spectrum efficiency with no transmit power increase. Combining multiantenna transceiver with relay network is essential not only to provide comprehensive coverage but also to help relieve co-channel interference in existing wireless systems in a cost effective fashion. For multiple-input multiple-output (MIMO) transmission, it is well-known that their performance and complexity can be improved by making channel state information (CSI) available at the transmitter side. This is usually achieved through a reverselink CSI feedback channel from receiver, e.g., there is a reverslink channel quality indicator channel (RCQICH) for CSI feedback in UMB (Ultra Mobile Broadband), a 3.5G mobile network standard developed by 3GPP2. In practice, CSI received by transmitters is not perfect and suffers from various impairments and limitations that include round-trip delay, channel estimation error, codebook limitation, etc. Therefore the actual link throughput is degraded. This kind of degradation becomes more serious if the end-to-end capacity is considered for a multi-hop MIMO relay network.

Figure 2. Noisy Gaussian binary erasure feedback channel with channel

MIMO beamforming with quantized feedback has been intensively investigated since 1990s [1]. MIMO channel quantization as well as codebook design in general is a NP-hard Voronoi decomposition problem. The Voronoi region for a uniform random codebook is known to be upper-bounded by the disk-covering problem solution and lower-bounded by the sphere-packing problem solution. These two problems themselves are still open. MISO/MIMO beamforming systems with perfect CQI Lloyd vector quantization (VQ) [2], different channel model [3] or different performance metrics [4], [5] have intensively been investigated. It is linked to Grassmannian line packing problem [6]. However, most of existing work is done without considering pilot design, channel estimation and the reliability of feedback, even though they are among the most important components of actual multi-antenna systems. In reality, MIMO CSI is estimated with forwardlink common pilot channels sent from each transmitter antenna. An overview of pilot-assisted transmission (PAT) including pilot placement and channel estimation can be found in [7]. In most multiantenna systems, pilot channels are designed to be orthogonal to other channels and periodically sent by transmitter. Nonorthogonal pilot design like superimposed pilots (SIP) has recently received much attention for channel estimation too [8]. Optimal pilot placement was investigated in [9]. Besides pilot design, the feedback capacity and reliability have intensively been investigated over decades too. Though feedback doesn’t increase the capacity of memoryless channels [10], [11], a feedback coding scheme with the decoding error probability decreasing more rapidly than the exponential of any order is achievable [12]. Since CSI feedback plays such a critical role in MIMO transmission, it is desired to understand how MIMO pilot and codebook design affects system behavior, what are the tradeoffs, etc. And these problems become more critical when a multi-hop MIMO relay network.

The feedback and sharing of CSI and/or network status information (NSI) help wireless relay network achieve high throughput and reliability with a little overhead increase. For example, CSI feedback helps nodes realize distributed cooperation for increasing the throughput and reliability of wireless relay networks. Cooperation diversity for wireless relay network has heavily been investigated in the past several years. The concept of distributed cooperation diversity is knowingly pioneered by Sendonaris et al. [13], where the transmitters cooperate with each other by repeating symbols of others. It shows that a higher rate is achievable with this cooperation. Almost at the same time, this concept is also developed through other techniques such as code combining [14], coherent soft combining [15], power control [16] and later opportunistic routing [17]. Most of them are implemented with CSI feedback in the assumption. Besides this, from a network perspective, it is known that NSI feedback can also assist each source terminal or relay terminal to shape the dynamic behavior of the network and increase network agility through proper resource allocation [18]. Due to the limitation of the measuring, link capacity and network resource in reality, however, most CSI or NSI sent back by receivers is neither perfect nor sufficient in nature. It is interesting and important to understand the effect of imperfect feedback on wireless link and network, which are still not clear from many perspectives.

Reference

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[2] A. Narula, et al. Efficient use of side information in multiple-antenna data transmission over fading channels. IEEE J. Select Areas in Communications, 16(8):1423–1436, October 1998.
[3] K. K. Mukkavilli, A. Sabharwal, E. Erkip and B. Aazhang. On beamforming with finite rate feedback in multiple-antenna systems. IEEE Trans Info. Theo., 49:2562–2579, October 2003.
[4] P. Xia and G. B. Giannakis. Design and analysis of transmit beamforming based on limited-rate feedback. In Proc. IEEE VTC, September 2004.
[5] J. C. Roh and B. D. Rao. Performance analysis of multiple antenna systems with vq-based feedback. In Proc. Asilomar Conference 2004, Pacific Grove, CA, November 2004.
[6] D. J. Love, R. W. Heath and T. Strohmer. Quantized maximal ratio transmission for multiple-input multiple-output wireless systems. In Proc. Asilomar Conf., Pacific Grove, CA, Nov. 2002.
[7] L. Tong,B. M. Sadler and M. Dong. Pilot-assisted wireless transmissions: general model, design criteria, and signal processing. IEEE Signal Processing Mag., 21(56):12–25, November 2004.
[8] M. Coldrey and P. Bohlin. Training-based mimo syetems: Part i/ii. Technical Report (http://db.s2.chalmers.se/), (R032/033), June 2006.
[9] M. Dong and L. Tong. Optimal design and placement of pilot symbols for channel estimation. IEEE Trans. on Signal Processing, 50(12):3055–3069, December 2002.
[10] C. E. Shannon. The zero error capacity of a noisy channel. IRE Trans. Inf. Theory, 2(3):8–19, September 1956.
[11] Y. H. Kim. Feedback capacity of the first-order moving average gaussian channel. IEEE Trans. on Inf. Theory, 52(7):3063–3079, July 2006. [12] A. J. Kramer. Improving communication reliability by use of an
intermittent feedback channel. IEEE Trans. Inf. Theory, 15:52–60, January 1969.
[13] A. Sendonaris, E. Erkip and B. Aazhang. User cooperation diversity - part i/ii. IEEE Trans. Commun., 51(11):1927–1948, Nov. 2003.
[14] T. E. Hunter and A. Nosratinia. Cooperative diversity through coding. In Proc. IEEE int. Symp. Info. Theory, page 220, 2002.
[15] J. N. Laneman. Cooperative Diversity in Wireless Networks: Algorithm and Archiectures. Ph.D. Thesis, MIT, Cambridge, MA, 2002.
[16] N. Ahmed, M. A. Khojastepour and B. Aazhang. Outage minimization and optimal power control for the fading relay channel. In IEEE Information Theory Workshop 2004, pages 458–462, Oct. 2004.
[17] C. K. Lo, R. W. Heath and S. Vishwanath. Opportunistic relay selection with limited feedback. In Vech. Tech. Conf. 2007, Dublin, Ireland, Apr. 2007.
[18] Special issue on networks and control. In IEEE Control Systems Magazine, February 2001.
[19] H. Blcskei, R. U. Nabar, . Oyman and A. J. Paulraj. Capacity scaling laws in mimo relay networks. IEEE Trans. Wireless Communications, pages 1433–1444, June 2006.
[20] Bo Wang, Junshan Zhang and Anders Host-Madsen. On the capacity of mimo relay channels. IEEE Transactions on Information Theory.