On September 10, 1996, Rockwell Semiconductor Syst Essay Example

filters which result in a significant decrease in high-frequency sounds by at least 35 dB at 4kHz.

[Back to top of page]QAM operates by adjusting both the amplitude and phase of a carrier sine wave signal. Each combination of amplitude and phase is called a "symbol." Symbols are information-carrying tokens sent from the transmitter to the receiver. In the past, these tokens were referred to as "baud" in honor of Emile Baudot, who created a 5-bit code for representing the alphabet in 1875. Each 5-bit token represented a letter or control code.

However, the term "baud" became misused to mean bits per second, causing confusion. Originally, a baud represented one bit when modems were introduced. As a result, 300 bits per second modems became known as 300 baud modems in technical jargon. The problem arose when multiple bits started being carried by one baud but still referred to as bits per second, frustrating modem designers.

To avoid this confusion, experts began using the term "symbol." When you modulate a sine wave, the resulting signal is no longer just one frequency sine wave; it has frequencies related to the modulated carrier signal. In QAM signals with modulation, bandwidth equals symbol rate. For instance, if 2400 symbols are sent per second, the modem signal's bandwidth will be 2400 Hz.

The V.32 modulation utilizes a carrier frequency of 1800 Hz and symbol rate of 2400 symbols per second resulting in bandwidth ranging from 600 Hz to 3000 Hz.As time passed, modem designers recognized the improvement in the telephone network and the availability of more bandwidth. This led to the development of newer modem modulations that took advantage of these wider channels. The

highest V.34 rate, for example, utilizes a carrier frequency of 1959 Hz and a symbol rate of 3429 symbols per second, creating a bandwidth ranging from approximately 244 Hz to 3674 Hz.

QAM modulation incorporates both amplitude and phase to transmit a signal, which can be visualized through vectors. Modem designers use vectors to represent the symbols being sent. For instance, Figure 2 illustrates a graph depicting a single symbol's amplitude and phase. However, when representing numerous symbols, the graph can become overcrowded and some symbols may have similar phase angles but different amplitudes. This overlap makes it challenging to differentiate between vectors with smaller amplitudes.

To address this issue, modem designers only plot dots at the endpoints of the vectors instead of representing all symbols individually. When multiple symbols are plotted on a graph in this manner, it forms a shape referred to as a "constellation," resembling a star map. Figure 3 showcases an example of such a simple constellation composed of four symbols.

This figure also demonstrates the concept of decision regions pertaining to symbol transmission from transmitter to receiver. Despite accurate transmission from the transmitter, the symbol can be altered by factors within the transmission channel, resulting in receipt of a different symbol altogether.The "error vector," which is the difference between transmitted and received symbols, can be caused by noise during symbol transmission. This can result in changes in amplitude and movement of the constellation point. However, if the received constellation point falls within the decision region, it will be considered as the correct symbol and its corresponding bits will be communicated. The size of the decision region decreases as more symbol points are used

by the modem, leading to a higher error rate in the presence of noise. Therefore, simply increasing the number of symbols does not necessarily guarantee a higher data rate, since there comes a point where data communication becomes impossible at an acceptable error rate. This is why V.34 modems rarely connect at 33.6 Kbps.

To achieve a 33.6 Kbps data rate with V.34, a large number of symbol points (1,664 symbols with 10.7 bits per symbol) must be utilized by the modem. However, due to limited transmit power, it is not possible to have an excessively large constellation size. Consequently, the symbol points need to be very close together which makes accurate distinction between symbols challenging for the receiver. As a result, the modem has to downgrade to a constellation with fewer symbol points.

Apart from transmit power limitations and proximity challenges with symbol points, other factors like available bandwidth also restrict operation at higher rates; however noise including Gaussian and quantization noise also plays a significant role in this process.

Figure 3 visually represents a four-point constellation showing assigned values for each symbol along with receiver decision region.
Throughout the years, modem designers have ingeniously utilized the error vector in various ways. One such application is transmitting a low bit rate control channel. The goal is to establish a 100 bit per second control channel between two modems for transmitting diagnostic information.

To achieve this, the error vector can be used as follows:
1. Choose a symbol from the most resilient part of the constellation to minimize noise interference.
2. Define perturbations of this chosen symbol to represent bits within the control channel.
3. For example, if the symbol is perturbed

leftwards, it represents a "1" in the control channel. If it's perturbed rightwards, it signifies a "0".
4. To compensate for noise-induced perturbations, send each bit multiple times over several symbol instances.
5. Use a voting technique if there are discrepancies due to noise-induced perturbations during transmission.
6. Alternatively, employ a Viterbi decoder that retains and aggregates actual error vectors over three transmissions for more efficiency.Mathematically, it can be shown that this technique surpasses a basic voting scheme where a decision is made for each error vector prior to applying voting. The real bit rate of the control channel depends on the symbol transmission frequency, which relies on the incoming bit pattern. Maintaining an average bit rate in the control channel is straightforward due to scrambler application to the incoming bits resulting in a pseudo-random transmitted bit pattern. Gordon Bremer from AT&T Paradyne developed a method where voice samples can be represented by this error vector, allowing simultaneous voice and data transmission in the analog domain. This technique has been standardized as V.61 by ITU.

To determine the number of constellation points needed for a 9600 bps operation with a 2400 symbol rate, we can substitute these values into Equation 2 (2bps/Rs = Ns).The calculation is as follows: Ns = 2bps/Rs = 29600/2400 = 24 = 16. Therefore, only a 16 point constellation is needed for operation at 9600 bps. Achieving 9600 bps operation was challenging in the past, but it may seem trivial by today's standards. The V.32 standard introduced echo cancellation, which was a computationally intensive technique. During that time, trellis codes were also developed by Gottfried Ungerboeck at IBM's Zurich Research Laboratory. Trellis codes are difficult

to explain intuitively, but in Figure 2 you can see how the decision region encompasses the transmitted symbol point. As more points are defined, the decision region becomes smaller and this can lead to incorrect decoding due to noise. To address this issue, subset constellations can be created by removing half or more of the points to increase the decision region around each remaining point. This allows for more accurate decoding even in the presence of noise, similar to trellis codes conceptually speaking.
Each symbol point represents a unique string of bits and if the receiver knows the constellation being used, it can decode the sent symbol more effectively.However, informing the receiver about which subset constellation to use presents a challenge.This challenge is resolved by allowing specific transitions from one state to another in the receiver through restricting valid transitions using an extra bit per symbol within a convolutional encoder.The receiver decodes symbols assuming a single constellation and analyzes the sequence of state transitions by tracing back. If there is an invalid state transition, the receiver will backtrack and analyze the error vectors for the symbols. It will employ Viterbi decoding to calculate the distance between the received symbol point and valid symbol points. Then, it will choose the closest valid symbol point that creates a legal sequence of state transitions. However, this requires an additional bit per symbol (for two-dimensional codes) or every two symbols (for four-dimensional codes). Adding an extra bit per symbol results in doubling the number of symbols and sacrificing 3 dB of signal-to-noise ratio (SNR) performance. Nevertheless, trellis code offers a coding gain of about 6 dB, leading to approximately 3

dB better SNR performance.

In today's digital telephone network, analog phone calls are transmitted digitally at a rate of 64 Kbps. Despite this, studies on DSL technology reveal that copper wires can handle speeds of 1.5 Mbps or higher. So why are we limited to achieving only 33.6 Kbps (V.34)? The answer lies in quantization "noise" and Shannon's Theorem published in 1948Quantization noise, also known as quantization error, occurs when an analog signal from a modem needs to be converted into digital format at the edge of the network. This conversion involves sampling the analog signal at regular intervals. However, there is an issue because while the analog signal can have any value, the digital value assigned to it can only take discrete values. The difference between the actual analog signal level and its assigned digital value is called quantization error or quantization noise. This term refers to a situation where noise causes the signal to jump to the quantization value. Figure 4 illustrates this process of quantizing an analog signal with its accompanying quantization error.

Shannon's influential paper established that there exists a limit on how much information can be transmitted over a channel in the presence of noise. Over time, his equation has proven accurate and reliable. The equation is as follows: bps = BW log2 (1+ P/N), where bps represents bits per second, BW denotes channel bandwidth, and P/N indicates the ratio of signal power to noise power. It should be noted that this power ratio is expressed as an actual ratio and not in decibels (dB). In accordance with the codec used, the telephone network in the United States has a noise floor

of 39.5 dB.Most network codecs have a noise floor of 35 to 36 dB, which falls short of the requirement in Shannon's theorem. To account for this, we modify the equation using dB. The unit for logarithmic power ratio is called the Bell (log10 P/N), named after Alexander Graham Bell. The abbreviation "dB" represents decibel (10 log10 P/N) and symbolizes Bell's name.

To substitute into Shannon's theorem, we solve the dB equation for P/N: dB = 10 log10 P/N. This leads to bps = BW log2 (1+ P/N) when substituted.

Assuming a channel bandwidth of 3000 Hz and a quantization noise floor of 35 dB, the equation becomes bps = 3000 log2 (1+ 1035/10) = 34,822. Thus, achieving data rates above 35 Kbps with ordinary modem techniques is impossible due to the codec's quantization noise floor.

However, if we can eliminate the quantization noise floor, higher data rates become achievable. For operation at 56Kbps, pulse amplitude modulation (PAM) replaces QAM while still applying the aforementioned concepts.The network diagram for 56Kbps operation assumes a fully digital network with a clear 64Kbps transmission between the Internet Service Provider and the subscriber's line card. This constraint will be relaxed in the future, but it helps simplify the explanation of the 56Kbps technique. Figure 5 illustrates the all-digital network, showing the digital connection of the service provider. Upon closer examination, the line card consists of a codec and a low pass filter positioned between the codec and the copper line. Similarly, the client modem includes a linear codec and a low pass filter. However, since the modem is provided to the customer, both the accuracy of the codec and filter characteristics can

be optimized for its operation. Please refer to Figure 6 for a schematic diagram depicting all components along from path from line card to customer's modem. It's important to note that only in downstream direction - from line card to customer's modem - is PAM technique used. In contrast, traditional QAM techniques are employed in upstream direction - from customer's modem to network. The ISP modem transmits eight-bit values to line card, which then generates specific voltage lasting 125 microseconds for each eight-bit value.When the values obtained from sampling an analog signal represent quantization values, they create a sequential series of voltage steps in the output that align with the original waveform. These voltage steps are then passed through a low pass filter to eliminate high frequency components, resulting in smoother voltage steps resembling the original analog signal.

In the case of PAM (Pulse Amplitude Modulation), the eight bit values sent by the ISP modem no longer represent samples of an analog signal but instead symbolize data. The network's codec has the capability to generate 255 different voltage levels, and at a sampling rate of 8,000 samples per second, 8,000 of these voltage levels are generated every second.

To achieve a transmission rate of 56,000 bits per second (bps), we need to determine how many quantization points are required using equation 2: Ns = 2bps/Rs (Equation 2). By applying this equation, we find that Ns is equal to 27 as calculated from Ns = 256,000/8,000. However, for transmitting at a rate of 56,000 bps, only 128 out of the total 255 quantization levels need to be used. This technique is known as a "128 PAM" technique.

In cases

where achieving a data rate of exactly 56,000 bps is not feasible due to limitations or constraints, a smaller number of quantization levels is utilized. For example, at a data rate of 48,000 bps only requires utilizing 64 quantization levels.

Data rates between integer powers can be achieved by employing fractional bit rates which allow for implementation of virtually any desired data rate. Determining appropriate data rate steps should consider expected line impairment steps and factors influencing transmission quality.Rockwell has established data rate steps of 2,000 bits for its K56flex technology, while traditional modems have established 2,400 bit steps. PAM (Pulse Amplitude Modulation) has been a well-understood technique for a long time. For example, ISDN BRI uses a technique called 2B1Q, which is essentially a four level PAM. T1 lines use alternate mark inversion (AMI), which is a type of PAM. Therefore, the technique used for 56Kbps modems is not new but its application to consumer modems is new.

The codec outputs a fixed voltage level for 125 microseconds (sampling rate of 8,000 times per second), represented in Figure 7 as a PAM pulse of duration T (125 microseconds). As this pulse passes through the low pass filter (part of the codec) between the codec and the copper line, only the lower frequencies remain due to the filtering out of higher frequencies. The low pass filter in the line card has a roll-off starting at -3 dB at 3400 hz and reaching at least -14 dB at 4,000 hz. This causes the pulse to adopt a characteristic shape, as crudely represented in Figure 8 which illustrates the pulse response of a band-limited channel incorporating a low-pass filter.

This represents the actual signal transmitted through the copper wire after passing through said filter.

Returning to the top of the page: The crucial aspect is that subsequent pulses are sampled while crossing axis during sample time from initial pulse.Failure to meet this requirement leads to a problem called intersymbol interference. In actuality, the signal on the line is a combination of the two signals displayed (typically, it is the sum of the actual transmitted signals). However, what frequencies will actually exist on the copper wire? According to Nyquist, we must sample at a rate that is at least double the bandwidth of the desired signal for accurate reproduction. Nyquist's theorem also applies in reverse - given a sampling rate, it is impossible to generate a signal with a frequency greater than half of the sampling rate. With a sampling rate of 8,000 times per second, the maximum frequency of the resulting signal on the analog line is 4,000 Hz. As a result, Pulse Amplitude Modulation (PAM) proves to be highly efficient in terms of bandwidth usage as it offers a minimum of two symbols per Hz of bandwidth. It should be noted that Quadrature Amplitude Modulation (QAM) only provides one symbol per Hz of bandwidth. This is one reason why faster speeds can be achieved with PAM techniques compared to QAM. Additionally, higher speeds can be attained with PAM due to removing quantization noise from the network codec. The text emphasizes using quantization levels in codecs as voltage levels for symbol representation. The remaining quantization noise exists solely in the customer's modem codec which is linear.The formula for quantization noise in a linear codec is

given as SQR = 1.76 + 6.02n + log10 (A/Amax), where SQR represents the signal to quantization error ratio, n represents the number of bits of sampling accuracy in the codec, and A/Amax denotes the ratio of the signal's voltage level to the maximum voltage level possible.

For signals with full range, each bit of accuracy in the codec corresponds to approximately 6 dB of quantization noise floor. Therefore, a typical 16-bit codec used in modems provides a noise floor of around 98 dB for full range signals. As a result, at such a high noise floor, quantization error becomes an insignificant impairment. However, for 56Kbps operation, other types of impairments become more dominant and limit the data rate on the channel.

This raises the question of how much SNR (Signal-to-Noise Ratio) a 56 Kbps modem requires. To determine this, we can refer back to Shannon's theorem. Let us start with Equation 6, which is a modified version of Shannon's theorem derived by us, where bps represents bits per second and BW represents bandwidth:

"bps = BW log2 (1+ 10dB/10)" (Equation 6)

To solve for SNR dB, we can manipulate Equation 6 as follows:

"bps/BW = log2 (1+ 10dB/10)"
"2 bps/BW = 1+ 10dB/10"
"10dB/10 = 2bps/BW -1"
"dB/10 = log10 (2bps/BW -1)".By substituting the bandwidth value of 3800 Hz (obtained by excluding the frequency band from zero to 200 Hz) into Equation 8, the resulting equation is "dB = 10 log10 (256000/3800 -1)". Simplifying further, we have "dB = 10 log10 (214.74 -1)". Therefore, in order to achieve a transmission rate of 56 Kbps, it is necessary for the signal-to-noise ratio on the line to exceed 45 dB. This level of ratio

can be achieved on real lines. However, there is a limitation in the United States where the transmit signal must not exceed -12 dBm.

It is important to consider the last term in equation 7 as it reduces the Signal-to-Quantization-Noise Ratio (SQR) of the codec when the received signal falls below its maximum signal (also known as dynamic range). Each decibel sacrificed to dynamic range decreases the noise floor of the codec. If more than approximately 53 dB is sacrificed to dynamic range on a 16-bit codec with a noise floor of 98 dB, achieving a transmission rate of 56 Kbps becomes impossible solely due to the noise floor of the codec in customers' modems.

However, quantization noise is typically not the main issue on the line in reality. Shell mapping techniques are used to comply with US FCC's transmit power limit and restricts usage of outermost quantization points. Nonetheless, shell mapping increases the number of quantization points required for operation at 56 Kbps to about144, which further reduces decision region size.

The problem of low received signal represents just one among several issues encountered in network operations.There are several issues related to robbed bit signaling and digital pads within the network. Robbed bit signaling is an older technique used on T1 lines for conveying call progress indications like logical dial tone, ring, busy, answer, etc. This technique involves taking the low order bit of every sixth voice sample for call progress.

The problems with 56Kbps technology involve identifying connections that use robbed bit signaling and finding a solution to accommodate it. One potential solution is to utilize two quantization points: one with a zero in the least significant

bit position and another with a one in the same position while keeping the rest of the bits unchanged. This approach allows for indicating one symbol but reduces the number of available quantization points and data rate since two quantization points are used for one symbol. However, this limitation only affects every sixth frame, minimizing its overall impact on the data rate.

During a telephone call, when commanded by the telephone switch, some attenuation is added to decrease feedback and echo. The amount of attenuation can vary from 0 dB (no attenuation) to 3 dB or 6 dB. In most cases, line cards achieve this attenuation in the analog domain by reducing the line's drive. However, newer generation line cards utilize a digital signal processor to achieve attenuation.To simplify attenuation, the signal is converted from m-law to linear form in the network. However, converting it back to m-law introduces challenges. In the analog domain, signal relationships remain intact despite attenuation. But in a digital pad, signals are assigned to the nearest m-law point during conversion, altering their relationship and making decoding harder for the receiver. Some points also fall between two quantization points, creating ambiguity in assigning them as "up" or "down". This adds complexity to decoding at the receiver. Detecting digital pads and accommodating them is similar to robbed bit signaling and poses key issues that Rockwell engineers have developed techniques for. PAM can be used in both upstream and downstream directions but using it in the upstream direction is more challenging.To enable PAM in the upstream direction, the client modem must assess line characteristics and pre-distort PAM signals to match filter characteristics of the

line. Additionally, these signals need to be synchronized with the network clock to ensure they reach codecs' analog to digital converter at the correct time. Overcoming these challenges allows for upstream rates exceeding 28.8 Kbps. However, it is unlikely that upstream rates will ever match downstream rates, resulting in asymmetrical operation remaining typical.

To comprehend how the 56Kbps technique operates, most individuals interested have likely read Rockwell's initial white paper published shortly after announcing this technology. While this paper provided a basic understanding, it lacked specifics about workings and network requirements. This document aims to offer more detailed information.

For those seeking deeper knowledge, reviewing papers submitted to TR30's PCM ad hoc committee is recommended. These papers cover various aspects of the technology separately as the committee works towards a draft recommendation encompassing all aspects of this technology, which should soon be available.

To grasp how the digital telephone network functions, referring to John Bellamy's book titled "Digital Telephony" is advised.The second edition of this book was published by Wiley in 1991. Good luck with your reading! It is also important to note that selecting K56 is the right choice. Using a mathematical technique provides benefits such as coding gain, which allows the modem to function effectively in noisy environments and maintain equal error rates. However, it should be mentioned that actual speeds achieved may vary depending on line conditions. FCC regulations limit speeds in the United States to less than 56 Kbps.