2.1.

H.264/AVC

H.264/AVC^4,5 is the de facto video coding standard used currently. H.264/AVC contains a series of new features, and it can compress video more effectively. It has been widely used in almost all forms of digital video coding. In this paper, H.264/AVC is used in the digital coding of video sequences. Since the quantization error and the compression rate increase with the quantization parameter (QP), QP is used as a variable to adjust the compression ratio based on the worst channel quality of the receivers group, and the basic digital video performance is also decided by QP.

2.2.

SoftCast

Katabi et al. ^21–23 have proposed the SoftCast scheme, which can broadcast one coded video signal to multiple receivers, while all the receivers can decode videos matching their channel qualities. SoftCast mainly consists of four parts: decorrelation, power allocation, whitening, and linear least square estimator (LLSE) decoding.

Similar to the digital video coding scheme, the first step of SoftCast is decorrelation. Discrete cosine transform (DCT) or discrete wavelet transform (DWT) have been used to remove space correlation of video frames in SoftCast. Moreover, 3D-DCT²³ or 2D-DWT+DCT²⁰ can also be applied in SoftCast to remove the space correlation and the time correlation simultaneously. In addition, similar to the digital decorrelation, DCast²⁵ removes the interframe correlation by inter prediction.

Another important step of SoftCast is power allocation, which minimizes the reconstruction errors by scaling the magnitudes of signals. Let $\mathbf{x}$ be a decorrelated signal, and it is divided into $N$ chunks based on its coefficient structure. Assume that the chunked signal is $\tilde{\mathbf{x}}$ and the $i$’th row of $\tilde{\mathbf{x}}$ corresponds to the $i$’th chunk. Next, the diagonal matrix ${\mathrm{\Lambda }}_x$, whose $i$’th diagonal element ${\lambda }_i$ is the variance of the $i$’th chunk, can be obtained. Assuming that the total power budget of SoftCast is $P$, we can get the power allocation matrix $\mathbf{G}$, which is a diagonal matrix with the $i$’th diagonal elements

Next, a Hadamard matrix $\mathbf{H}$ is employed as the whitening matrix to balance packets with equal importance. We can get the whitening signal $\widehat{\mathbf{y}}=\mathbf{H}\mathbf{G}\tilde{\mathbf{x}}$. Therefore, if these whitening chunks are assigned to packets, the packets will have the same power and it can provide better packet loss protection.²¹ After being transmitted in an interference environment, the received signal is

At the decoder, the chunked signal can be reconstructed by an LLSE decoder, and the reconstructed signal is

Different from the traditional digital video coding scheme, signals are coded without quantization and entropy coding in SoftCast, and videos are transmitted by analog transmission. Therefore, it can completely avoid the cliff effect. Thus, it can achieve effective compression, data protection, and transmission performance. What is more, with the power allocation algorithm and the LLSE decoder,³³ SoftCast can reach the MMSE of video multicast.

2.3.

ParCast

ParCast²⁶ is a video coding scheme designed for single-user MIMO video transmission, while SoftCast is a video coding scheme designed for multiple users’ multicast. The MIMO channel is first divided into subchannels by singular value decomposition (SVD) in ParCast. Then, different from the SoftCast²¹ scheme, which allocates different source chunks with different power, ParCast allocates the better subchannels to the more important data chunks and discards some bad chunk–subchannel pairs to reallocate more power to the important pairs before power allocation.

Assuming that the $M\times N$ MIMO channel state matrix is $\mathbf{H}$, it can be decomposed into $M$ orthogonal subchannels by SVD, i.e.,

In ParCast, the encoder removes the temporal and spatial redundancy by 3D-DCT³⁴ first. Each group of DCT coefficients is divided into chunks uniformly and all the chunks are sorted by variances. Then all the chunks are assigned to the available subchannels based on the principle that higher-variance chunks are transmitted over higher-gain subchannels. After that, the encoder allocates transmission power to each chunk based on joint consideration of source and channel. Next, data are precoded by matrix $\mathbf{V}$, then transmitted over the MIMO system. Correspondingly, the receiver will multiply the received signal by ${\mathbf{U}}^{\mathrm{H}}$ as precoding at the decoder to divide the MIMO channel into subchannels. The whole encoding procedure ensures that the important data in a frame gets more protection by matching them to high-gain subchannels. To achieve the MMSE of video transmission, the analogous water-filling power allocation strategy, i.e., the SoftCast power allocation strategy, is adopted. Therefore, the received signal is

Similarly, the receiver can decode the original signal using the LLSE decoder. The optimal decoder is

Based on ParCast, ParCast+ is presented in Ref. 35 to feature improved video source decorrelation and more flexible source-subchannel mapping. Specifically, ParCast+ adopts a motion-aligned three-dimensional (3-D) transform to decorrelate the source, which is generally considered more efficient at compacting the source energy than the 3D-DCT in ParCast. However, the analog data in the HDA scheme is the residual, which hardly has relevance in the time domain. Therefore, in our proposed HDA scheme in MIMO, we adopt ParCast to deal with the analog data.

Different from the SoftCast scheme, the source and channel are considered jointly in ParCast. The chunk–subchannel pairs are powered by the SoftCast power allocation strategy, so it can achieve the MMSE of video transmission in MIMO with the corresponding LLSE decoder.

2.4.

Hybrid Digital-Analog Scheme

Apart from the digital schemes and the analog schemes, there are still many HDA schemes proposed in recent years, e.g., the WaveCast video delivery scheme in Ref. 24, the DCast video delivery scheme in Ref. 25, and the WSVC video delivery scheme in Ref. 20. These schemes are all designed for video multicast.

WaveCast first transforms the video by 3D-DWT, then these transformed coefficients are powered by the SoftCast power allocation algorithm. Different from the SoftCast scheme, which transmits analog signals directly, WaveCast modulates the analog coefficients by a very dense constellation (64K-QAM) and codes the metadata by FEC with binary phase shift keying (BPSK). After that, the modulated signals are transmitted over the OFDM channel.

In DCast, the original signals are first transformed by DCT. Then two successive coset coding modules are applied to classify each DCT coefficient into most important bits, least important bits, and the remaining middle bits. Next, the least important bits are coded by SoftCast; meanwhile, the middle bits are coded by FEC with BPSK to be transmitted in the OFDM channel, and the most important bits are discarded since they have high correlation with the decoder prediction and can be guessed at the decoder.

The HDA scheme in WSVC maps the digital signals and the analog signals to the same constellation. In WSVC, video is decomposed into LL, LH, HL, and HH bands by 2D-DWT first. Then, the LL band is coded by H.264/AVC, and the output bitstream is coded by convolutional code with BPSK. Next, the residuals of the LL band quantization and the other three bands are decomposed by temporal DCT, and the output decomposed residuals are coded by SoftCast. Finally, the output digital encoding signals (as coding signals of base layer) and the output SoftCast coding signals (as coding signals of enhancement layer) are superposed, then transmitted over the OFDM channels. Specifically, these analog coefficients powered by SoftCast are divided into two states, i.e., the “big” state and the “small” state. Then, the coefficient feature of SoftCast is taken into account in WSVC and the digital bitstream is superposed with the “small” analog coefficients. Additionally, these superposed coefficients are mapped to the I component of the constellation diagram, while the “big” analog coefficients are mapped to the Q component. Therefore, though the digital bitstream is slightly interfered with by the “small” analog coefficients; it is orthogonal to the “big” analog coefficients.

In addition, an effective power allocation algorithm for the analog part and the digital part is designed in WSVC, where the digital signal can still be reconstructed correctly from the superposed signals interfered with by “small” coefficients and channel noise. With the application of the HDA scheme, WSVC integrates the advantages of digital coding and analog coding, i.e., high-coding efficiency and graceful degradation with channels. Therefore, it is able to broadcast one video to multiple receivers while each receiver can decode video performances matching its channel qualities. What is more, the WSVC scheme outperforms other hybrid schemes significantly, e.g., $\mathrm{SVC}+\mathrm{HM}$ and DCast.

In Sec. 3, a new HDA scheme is proposed to further improve video performance. The HDA scheme is also applied to the video transmission in MIMO to certify the performance.

3.1.

Digital Encoding of Hybrid Digital-Analog Video Multicast

In the proposed video multicast scheme, a video sequence is first encoded by H.264/AVC. Then, a low-rate convolutional code is used as the FEC to adapt robustly to channel SNR variability. To ensure that the digital signals can be decoded by all the receivers with different channel qualities, the FEC code rate is set to guarantee that the BER is less than the target BER, even when the modulated digital signals are transmitted over the worst channel. Assuming that the digital signal coding rate equals the channel bandwidth, since the FEC code rate is decided by the channel qualities, the quantization parameter (QP) that decides the compression rate of H.264/AVC is also decided by channel qualities. When the channel quality is bad, a large QP will be adopted; a small QP will be adopted when the channel quality is good. Next, the BPSK modulator is employed to modulate the digital signal, and the H.264/AVC video information focuses on the real part of the modulated digital signals ${\mathbf{x}}_{md}$. Assuming that power allocated to the digital signal is $P_d$, the powered digital signal is ${\mathbf{x}}_d=\sqrt{P_d}{\mathbf{x}}_{md}$.

3.2.

Analog Encoding of Hybrid Digital-Analog Video Multicast

The residuals of H.264/AVC quantization are sent to the analog encoder and powered by SoftCast to improve the performance of H.264/AVC. Information stored in the residuals depends on the QP set in H.264/AVC. The bigger the QP, the more information stored in the residuals, and the more performance gains provided by the residuals. In the analog part, the residual signals ${\mathbf{x}}_{\text{residual}}$ are first decomposed by 3D-DCT, then uniformly divided into $n$ chunks. Next, it is powered by SoftCast, and the power factor of the $i$’th chunk is

3.3.

Hybrid Digital-Analog Mapping and Power Allocation

To make full use of the channel resource, signal coding rates of the digital and analog parts are designed to be the same and equal to the channel bandwidth. Then, the transmitted HDA signal $x$ is

Fig. 2

Mapping of digital signals and analog signals to I/Q components of hybrid signals.

Once the received digital stream can be decoded, if the power allocated to the digital signals $P_d$ is still increased, performance of the digital coding does not improve synchronously any longer. Therefore, $P_d$ should be the power that can just support digital signal being decoded accurately under all the channel conditions. Assuming that the whole sending power is $P$, the power allocated to the analog part is $P_a=P-P_d$. Moreover, for the analog signals, the higher the $P_a$, the more analog gains can be obtained and the better the video performance that can be achieved. If we test binary signals coded by convolutional code with BPSK modulation, ${\gamma }_0$, which is the minimum SNR where the decoding BER is smaller than the target BER (it is set to ${10}^{-6}$ in our scheme), can be obtained. Then, for the entire channel SNRs, the following equation should be satisfied

Let $N_m$ be the maximum noise variance and ${\gamma }_m=P/N_m$ be the minimum channel SNR of the receiver group. Then the minimum power allocated to the digital signal is

3.4.

Decoding of Hybrid Digital-Analog Video Multicast

Since $x_d$ and $x_a$ are mutually orthogonal in the hybrid signal, the digital signals and the analog signals will not interfere with each other. Therefore, the decoder can decode the digital signals from the hybrid signal by BPSK demodulator, Viterbi decoder, and H.264/AVC decoder⁷ directly. The analog signals can be obtained by extracting the imaginary part of the hybrid modulation signals, then the residual signals can be decoded by the LLSE decoder.³³ In the end, through superimposing the decoded digital signals and the decoded analog signals, the original video can be acquired. Since the H.264/AVC stream (the digital signals) can be decoded accurately by all the receivers with different channel qualities, the basic video can be obtained by all the receivers. In addition, receivers with different channel qualities can decode different amounts of information from the analog signals and obtain different analog gains. Therefore, receivers with better channels can receive better video, and the video quality is better than that transmitted in the H.264/AVC scheme. Thus, the proposed HDA video multicast scheme can achieve graceful degradation while improving video performance.

4.1.

Relation Between Multicast and Multiple-Input Multiple-Output

The proposed HDA scheme in multicast was designed with single-antenna links oblivious for multicast or broadcast. In fact, OFDM decomposes a wideband channel into a set of mutually orthogonal subcarriers, and the channel gains across these subcarriers are usually different.³⁶ With MIMO, each subcarrier is further divided into a set of spatial subchannels, again with different channel gains. In particular, error behavior differs across subchannels. If a one-size-fits-all code rate is used for a few or all subchannels, it generally needs to be conservative, and hence suboptimal, to accommodate the worst subchannels. Therefore, in this scene, unicast over a MIMO-OFDM link can assemble a multicast channel. With this in mind, we present the proposed HDA in MIMO.

However, there are some differences between unicast over a MIMO-OFDM link and a multicast channel. First, in MIMO-OFDM, a channel-dependent precoding operation is often necessary to make the spatial subchannels on the subcarrier mutually orthogonal so that the signals do not interfere with one another along different subchannels. Second, when some subchannels in MIMO have very poor performance, they can be discarded, and their power needs to be returned to the overall power budget for the other good subchannels. So the proposed HDA in multicast without precoding is not suitable for directly running over MIMO.

In this section, we propose the HDA scheme in MIMO to handle video unicast over a MIMO-OFDM link. The proposed HDA scheme is also applied to video transmission in MIMO, as shown in Fig. 3. Similar to the HDA video multicast scheme, videos are also coded by H.264/AVC first. In contrast, residuals of H.264/AVC in the MIMO system are coded by ParCast, which tailors the video unicast quality to the MIMO-OFDM channel. Compared with SoftCast, ParCast first employs SVD-based precoding to avoid interference between received signals on different subchannels. Then, ParCast allocates the better subchannels to the more important data chunks and discards some bad chunk–subchannel pairs to reallocate more power to the important pairs before power allocation. Moreover, in our proposed HDA scheme in MIMO, new power allocation algorithms are designed for the new case.

Fig. 3

Framework of the proposed hybrid digital-analog video scheme in MIMO.

4.2.

Digital Encoding of Hybrid Digital-Analog in Multiple-Input Multiple-Output

In the digital part, video frames are first encoded by H.264/AVC in groups, and the residuals of each group are sent to the analog encoder. Next, the H.264/AVC bitstream is coded by convolutional code with BPSK, then the modulated bitstream is divided into segments to be sent by multiple antennas. Note that the coding rate, which is decided by the convolutional code and the compression ratio of QP, cannot exceed the bandwidth, and the bitstream should be decoded by the MIMO receiver.

To guarantee that the received digital signals are interfered with by noise uniformly, a power allocation algorithm must be carried out before compounding digital signals and analog signals. Assuming that power allocated to the digital encoder is $P_d$, subchannel gains are $s_i$, $i=\mathrm{1,2},\dots ,N$, where $N$ is the number of subchannels used, and the digital power factor of the $i$’th segment is $g_{d,i}$. Then, to reach equal error protection of the digital signal, Eq. (15) should be satisfied

4.3.

Analog Encoding of Hybrid Digital-Analog in Multiple-Input Multiple-Output

Residuals of H.264/AVC coding are sent to the analog encoder, then divided into chunks and coded by ParCast. Let power allocated to the analog encoder be $P_a$, and the analog power factor of the $i$’th chunk is

After being encoded by ParCast, the analog signal is decomposed into chunks to be transmitted by antennas. Here we call the coded signal $x_a$. With the gains of residuals, performance of H.264/AVC can be improved significantly and graceful degradation can be reached.

4.4.

Hybrid Digital-Analog Mapping and Power Allocation in Multiple-Input Multiple-Output

To make full use of channel bandwidth, the signal coding rates of digital signal segments and those of analog signal chunks are also designed to be the same and equal to the channel bandwidth. Then the coded digital signals and coded analog signals are mapped to the HDA signals by the proposed HDA mapping scheme, as shown in Eq. (5) and Fig. 2. Thus, the digital signal and the analog signal are mutually orthogonal and do not interfere with each other.

Similar to the HDA scheme in multicast, power allocated to the digital signals $P_d$ should be power that can just support the digital stream to be decoded when transmitted over the MIMO channel. The rest of the power is allocated to the analog signals. Let the whole sending power budget be $P=P_a+P_d$.

When the binary signal is tested by convolutional code with BPSK, ${\gamma }_0$, which is the minimum SNR when the decoding BER is smaller than the target BER (it is ${10}^{-6}$ in our scheme), can be calculated. Then, the following equation should be satisfied to guarantee that the digital signal can be decoded when transmitted over the MIMO channel

4.5.

Decoding of Hybrid Digital-Analog in Multiple-Input Multiple-Output

Assume that the MIMO channel state matrix is $\mathbf{H}$ and it is decomposed by SVD, i.e., $\mathbf{H}={\mathbf{U}\mathbf{S}\mathbf{V}}^{\mathrm{H}}$. Then the precoded HDA signals are $\tilde{\mathbf{x}}=\mathbf{Vx}$ and the received HDA signals are

5.1.

Simulation Environment

Test videos: we select a few representative video sequences, including foreman, mobile, news, bus, football, akiyo, tennis, container, and coastguard. They are in .cif format, with a frame size of $352\times 288$ pixels. These videos have different motion characteristics, background textures, and energy distributions. For example, news and akiyo have a smooth background and little motion. They are therefore easily compressed with a conventional video codec. Container has many small moving objects, and there is continuous movement in the whole scene due to camera movement. Foreman contains an active close-up object and panning background. Football and coastguard both include large texture areas and complex motion. Consequently, both are challenging cases for conventional compression systems.

Performance metric: to evaluate the video delivery quality, we use the standard peak signal-to-noise ratio (PSNR) and the structural similarity (SSIM) index as performance metrics.

The PSNR is a standard objective measure of video quality and is defined as a function of the mean squared error (MSE) between all pixels of the decoded video and the original version as follows

Unlike PSNR, the SSIM index is a full reference metric, in other words, the measuring of image quality based on an initial uncompressed or distortion-free image as reference. The SSIM emphasizes that the human visual system (HVS) is highly adapted to extract structural information from visual scenes. Therefore, a measurement of structural similarity (or difference) should provide a good approximation of perceptual image quality. The SSIM index is defined as a product of luminance, contrast, and structural comparison functions, and it is a decimal value between 0 and 1. A value of 0 means zero correlation with the original image, and 1 means the exact same image. Through this index, image and video compression methods can be effectively compared.

Schemes for comparison: we compared the proposed HDA video multicast scheme with three reference schemes, namely H.264/AVC, SoftCast, and WSVC. In our proposed HDA scheme, 3D-DCT is applied to remove space and time correlation of video residuals in one group of pictures (GOP). The GOP size is set to 16 in our simulation. Next, the transformed coefficients of residuals are divided into $44\times 36$ chunks to be encoded by SoftCast. In addition, the hybrid signal is transmitted with a constant power budget $P$. ${\gamma }_0$ of different convolutional code rates has been tested as the prior information, as shown in Table 1.

Table 1

γ0 of different FEC code rate.

In the WSVC scheme,²⁰ the parameter settings are mostly similar to the proposed HDA scheme; only the QPs and FEC code rates, which are decided by the channel bandwidth and channel quality, are different. What’s more, performances of the 3D-DCT SoftCast scheme²³ and the traditional H.264/AVC digital video scheme are also introduced. Except for the WSVC scheme, hybrid signals are transmitted with the same channel bandwidth and the signal coding rate that equals the bandwidth. On the other hand, analog signals are divided into two parts and only the low-frequency layer of DWT coefficients is coded by H.264/AVC in WSVC,⁴ and bandwidth used in WSVC is just half of the bandwidth used in other schemes. Thus, WSVC schemes with bandwidth equal to that of other schemes is also simulated and the signal data are repeated in this simulation with the same power budget $P$.

5.2.

Parameter Analysis

In this subsection, we set different parameters in our proposed HDA scheme and analyze their roles. Since results for all tested video sequences exhibit similar trends, only the performances of foreman are shown in this subsection.

Figure 4 shows the PSNR performances of our scheme when processed at different convolutional code rates and different QPs. It is obvious that the performance of our scheme is much better than that of the pure H.264/AVC scheme when coded at the same digital coding environments, i.e., the same digital coding system and the same digital coding parameters. When the convolutional code rate is 1/4, the corresponding ${\gamma }_0$ is 1 dB and the corresponding QP is 34. Then, the curve “H.264/AVC, $\mathrm{QP}=34$” shows the performance of the conventional video multicast scheme, and it equals the case of our scheme when ${\gamma }_0={\gamma }_m=1\mathrm{dB}$.

Fig. 4

PSNR of “foreman_cif.yuv” at different parameters and different schemes, where (1/4,1,4) refers to (FEC code rate, ${\gamma }_0$,${\gamma }_m$), the “H.264/AVC, $\mathrm{QP}=34$” is coded by H.264/AVC with 1/4 convolutional code with BPSK and it equals the case “HDA-1/4,1,1.” QPs of HDA schemes are all 34 at $\text{code rate}=1/4$, while QP of HDA scheme is 35 at $\text{code rate}=1/5$.

It also can be seen that the overall performance of our scheme increases with ${\gamma }_m$ when coded at the same convolutional code rate 1/4. However, the cliff points where the digital signals can just be decoded also move with ${\gamma }_m$. Since ${\gamma }_m$ is the minimum SNR of the receiver group, all the receivers of different cases can decode videos with different qualities. Since ${\gamma }_0$ of the FEC code rate 1/4 is 1 dB and ${\gamma }_m\ge {\gamma }_0$, a higher code rate should be adopted when the minimum SNR of the receiver group is smaller than the ${\gamma }_0$ and the code rate is 1/4. For example, when the minimum SNR is 0 dB, the strategy whose code rate is 1/5 and QP is 35 is adopted; then this strategy can cover receivers whose SNRs range from 0 to 14 dB, as shown in Fig. 4. Therefore, when the worst channel SNR is low, a higher coding rate with a larger QP is adoptable. A relatively lower coding rate with a smaller QP can be adopted to improve the basic H.264/AVC digital video quality when the worst channel SNR is high.

The power allocated to the digital signals $P_d$ and the power allocated to the analog signals $P_a$ at different coding parameters and different coding schemes are shown in Fig. 5. Obviously, $P_a$ increases with ${\gamma }_m$ at the same parameters. Therefore, if the cliff point is bigger (i.e., the minimum SNR of all the receivers’ channels is bigger), more power will be allocated to the analog part, the performance gains based on analog signals will be higher, and the entire video performance will be better. Even though video is transmitted at the same FEC code rate (1/4) and the same ${\gamma }_m$ (4 dB), the power allocated to $P_a$ and $P_d$ in the proposed scheme and that in WSVC are not the same. Because the digital signals in WSVC are not only interfered with by the channel noise, but also by the “small” analog signals, more power will be allocated to the digital part to ensure accurate decoding of digital signals. As a result, the analog gains of WSVC are lower than the proposed scheme. It can also be seen that the analog power at ($1/5,-0.5,0$) is less than the analog power when the FEC code rate is 1/4, so the analog gains are much lower.

Fig. 5

Power allocated to digital part and analog part. Parameter refers to (FEC code rate,${\gamma }_0$, ${\gamma }_m$).

5.3.

Simulation Results

Figure 6 shows performance of the proposed scheme when compared with other schemes. Assuming that SNRs of the receiver group range from 4 to 14 dB, parameters (1/4,1 dB,4 dB) can be adopted to cover all the receivers. Suitable QPs should be adopted first, as shown in Table 2.

Fig. 6

PSNR comparison in multicast: (a) football, (b) coastguard, (c) foreman, (d) container, (e) news, (f) akiyo.

Table 2

Parameters when processing different sequences.

As shown in Fig. 6, WSVC is about 3 to 8 dB better than SoftCast. PSNRs of our scheme are about 1 to 5 dB higher than WSVC. Since only the low-frequency layers of DWT coefficients in WSVC are encoded by H.264/AVC, PSNR performance of WSVC may be worse than the pure H.264/AVC digital transmission scheme with the same QP at some bad channels. Power allocation of the proposed HDA multicast scheme depends on ${\gamma }_m$ and ${\gamma }_0$; $P_a$ and $P_d$ of different sequences are the same. However, power allocation of the WSVC scheme is not only based on ${\gamma }_m$ and ${\gamma }_0$, but also on variances of all the chunks. So power allocations of WSVC schemes change with parameters. Though quantization PSNRs (QPSNRs) of the proposed scheme are smaller than those of the WSVC scheme, the proposed HDA scheme still outperforms the WSVC scheme owing to the analog gains.

To certify the performance of the HDA scheme, Fig. 7 depicts the SSIM values for the tested video sequences. It can be seen that for different SNRs, the proposed HDA scheme outperforms the WSVC and SoftCast since it achieves better visual quality. The visual quality comparison is given in Fig. 8. The channel SNR is set to be 4 dB. For all schemes, the PSNRs and SSIMs are above 30 dB and 0.8, respectively; therefore, the figures are reconstructed well. However, there is still slight visual improvement in our scheme.

Fig. 7

SSIM comparison in multicast: (a) football, (b) coastguard, (c) container, (d) news.

Fig. 8

Visual quality comparison; SNR is 4 dB. The columns from left to right: the original frame, SoftCast, WSVC, and the proposed HDA scheme: (a) PSNR, SSIM, (b) 32.5 dB, 0.84, (c) 37.2 dB, 0.92, (d) 41.2 dB, 0.96, (e) PSNR, SSIM, (f) 32.9 dB, 0.92, (g) 34.2 dB, 0.92, (h) 36.1 dB, 0.95.

6.1.

Simulation Environment

The test videos are shown in Sec. 5.1. The GOP size is set to 16 in our simulation. We assume there is a $64\times 64$ MIMO channel system²⁶ whose channel matrix $\mathbf{H}$ is a Gaussian complex matrix with zero mean and unit variance in each row. We also assume that the channel estimation is perfect; then the matrix is divided into 64 subchannels by SVD. In our simulation, compression ratios of different QPs and BERs of different FEC code rates (i.e., convolutional code rates in our scheme) have been tested as the prior information. Signal coding rates of each chunk are designed to be the same and equal to the bandwidth.

We compared the proposed HDA video multicast scheme with the reference schemes, namely ParCast²⁶ and ParCast+.³⁵ Our proposed HDA scheme is first coded by H.264/AVC. The coefficients of residuals are divided into 64 $44\times 36\times 16$ chunks to be encoded by ParCast. Meanwhile, the modulated digital stream is also divided into chunks with $44\times 36\times 16$ values in each chunk. The hybrid signal is transmitted over the MIMO channel with a constant total power budget $P$. In the ParCast scheme, each GOP is processed by 3D-DCT³⁴ first to remove spatial and temporal correlations. However, ParCast+ adopts a motion-aligned 3-D transform to decorrelate the source since simple ParCast and ParCast+ transmission need only half bandwidth when compared with the HDA scheme. To utilize extra bandwidth efficiently and benefit from a subchannel diversity gain, they use only the high-gain subchannels and discard the low-gain subchannels.

6.2.

Parameter Analysis

In this subsection, different parameters of our proposed HDA scheme are set and analyzed. Since results for all tested video sequences exhibit similar trends, only performances of foreman are shown. The target MIMO channel SNR ranges from 1 to 14 dB. The minimum ${\gamma }_m$ is 1 dB. In order to ensure that the BER is smaller than the target BER ${10}^{-6}$, the following equation should be reached

As shown in Table 1, the FEC code rate 1/4 can be adopted. Then QP is set to 37 without going beyond the channel bandwidth. Figure 9 shows the power assigned to the digital part $P_d$ and the power assigned to the analog part $P_a$. It is obvious that $P_a$ increases with SNR (${\gamma }_m=\mathrm{SNR}$), and the analog gains of our scheme improve accordingly. Therefore, in our scheme, when the SNR increases, the overall performance is improved by increasing ${\gamma }_m$ rather than changing the FEC code rate. In addition, the performance increases gracefully while it is jumpy in traditional digital transmission schemes. Since $P_a$ is less than 10% of $P$ when $\mathrm{SNR}=1\mathrm{dB}$, the analog gain is much smaller than that of other cases when ${\gamma }_m$ is big, and the overall PSNR performance at $\mathrm{SNR}=1\mathrm{dB}$ does not outperform the traditional digital transmission scheme significantly.

Fig. 9

Power allocated to digital part and analog part. The code rate is 1/4, QP is 37, ${\gamma }_0$ is 1 dB, and ${\gamma }_m$ is set to be the same as SNR.

As shown in Table 3, even the QPSNR of H.264/AVC decreases with QP, and the degradation is very small. What’s more, a large QP results in a high-compression ratio of H.264/AVC, and more low-gain subchannels are discarded for digital transmission. Therefore, performance can be improved by increasing QP properly, as shown in Fig. 10. When we change QP from 37 to 38, the parameter $\mathfrak{R}$ decreases very quickly since there are four bad subchannels that are discarded. Then, power allocated to the analog signal increases from 5.7% to 30.68%, and the overall performance increases about 1 dB even though there is a 0.7-dB degradation in quantization. However, when we increase QP continuously, the analog gains no longer increase quickly, while the QPSNR degrades continuously. The result is that the overall PSNR performance no longer increases with QP.

Table 3

Parameters as QP changes at SNR=1  dB.

Fig. 10

PSNR of “foreman_cif.yuv” at different QPs. The FEC code rate is 1/4, ${\gamma }_0$ is 1 dB, and ${\gamma }_m$ is set to be the same as SNR.

As shown in Table 4, even though $P_a$ increases with QP, the PSNR performance decreases slightly at $\mathrm{SNR}=5\mathrm{dB}$. In conclusion, when $P_a$ is very small, the PSNR performance can be improved by increasing QP slightly (increasing $P_a$ to be more than 30%; meanwhile, the degradation of QSNR is small).

Table 4

Parameters as QP changes at SNR=5  dB.

6.3.

Simulation Results

In this subsection, we compare our proposed scheme with the reference schemes. First, the relationship between our proposed scheme H.264/AVC is illustrated. As shown in Fig. 11, if we allocate all the power $P$ to the digital part in our HDA scheme, then the progress degenerates into H.264/AVC video transmission in the designed MIMO system and the PSNR is about 33.3 dB. In most cases, the analog data in our scheme should be transmitted to improve the overall performance. Since the ParCast scheme with half bandwidth needs to employ all the subchannels, while the ParCast scheme with full bandwidth can just employ the half higher-gain subchannels, the “ParCast-full” curve outperforms the “ParCast-half” curve.²⁶ As shown in Fig. 11, performance of the proposed HDA scheme is much better than that of the pure ParCast and ParCast+ schemes in MIMO channel systems. What’s more, the proposed scheme can also overcome the cliff effect completely, and the PSNR performance increases with the channel quality.

Fig. 11

PSNR of “foreman_cif.yuv” at different schemes. The red curve is the PSNR curve of the proposed scheme with $\mathrm{QP}=37$. “ParCast-half” is the analog curve with half bandwidth, and “ParCast-full” is the analog curve with bandwidth equal to that of our scheme.

Apart from the foreman, the other CIF video sequences mentioned above are also processed to certify performance of the proposed HDA scheme. Suitable QPs should be adopted, as shown in Table 5. As shown in Fig. 12, our scheme performs about 7 dB better than the pure ParCast scheme.

Table 5

Parameters when processing different sequences.

Fig. 12

PSNR comparison in MIMO: (a) akiyo, (b) coastguard, (c) football.