What is walsh Function..??

The firs time I ran across CDMA it seemed unworkable. CDMA stands for code-division multiple access, and the basic technique relies on mathematical oddities called Walsh functions. These are functions that everywhere take either the value 0 or 1 and are essentially pseudo-random codes. But they are very carefully constructed pseudo-random codes. If you encode a data stream (voice) with one Walsh function and process it with another at the receiver you get essentially zero. If you process it with the same Walsh function you recover the original data. This allows everyone to transmit at once using the same frequencies, and only the data stream you are trying to listen to gets through. It is sometimes explained as being like at a nosiy party, and being able to pick out a particular voice by tuning your ear into it.
Years ago I had done some graduate work in mathematics, so I’d actually come across Walsh functions and so the idea of CDMA was very elegant. However, my experience of very elegant ideas is that they get really messy when they meet real-world issues. Force-directed placement, for example, seems an elegant concept but it gets messier once your library cells are not points and once you have to take into account other constraints that aren’t easily represented as springs. So I felt CDMA would turn out to be unworkable in practice. CDMA has its share of complications to the basic elegant underpinning: needing to adjust the transmit power every few milliseconds, needing to cope with multiple reflected, so time-shifted, signals and so on.
At the highest level what is going on is that GSM (and other TDMA/FDMA standards) could get by with very simple software processing since they put a lot of complexity in the air (radio) interface and didn’t make optimal use of bandwidth. CDMA has a very simple radio interface (ignore everyone else) but requires a lot of processing at the receiver to make it work. But Moore’s law means that by the time CDMA was introduced, 100 MIPS digital signal processors were a reality and so it was the way of the future.
Of course, my guess that CDMA was too elegant to be workable was completely wrong. Current and future standards for wireless are largely based on wide-band CDMA, using a lot of computation at the transmitter and, especially, receiver to make sure that bandwidth is used as close to the theoretical maximum as possible.
But before CDMA turned out to be a big success Qualcomm was struggling. In about 1995 VLSI tried to license CDMA to be able to build CDMA chips as well as the GSM chips that they already built. Qualcomm had “unreasonable” terms and were hated in the industry since they charged license fees to people who licensed their software, people who built phones (even if all the CDMA was in chips purchased from Qualcomm themselves) and people who built chips (even if they only sold them to people who already had a Qualcomm phone license). They were hated by everyone. Now that’s differentiation. The royalty rates were too high for us and we ended up walking from the deal.
I was in Israel 2 days from the end of a quarter when I got a call from Qualcomm. They wanted to do a deal. But only if all royalties were non-refundably pre-paid up front in a way they could recognize that quarter. Sounds like an EDA license deal! We managed to do a deal on very favorable terms (I stayed up all night two nights in a row, after a full day’s work, since I was 10 hours different from San Diego, finally falling asleep before we took off from Tel Aviv and having to be awakened after we’d landed in Frankfurt). The license was only about $2M or so in total I think, but that was the relatively tiny amount Qualcomm needed to avoid having a quarterly loss and impacting their stock price and so their ability to raise the funds that they would need to make CDMA a reality. Which they proceeded to do.

Why is it used in GSM..??

A method for improving the bandwidth of wireless CDMA systems by using a pseudo-randomly shuffled Walsh-Hadamard code is described. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present invention. It will be obvious, however, to one skilled in the art that the present invention may be practiced without these specific details. In other instances, well-known structures and devices are shown in block diagram form in order to avoid obscuring the present invention.

In contrast to Frequency Division Multiple Access (FDMA), which allocates the frequency band into a number of frequency slots, or Time Division Multiple Access (TDMA), which allocates the frequency band into predefined intervals of time in which users are allowed to use, Code Division Multiple Access (CDMA) gives the right to use the frequency band to all users simultaneously all the time. This is enabled by using a technique known as "spread spectrum." Each user is assigned a code which spreads its signal bandwidth in such a way that only the same code can recover it at the receiver end. This technique has the property that the unwanted signals with different codes appear to be "noise" to the receiver. Basically, spread spectrum is a means of transmission whereby the data occupies a larger bandwidth than necessary. Bandwidth spreading is accomplished before the transmission through the use of a code which is independent of the transmitted data. The same code is then used to demodulate the data at the receiving end. As such, spread spectrum modulations is ideal for use in dense, urban areas where there is a great amount of interference.

FIG. 1 shows a prior art CDMA base station system using Walsh functions and a separate pseudo-random code. User signals (e.g., digitized voice signals or digital packetized data) are first modulated by a Walsh function. As stated above, one advantage of CDMA for personal communication services is its ability to accommodate many users on the same frequency at the same time. This is accomplished by assigning a specific code to each user. Only that particular code can demodulate the transmitted signal for that particular user. More specifically, each user is assigned an orthogonal code. Since the codes are orthogonal, users with different codes do not interfere with each other. One important set of orthogonal codes is the "Walsh" set. Walsh functions are generated using an iterative process of constructing a "Hadamard" matrix. Starting with H1=[0], the Hadamard matrix is built by: ##EQU1##

For example, the Walsh codes of lengths two and four are shown respectively as: ##EQU2##

From the corresponding matrices shown above, the Walsh codewords are given by the rows. These Walsh codes are important because they form the basis for orthogonal codes with different spreading factors. This property is useful when signals with different spreading factors share the same frequency channel. The period of time needed to transmit a single modulation symbol is called a Walsh symbol interval and is equal to 1/4800 second (i.e., 208.33 μs). The period of time associated with 1/64 of the modulation symbol is referred to as a Walsh "chip" and is equal to 1/307,200 (i.e., 3.255)

For the forward channel, the Walsh functions are used to eliminate multiple access interference among users in the same cell. This can be achieved due to the orthogonality of the waveforms. All users within the same cell are synchronized since the waveforms maintain orthogonality if they are aligned in time. Referring to FIG. 1, the input data (e.g., digitized human speech or packetized data) is modulated by one of the orthogonal Walsh functions. Next, the signal is modulated by the pseudo-random number code. A chip rate for running the pseudo-random number is 1.2288 Mega chips per second (Mcps). Finally, all users of that cell are summed and transmitted on the carrier.

FIG. 2 shows a prior art CDMA process in a mobile station. First, the coherent carrier is removed. Next, the signal is demodulated by multiplying it with the synchronized pseudo-random number. This is the same pseudo-random number associated with the base station. Finally, the signal is multiplied by the synchronized Walsh function in order to eliminate interference due to other users' transmission within that cell.

In the prior art, it is widely recognized that the Walsh-Hadamard codes do not exhibit the optimal spreading behavior. These codes do not spread data as well as pseudo-random sequences because their power spectral density is concentrated in a small number of discrete frequencies. As such, the prior art designs have two separate modulation steps. One is used to multiply the input data signal by the Walsh-Hadamard function in order to eliminate interference. And a second, separate multiplication occurs when the signal is modulated by the pseudo-random number generator in order to provide better spectrum spreading. As shown above, the rate by which the signal is modulated by the Walsh/Hadamard function is one-quarter that of the rate by which the signal is modulated by the pseudo-random number (i.e., 307.219kHz versus 1.2288 MHz). The modulation is run at two different rates in order to minimize DC biasing. However, this translates into having a single data bit being transmitted every four chips.

The present invention transmits one data bit per chip. Essentially, this means that the present invention improves the bandwidth by a factor of four. Four times the amount of information can be transmitted as compared with that of the prior art CDMA schemes. The present invention improves the efficiency of CDMA systems by 400 percent. The method by which this improvement is accomplished entails generating a Walsh/Hadamard function and scrambling its rows. The Walsh/Hadamard function is used to eliminate interference between users on the same cell according its physical properties as described above. However, by scrambling the rows, the spectral density is spread out. The signal is thereby maximally spread out. By scrambling the rows, one can achieve the same effect as was achieved in the prior art of modulating the signal with a pseudo-random number. The scrambled Walsh/Hadamard function achieves both objectives in a single modulation step. Thus, by using the present invention, one bit of user information can be transmitted per chip.

FIG. 3 shows the currently preferred embodiment of a coding scheme for a CDMA transmitter according to the present invention. A memory chip contains a lookup table 302. The lookup table comprises a pre-generated set of codes. These codes correspond to a Walsh/Hadamard function with pseudo-randomly scrambled rows. In the currently preferred embodiment, rather than storing a 2^N by 2^N scrambled Hadamard function, a more efficient code is stored by using lossless compression. It has been recognized that one property of a Hadamard matrix is that each column is the XOR of the power-of-two numbered columns with a corresponding set bit in the selected channel code number. Thereby, one can compress the Hadamard matrix by storing only the power-of-two numbered columns. In other words, the pseudo-randomly shuffled Hadamard matrix can be compressed and stored as an N by 2^N matrix. To recover all desired columns of the original matrix, one can XOR together the columns corresponding to the bits set to "1" in the desired column number. Then, constructively take the output of the table, bit-wise AND the table output with the channel select code (both N bits) and XOR the resulting N bits together. User data, such as digitized speech or packetized data, is input to multiplier 303. The user data is modulated by multiplying the user data with one of the codes contained within the lookup table 302 by multiplier 303. The resulting signal is then transmitted on a carrier 304 by means of an RF transmitter. A counter 301 is used as a pointer into the lookup table, which enables multiple users to transmit on the same cell. In the currently preferred embodiment, the modulation occurs at 1.2288 Mega chips per second with one data bit being transmitted per chip.

FIG. 4 shows the currently preferred embodiment of a de-coding scheme for a CDMA receiver according to the present invention. First, the carrier is removed from the received signal by multiplier 401. Next, multiplier 402 is used to demodulate the received signal according to matching code stored in lookup table 403. A memory chip (DRAM, SRAM, FLASH, ROM, etc.) contains the same lookup table as that of the transmitting CDMA system. In other words, the lookup table has the identical Walsh/Hadamard codes with its rows scrambled same as that of the corresponding transmitter. The contents of lookup table 403 of the receiver shown in FIG. 4 is exactly the same as the contents of the lookup table 302 of the transmitter shown in FIG. 3. A counter 404 is used as a pointer to the code which is to be used in lookup table 403. The two counters (i.e., counter 301 in the transmitter and counter 404 of the receiver) are synchronized in time. This synchronization maintains orthogonalty and enables the receiver to correlate the Walsh/Hadamard codes. The synchronization is achieved by transmitting a pilot signal to enable the receiver to recover synchronization, or by other methods (e.g., servoing to correlation peaks in the coded data stream).

As stated above, the present invention entails scrambling the rows of the traditional Walsh/Hadamard function. More specifically, the rows are shuffled by a random integer sequence. The resulting codes are unique in that the same codes are not used twice. These codes are then stored in the lookup table. In the currently preferred embodiment, the lookup table is 14×16 k size (i.e., fourteen bits by 16 k). An exemplary set of compressed Walsh/Hadamard codes with randomized codes is shown in Appendix A. Note that the compressed codes of the 14 bits by 16 k words has the least significant seven bits repeated in the two 8 k halves of the table (but still requires each 14 bit number to appear once only). Furthermore, in one embodiment, the present invention can readily be adapted to work on traditional wireless CDMA handsets. An exemplary 8 bit by 256 word compressed pseudo-randomly shuffled Hadamard matrix which can be used for traditional CDMA applications is shown in Appendix B.

There are several advantages by implementing the randomized Walsh/Hadamard function. Namely, one can obtain four times the number of codes in the same bandwidth as compared with that of the prior art. By aggregating multiple channels coded with each of the orthogonal codes, the data rates can be effectively increased by a factor of four. Furthermore, making better use of the air waves translates into lower costs. In addition, the present invention is primarily DC free (although this is not strictly necessary).
This eliminates problems associated with DC biasing. Another advantage of the present invention is that the rows can be shuffled such that the signal spectrum is maximally spread so as to not violate FCC regulation. Maximally spreading the signal across all bands (120 kHz) means that one can broadcast with a higher overall power output. This results in greater reliability, further range, improved signal-to-noise ratio, and better signal quality.

It should be noted that the present invention can be applied to any modulation scheme, either wireless or hard-wired, which utilizes a spread-spectrum technique. In particular, the present invention can be applied to CDMA cellular handsets as well as other wireless mobile CDMA devices or appliances. Current cell phones can be modified to use the present invention with minimal cost to achieve a huge performance gain. Moreover, the present invention can be expeditiously applied to peer-to-peer wireless applications. Furthermore, although the description set forth above is directed to a Walsh/Hadamard function, the present invention can use any orthogonal function and is not limited to Walsh/Hadamard.

FIG. 5 is a flowchart describing the steps for the improved coding scheme as applied to a CDMA system according to the present invention. Initially, an orthogonal function is used, step 501. Each user is assigned to a unique code. This is done so that the resulting orthogonal waveforms of the different users do not interfere with one another. In the currently preferred embodiment, a Hadamard function is used. The Hadamard function is a Walsh function which contains one row of all 0's, with the remaining rows each having an equal number of 1's and 0's. The rows of this Hadamard function are then shuffled in a pseudo-random manner, step 502. This is done so that the spectral density of the resulting transmitted RF signal is maximally spread across the available spectrum. The codes are then stored in lookup tables, step 503. Each mobile wireless device assigned to a particular cell has a lookup table containing the same set of codes and the base station (if any) also contains the same set of codes for that cell. It should be noted that the codes are pre-computed once and stored in the lookup tables; they need not be regenerated. Furthermore, in the currently preferred embodiment, the lookup tables exist in a compressed form, by taking advantage of the property of Hadamard matrices that each column is the exclusive-or (XOR) of the power-of-two numbered columns with a corresponding set (i.e. to "1") bit in the selected channel code number.

Consequently, for transmissions, the data signal is modulated by one of the codes found in the lookup table, step 504. The modulated signal is then broadcast over the air on a carrier, step 505. The RF signal is received by the intended mobile device, step 506. The carrier is removed, step 507. And the received signal is then demodulated according to a matching code derived from the receiver's lookup table, step 508. The transmitted information can then be extracted, step 509.

In one embodiment of the present invention, the data stream is parallelized by aggregating n number of channels. Aggregation of multiple channels yields greater bandwidth. For example, one can aggregate 32 channels to transmit a 32-bit word; aggregate 64 channels to transmit 64 bits; aggregate 128 channels to transmit 128 bits in parallel, etc. (one channel for each bit). In the currently preferred embodiment, combinations and variations of 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, etc. channels can be aggregated together. By aggregating 16 K or greater number of channels, one can approach transmission of one data bit per chip. Furthermore, ECC bits can be aggregated. The improved efficiencies provided by the shuffled Hadamard function described above grants CDMA designers additional margin to aggregate greater numbers of channels together for improved bandwidth.

Therefore, a method of improving bandwidth of wireless CDMA systems by shuffling the rows of a Walsh/Hadamard function in a pseudo-random manner has been disclosed. It should be noted that although the present invention has been described with reference to wireless and RF technology, the present invention is applicable to wired technologies as well (e.g., cable, transmission lines, etc.).

The foregoing descriptions of specific embodiments of the present invention have been presented for purposes of illustration and description. They are not intended to be exhaustive or to limit the invention to the precise forms disclosed, and obviously many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and its practical application, to thereby enable others skilled in the art to best utilize the invention and various embodiments with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the Claims appended hereto and their equivalents.

01. Explain the wireless LAN architecture and also explain the terms “Infrastructure Mode” and “Adhoc Mode”. [4]

Infrastructure network not only provide access to other networks, but also include forwarding functions, medium access control etc. In Infrastructure Mode, communication take place only between the wireless nodes and the access points, but not directly to the wireless node. The access point does not just control medium access, but also acts as a bridge to other wireless or wired network. In Adhoc Mode, each node can communicate directly with other nodes, so no access point controlling medium access is necessary. Nodes within an Adhoc network can only communicate if they can reach each other physically, i.e., if they are within each other’s radio range. Nodes cannot communicate with each other if they are not within the same radio range. In Adhoc Mode, the complexity of each node is higher as every node has to implement medium access mechanism, mechanism to handle hidden or exposed terminal problems.

02. Write short note on: Bluetooth Protocol Stack [6]

The Bluetooth Protocol Stack can be divided into a Core Specification (Bluetooth, 2001a) and a Profile Specification (Bluetooth, 2001b). Core Specification: Describes the protocol from Physical Layer to Data Link Control Layer. Profile Specification: Describes many protocols needed adopt the wireless Bluetooth Technology to legacy and new applications. Core Specification of Bluetooth:

1. Radio: Specification of air Interface i.e., frequencies, modulation and transmit power.

2. Baseband: Description of connection establishment packet formats, timing and basic Qos parameters.

3. Link Manager Protocol: Link Setup and management between devices including security function.

4. Logical Link Control and Adaptation Protocol: Adaptation of higher layer to baseband.

5. Service Discovery Protocol: Device discovery and querying of service characteristics.

6. Cable Replacement Protocol (RFCOMM): It allows replacement of serial line cables and enables many legacy application and protocol to run.

7. Telephony Control Protocol Specification – (TCSBIN): It describes a bit oriented protocol that defines call controlling signals for the establishment of voice and data calls between Bluetooth devices.

8. Host Controller Interface (HCI): Provides a common interface to the baseband controller and link manager and access to the hardware status and control register.

9. TCP/ IP use Bluetooth Network Encapsulation Protocol (BWEP).

10. OBject EXchange Protocol (OBEX): Calendar and business card can be exchanged using OBEX.

11. Audio: It use baseband layer after encoding audio signal.

03. Explain briefly the types of links available with Bluetooth network. [4]

Bluetooth uses two types of links :

(i) A Synchronous Connection Oriented Link

(ii) An Asynchronous Connectionless Link.

Synchronous Connection Oriented Link (SCO): for this type of link, the master reserves 2 consecutive slots (forward and return slots) at fixe d intervals. A master can support up to 3 simultaneous SCO links to the same slave or to different slaves. A slave supports up to 2 links from different masters and up to 3 links from the same master. Using SCO links, 3 different types of single slot packet can be used. Each SCO link caries voice at 64 kbps and no Forward Error Correction (FEC), 2/3 FEC or 1/3 FEC can be selected. FEC always causes an overhead but avoids re transmission of data with a higher frequency.

Asynchronous Connectionless Link (ACL): in ACL, master uses a polling scheme. A slave may only answer if it has been addressed in the preceding slot. Only 1 ACL link can exist between a master and a slave. For ACL is carrying data 1 - slot, 3 - slot or 5 - slot packets can be used. Data can be protected using 2/3 FEC scheme. Overhead introduced by FEC might be too high. Bluetooth therefore offers a fast Automatic Repeat reQuest or ARQ scheme for reliable transmission.

04. PACS or, Personal Access Communication System:
Fig. Functional Architecture for PACS

In PACS, multiple portable handsets are supported by individual radio ports (RPs) using TDMA with FDD to distinguish between uplink and downlink channel.

RP then subtend on individual radio port control units (RPCUs). The user traffic across the P interface between an RP and an RPCU is separated from the control signals for management of radio functions by using an embedded operation channel (EOC). The RP to RPCU transmission link may take the form of DSL or HDSL. Whereas the P interface for signaling between the RP and RPCU is a provider specific interface, the C interface between the RPCU and the ISDN/ AIN (Advanced Intelligent Network) switch is based on the ISDN basic rate interface (BRI).

RP are mounted on utility poles or building walls, RPCU provide management and control functions for managing radio resources. The access manager (AM), may be integrated with RPCU or operate as a standalone unit, support tasks such as remote database query, assisting in call setup and delivery, automatic link transfer (ALT). The access manager functions may reside in AIN (Advanced Intelligent Network) as a service control point (SCP), an intelligent peripheral (IP) or a switch adjust.

Radio Aspects:

The frame for the PACS radio has duration of 2.5 ms at 400 frames / s. The uplink transmissions from the PACS subscriber unit (SU) utilize TDMA, and the handset receivers operate in the TDM mode for the downlink signaling in PACS supports a system broadcast channel (SBC) they may be deployed by one of the following channel.

— An alternating channel (AC) for alerting SUs to incoming calls.

— A system information channel (SIC) to broadcast system information.

— A priority request channel (PRC) to be used by SUs for emergency call.

The information is carried in the 80 bit fast channel (FC) or 10 bit slow channel (SC).

A time slot in the PACS frame consist of 120 bits with80 bits allocated for the payload (user and signaling traffic) and 40 bits for overhead in downlink and uplink frame.

Downlink:

— Synchronization channel (14 bits) provides synchronization.

— A slow channel (10 bits) used for transporting additional synchronization patterns, errors etc.

— A 15 bit cyclic redundancy check (CRC)

— A power bit for optimizing power output at the subscriber unit.

Uplink:

12 bits are used as guard lines between two consecutive time slots, which are followed by 2 bits priming differential decoder at the radio ports.

The 10 bits SC for slow channel and 80 bits FC used as fast channel and a reserved bit.

Multiple Access with Collision Avoidance for Wireless

Multiple Access with Collision Avoidance for Wireless (MACAW)^[1] is a slotted Medium Access Control (MAC) protocol widely used in Ad-hoc networks^[2]. Furthermore, it is foundation of many other MAC protocols used in Wireless Sensor Networks (WSN)^[2]. The IEEE 802.11 RTS/CTS mechanism is adopted from this protocol ^[3][4]. It uses RTS-CTS-DS-DATA-ACK frame sequence for transferring data, sometimes preceded by an RTS-RRTS frame sequence, in view to provide solution to the hidden terminal problem^[1]. Although protocols based on MACAW, such as S-MAC, use carrier sense in addition to the RTS/CTS mechanism, MACAW does not make use of carrier sense^[1].

Principles of operation

An example to illustrate the principle of MACAW. It is assumed that only adjacent nodes are in transmission range of each other. Assume that node A has data to transfer to node B.

Node A initiates the process by sending a Request to Send frame (RTS) to node B. The destination node (node B) replies with a Clear To Send frame (CTS). After receiving CTS, node A sends data. After successful reception, node B replies with an acknowledgement frame (ACK). If node A has to send more than one data fragment, it has to wait a random time after each successful data transfer and compete with adjacent nodes for the medium using the RTS/CTS mechanism ^[1].

Any node overhearing an RTS frame (for example node F and E in the illustration) refrains from sending anything until a CTS is received, or after waiting a certain time. If the captured RTS is not followed by a CTS, the maximum waiting time is the RTS propagation time and the destination node turn around time.

Any node (node C and node E) overhearing a CTS frame refrains from sending anything for the time until the data frame and ACK should have been received (solving the hidden terminal problem), plus a random time. Both the RTS and CTS frames contain information about the length of the DATA frame. Hence a node uses that information to estimate the time for the data transmission completion ^[1].

Before sending a long DATA frame, node A sends a short Data-Sending frame (DS), which provides information about the length of the DATA frame. Every station that overhears this frame knows that the RTS/CTS exchange was successful. An overhearing station (node F), which might have received RTS and DS but not CTS, defers its transmissions until after the ACK frame should have been received plus a random time ^[1].

To sum up, a successful data transfer (A to B) consists of the following sequence of frames:

“Request To send” frame (RTS) from A to B
“Clear To Send” frame (CTS) from B to A
“Data Sending” frame (DS) from A to B
DATA fragment frame from A to B, and
Acknowledgement frame (ACK) from B to A.

MACAW is a non-persistent slotted protocol, meaning that after the medium has been busy, for example after a CTS message, the station waits a random time after the start of a time slot before sending an RTS. This results in fair access to the medium. If for example node A, B and C have data fragments to send after a busy period, they will have the same chance to access the medium since they are in transmission range of each other.

RRTS

Node D is unaware of the ongoing data transfer between node A and node B. Note D has data to send to node C, which is in the transmission range of node D. D initiates the process by sending an RTS frame to node C. Node C has already deferred its transmission until the completion of the current data transfer between node A and node B (to avoid co-channel interference at node B). Hence, even though it receives RTS from node D, it does not reply back with CTS. Node D assumes that its RTS was not successful because of collision and hence proceeds to backoff (using an exponential backoff algorithm).

If A has multiple data fragments to send, the only instant when node D successfully can initiate a data transfer is during small gaps in between that node A has completed data transfer and completion of node B next CTS (for node A next data transfer request). However, due to the node D backoff time period the probability to capture the medium during this small time interval is not high. To increase the per-node fairness, MACAW introduces a new control message called "Request for Request to Send" (RRTS).

Now, when node C which cannot reply earlier due to on going transmission between node A and node B, sends an RRTS message to node D during next contention period, the recipient of the RRTS (node D) immediately responds with an RTS and the normal message exchange is commenced. Other nodes overhearing an RRTS defer for two time slots, long enough to hear if successful RTS-CTS exchange occurs.

To summarize, a transfer may in this case consist of the following sequence of frames between node D and C:

“Request To send” frame (RTS) from D to C
“Request for Request to send” frame (RRTS) from C to D (after a short delay)
“Request To send” frame (RTS) from D to C
“Clear To Send” frame (CTS) from C to D
“Data Sending” frame (DS) from D to C
DATA fragment frame from D to C, and
Acknowledgement frame (ACK) from C to D.

Unsolved problems

MACAW does not solve the exposed terminal problem. Assume that node G has data to send to node F in our example. Node G has no information about the ongoing data transfer from A to B. It initiates the process by sending an RTS signal to node F. Node F is in the transmission range of node A and cannot hear the RTS from node G, since it is exposed to co-channel interference. Node G assumes that its RTS was not successful because of collision and hence backoff before it tries again. In this case, the solution provided by the RRTS mechanism will not improve the situation much since the DATA frames sent from B are rather long compared to the other frames. The probability that F is exposed to transmission from A is rather high. Node F has no idea about any node interested in initiating data transfer to it, until G happens to transmit an RTS in between transmissions from A.

Furthermore, MACAW might not behave normally in multicasting.

Walsh code:-

The Walsh code is used to uniquely define individual communication channels. Walsh codes are mathematically orthogonal codes. As such, if two Walsh codes are correlated, the result is intelligible only if these two codes are the same. As a result, a Walsh-encoded signal appears as random noise to a CDMA capable mobile terminal, unless that terminal uses the same code as the one used to encode the incoming signal.

The Walsh code is calculated by the Walsh function.
Advantage of public-key cryptography
A commonly cited advantage of public-key cryptography is that, with N users, only N keys are required for any pair of these users to communicate privately, while N(N-1)/2 keys (of the order of N^2) are required without public-key cryptography.
This does point to a real advantage of public-key cryptography, but the statement as commonly encountered needs some amplification to make this clear.
If N people are actively communicating with each other, each one needs to keep on file the keys of the other N-1 people. This is true whether they are agreed-upon secret keys, or public keys. But without the use of public-key methods, each person needs to have keys for communicating with everyone else at the start. With public-key methods, if each site simply has its own key, plus a certificate with which to demonstrate the authenticity of its public key, any two sites can later begin secure communications. If one site acts as a key server, even using conventional secret key methods, each site would only need initially a secret key to communicate with the key server; however, in that case, any two sites not having previously communicated would be dependent on the availability of the server to establish secure communications. It is in this that the advantage of having fewer keys to contend with actually consists.
Note, therefore, that no significant practical disadvantage is incurred if two sites, after establishing communications by public-key methods, generate a conventional key to be used in all future communications, since, unless maintaining a key ring is entirely avoided, and each site obtains the other site's public key for every transmission, a list of sites with their keys is already being maintained. Maintaining such a secret key, in addition to one's own private key, does pose a slight additional security risk, as its compromise allows both, rather than one, side of communications between oneself and other parties to be read.
In principle, the information needed to encrypt something in a public-key system is equivalent to the information needed to decrypt it. Only the relative intractability of the mathematical problem that separates the private key from the public key makes a public-key method secure.
This created understandable nervousness on the part of the British authorities, who feared that a "magic screw" could be uncovered which, once turned, would cause the whole system to fall apart, or, in other words, would vitiate the security of their communications if they were to base them upon a public key method. Also, in the time between the original discovery of those methods and their open discovery, while the microprocessor revolution was in its early stages, the computing equipment required for handling large-number arithmetic would still have been bulky and expensive.

1. Compute two large primes, which are typically named P and Q.

2. Using P and Q, you compute a number N=P×Q, which is called the modulus of the keys being generated.

3. Compute the totient of the modulus. For any integer, I, the totient of I (written φ(I)) is the number of integers smaller than I that are relatively prime to I. Because P and Q are prime, φ(P×Q)=(P-1)×(Q-1). (The totient of P is P-1, because there are P-1 numbers relatively prime to P; the totient of Q is Q-1 for the same reason; and since P and Q are (trivially) relatively prime to each other, the totient of P×Q is (P-1)×(Q-1)).

4. Choose an integer, E, smaller than and relatively prime to φ(N). E is called the public key exponent.

5. Compute an integer D such that D×E=1 mod φ(N). D is called the private key exponent.

The public key is the pair (N, E) of the modulus and the public key exponent; and the private key is the pain (N, D) of the modulus and the private key exponent. So you've got your key pair.

Encryption and decryption are amazingly simple.
Suppose that the ubiquitous Alice and Bob want to communicate. Alice gives Bob her public key, (N, E). Now, when Alice wants to send a message to Bob, she encodes the plaintext of the message as an integer, M. (I'll leave the exact encoding of plaintext open for now.) To encrypt with her private key, (N, D), she takes that integer and computes:

Ciphertext = M^D mod N

Then to decrypt the message, Bob uses his key pair, and computes:

M = Ciphertext^E mod N

For Bob to encrypt a message for Alice, he does exactly the same thing that he did to the ciphertext - except he does it to the encoded message, M. For Alice to decrypt that, she does exactly what she did to encrypt the original M, except that she uses the ciphertext she recieved from Bob instead of the encoded plaintext M. In other words, if you've got a ciphertext message encrypted by the private key, decrypting it is exactly the same process as encrypting a plaintext with the public key, and vice versa. (This point is what used to cause me lots of confusion remembering what was symmetric and what was assymetric - RSA style asymmetric encryption is really very symmetric in how the algorithm works.)
How can this possibly work? On the face of it, it looks ridiculous! You encode by exponentiating once; you decode not by taking a root, but by exponentiating again!
It all comes back to the way the keys were generated. If we look at the process in terms of modulo arithmetic, it's pretty easy to see why it works:

Take an original message, M. Encrypted, it's C = M^D mod N.
Now, take the ciphertext, C, and decrypt it. M' = C^E mod N.
Now, expand C: M' = (M^D mod N)^E mod N.
Now, we can combine the exponents: M' = M^D×E mod N.
D×E = 1 mod N.
By some trickiness, related to the fact that D and E are relative primes related to both each other and N by their relation to the totient of N, we can show that the fact that D×E = 1 mod N means that M' = M^D×E = M¹ = M.

Watch how we can walk through a ridiculously simplified example. Let's start with a pair of primes - 29 and 61.

Generate keys:

First, we compute the modulus: 29×61=1769.
Then we compute the totient: 1680.
Then we choose an E which is relatively prime with 1680. To make things easy, I'll just pick a prime number: E=13.
Now, I need to compute a D, such that D×E=1 mod 1680; or to pull out a bit of standard terminology, D is the modular multiplicative inverse of E mod 1680. Doing that is an exercise in modulo arithmetic which gets beyond the scope of what I want to talk about today, so I'll cheat: whipping out Mathematica, I get D=517.
So, the public key is (1769,13), and the private key is (1769,517).

=================

A pseudo random noise sequence code generating circuit has a sequence generator (11) for sequentially generating a maximum length linear code sequence at an N-chip cycle and a first to (N-1)th vector multiplier (12 to 14) for obtaining values of skipped portions in the sequence generator by vector multiplication. It does so on the basis of the state value (S1) of a register forming the sequence generator, and generates a successive pseudo random noise sequence code based on an output of the sequence generator (PN1) and outputs of the first to the (N-1)th vector multiplier (PN2 to PN4). Thereby, the operating rate can be reduced to 1/N as compound to the prior art, and the operating voltage and electric power consumption can be reduced.

==========

Processing Gain

In spread spectrum, the data is modulated by a spreading signal which uses more bandwidth than the data signal. Since multiplication in the time domain corresponds to convolution in the frequency domain, a narrow band signal multiplied by a wide band signal ends up being wide band. One way of doing this is to use a binary waveform as a spreading function, at a higher rate than the data signal.

Here the three signals corresponds to x(t), c(t) and m(t) discussed above. The first two signals are multiplied together to give the third waveform.
Bits of the spreading signal are called chips. On the above figure, Tb represents the period of one data bit and Tc represents the period of one chip. The chip rate, 1/Tc, is often used to characterize a spread spectrum transmission system.
The Processing Gain or sometimes called the Spreading Factor is defined as the ratio of the information bit duration over the chip duration:
PG = SF = Tb / Tc
Hence, it represents the number of chips contained in one data bit. Higher Processing Gain (PG) means more spreading. High PG also means that more codes can be allocated on the same frequency channel (more on that later).

Pseudo-Noise Sequences

So far we haven't discussed what properties we would want the spreading signal to have. This depends on the type of system we want to implement. Let's first consider a system where we want to use spread spectrum to avoid jamming or narrow band interference.
If we want the signal to overcome narrow band interference, the spreading function needs to behave like noise. Random binary sequences are such functions. They have the following important properties:

Balanced: they have an equal number of 1's and 0's
Single Peak auto-correlation function

In fact, the auto-correlation function of a random binary sequence is a triangular waveform as in the following figure, where T_C is the period of one chip:
In fact, the auto-correlation function of a random binary sequence is a triangular waveform as in the following figure, where T_C is the period of one chip:

Hence the spectral density of such a waveform is a sinc function squared, with first zeros at ± 1/T_C
PN sequences are periodic sequences that have a noise like behavior. They are generated using shift registers, modulo-2 adders (XOR gates) and feedback loops. The following diagram illustrates this:

The maximum length of a PN sequence is determined by the length of the register and the configuration of the feedback network. An N bits register can take up to 2^N different combinations of zeros and ones. Since the feedback network performs linear operations, if all the inputs (i.e. the content of the flip-flops) are zero, the output of the feedback network will also be zero. Therefore, the all zero combination will always give zero output for all subsequent clock cycles, so we do not include it in the sequence. Thus, the maximum length of any PN sequence is 2^N-1 and sequences of that length are called Maximum-Length Sequences or m-sequences. They are useful because longer sequences have better properties (this page explains a little more). Feedback configurations for m-sequences are tabulated and can be found in the literature.
PN sequences are therefore periodic noise like binary functions generated by a network of feedback loops, modulo-2 adders and flip-flops. Maximum length PN functions have a period of 2^N-1.

Multiple-Access

The advantage of CDMA for personal communication services is its ability to accommodate many user on the same frequency at the same time. As we mentioned earlier, a specific code is assigned to each user and only that code can demodulate the transmitted signal.
There are two ways of separating users in CDMA:

Orthogonal Multiple Access
Non-orthogonal Multiple Access or Asynchronous CDMA

Orthogonal Multiple Access

Each user is assigned one or many orthogonal waveform derived from an orthogonal code. Since the waveforms are orthogonal, users with different codes do not interfere with each other. Orthogonal-CDMA or O-CDMA requires synchronization among the users, since the waveforms are orthogonal only if they are aligned in time.
Orthogonal Codes
An important set of orthogonal code is the Walsh set. Walsh functions are generated using an iterative process of constructing a Hadamard matrix. starting with H₁ = [0]. The Hadamard matrix is built by:

For example, here are the Walsh-Hadamard codes of length 2 and 4 respectively:

From the corresponding matrix, the Walsh-Hadamard codewords are given by the rows. Note that we usually map the binary data to polar form so we can use real numbers arithmetic when computing the correlations. So 0's are mapped to 1's and 1's are mapped to -1.
Walsh-Hadamard codes are important because they form the basis for orthogonal codes with different spreading factors. This property becomes useful when we want signals with different Spreading Factors to share the same frequency channel. The codes that posses this property are called Orthogonal Variable Spreading Factor (OVSF) codes. To construct such codes, it is better to use a different approach than matrix manipulation. Using a tree structure allows better visualization of the relation between different code length and orthogonality between them.
For example, let's see if the second codeword of W₂ which we will denote W_2.2 and the third codeword of W₄, W_4.3, are orthogonal. Since they are of different length, we repeat W_2.2 to match the length of W_4.3. Hence we get the following two codewords, in polar form:

W_2.2 => (1 -1 | 1 -1) and W_4.3 => (1 1 -1 -1)

Computing the orthogonality, we get: (multiplying elements by elements)

(1 x 1) + (-1 x 1) + (1 x -1) + (-1 x -1) = 1 - 1 - 1 + 1 = 0

Hence, W_2.2 and W_4.3 are orthogonal.

However, the auto-correlation function of Walsh-Hadamard codewords does not have good characteristics. It can have more than one peak and therefore, it is not possible for the receiver to detect the beginning of the codeword without an external synchronization scheme. The cross-correlation can also be non zero for a number of time shifts and un-synchronized users can interfere with each other. This is why Walsh-Hadamard codes can only be used in synchronous CDMA.
Walsh-Hadamard codes do not have the best spreading behavior. They do not spread data as well as PN sequences does because their power spectral density is concentrated in a small number of discrete frequencies.

Non-Orthogonal CDMA

The concept behind this is to give up orthogonality among users and reduce the interference by using spread spectrum techniques. PN sequences are used to spread the spectrum. The family of PN sequences, called Gold sequences are in particular popular for non-orthogonal CDMA. Gold sequences have only three cross-correlation peaks, which tend to get less important as the length of the code increases. They also have a single auto-correlation peak at zero, just like ordinary PN sequences.
Gold sequences (codes) are constructed from the modulo-2 addition of two maximum length preferred PN sequences. By shifting one of the two PN sequence, we get a different Gold sequence. This property can be use to generate codes which will permit multiple access on the channel.
The use of Gold sequences permits the transmission to be asynchronous. The receiver can synchronize using the auto-correlation property of the Gold sequence.

CDMA Spectrum

CDMA is a form of Direct Sequence Spread Spectrum communications. In general, Spread Spectrum communications is distinguished by three key elements:

The signal occupies a bandwidth much greater than that which is necessary to send the information. This results in many benefits, such as immunity to interference and jamming and multi-user access, which we’ll discuss later on.
The bandwidth is spread by means of a code which is independent of the data. The independence of the code distinguishes this from standard modulation schemes in which the data modulation will always spread the spectrum somewhat.
The receiver synchronizes to the code to recover the data. The use of an independent code and synchronous reception allows multiple users to access the same frequency band at the same time.

In order to protect the signal, the code used is pseudo-random. It appears random, but is actually deterministic, so that the receiver can reconstruct the code for synchronous detection. This pseudo-random code is also called pseudo-noise (PN).

Three Types of Spread Spectrum Communications

There are three ways to spread the bandwidth of the signal:

Frequency hopping. The signal is rapidly switched between different frequencies within the hopping bandwidth pseudo-randomly, and the receiver knows before hand where to find the signal at any given time.
Time hopping. The signal is transmitted in short bursts pseudo-randomly, and the receiver knows beforehand when to expect the burst.
Direct sequence. The digital data is directly coded at a much higher frequency. The code is generated pseudo-randomly, the receiver knows how to generate the same code, and correlates the received signal with that code to extract the data.

Direct Sequence Spread Spectrum

CDMA is a Direct Sequence Spread Spectrum system. The CDMA system works directly on 64 kbit/sec digital signals. These signals can be digitized voice, ISDN channels, modem data, etc.

Signal transmission consists of the following steps:

A pseudo-random code is generated, different for each channel and each successive connection.
The Information data modulates the pseudo-random code (the Information data is “spread”).
The resulting signal modulates a carrier.
The modulated carrier is amplified and broadcast.

Signal reception consists of the following steps:

The carrier is received and amplified.
The received signal is mixed with a local carrier to recover the spread digital signal.
A pseudo-random code is generated, matching the anticipated signal.
The receiver acquires the received code and phase locks its own code to it.
The received signal is correlated with the generated code, extracting the Information data.

Implementing CDMA Technology

CDMA works on Information data from several possible sources, such as digitized voice or ISDN channels. Data rates can vary, here are some examples:

	Data Source	Data Rate
Voice	Pulse Code Modulation (PCM)	64 kBits/sec
	Adaptive Differential Pulse Code Modulation (ADPCM)	32 kBits/sec
	Low Delay Code Excited Linear Prediction (LD-CELP)	16 kBits/sec
ISDN	Bearer Channel (B-Channel)	64 kBits/sec
	Data Channel (D-Channel)	64 kBits/sec

The system works with 64 kBits/sec data, but can accept input rates of 8, 16, 32, or 64 kBits/sec. Inputs of less than 64 kBits/sec are padded with extra bits to bring them up to 64 kBits/sec.

For inputs of 8, 16, 32, or 64 kBits/sec, the system applies Forward Error Correction (FEC) coding, which doubles the bit rate, up to 128 kbits/sec. The Complex Modulation scheme (which we’ll discuss in more detail later), transmits two bits at a time, in two bit symbols. For inputs of less than 64 kbits/sec, each symbol is repeated to bring the transmission rate up to 64 kilosymbols/sec. Each component of the complex signal carries one bit of the two bit symbol, at 64 kBits/sec, as shown below.

Generating Pseudo-Random Codes

For each channel the base station generates a unique code that changes for every connection. The base station adds together all the coded transmissions for every subscriber. The subscriber unit correctly generates its own matching code and uses it to extract the appropriate signals. Note that each subscriber uses several independant channels.

In order for all this to occur, the pseudo-random code must have the following properties:

It must be deterministic. The subscriber station must be able to independently generate the code that matches the base station code.
It must appear random to a listener without prior knowledge of the code (i.e. it has the statistical properties of sampled white noise).
The cross-correlation between any two codes must be small (see below for more information on code correlation).
The code must have a long period (i.e. a long time before the code repeats itself).

Code Correlation

In this context, correlation has a specific mathematical meaning. In general the correlation function has these properties:

It equals 1 if the two codes are identical
It equals 0 of the two codes have nothing in common

Intermediate values indicate how much the codes have in common. The more they have in common, the harder it is for the receiver to extract the appropriate signal.
There are two correlation functions:

Cross-Correlation: The correlation of two different codes. As we’ve said, this should be as small as possible.
Auto-Correlation: The correlation of a code with a time-delayed version of itself. In order to reject multi-path interference, this function should equal 0 for any time delay other than zero.

The receiver uses cross-correlation to separate the appropriate signal from signals meant for other receivers, and auto-correlation to reject multi-path interference.

Pseudo-Noise Spreading

The FEC coded Information data modulates the pseudo-random code, as shown in Figure 2a. Some terminology related to the pseudo-random code:

Chipping Frequency (fc): the bit rate of the PN code.
Information rate (fi): the bit rate of the digital data.
Chip: One bit of the PN code.
Epoch: The length of time before the code starts repeating itself (the period of the code). The epoch must be longer than the round trip propagation delay (The epoch is on the order of several seconds).

Processing Gain

An important concept relating to the bandwidth is the processing gain (Gp). This is a theoretical system gain that reflects the relative advantage that frequency spreading provides. The processing gain is equal to the ratio of the chipping frequency to the data frequency.
In telecommunications, the term protocol data unit (PDU) has the following meanings:

Information that is delivered as a unit among peer entities of a network and that may contain control information, address information, or data.
In layered systems, a unit of data that is specified in a protocol of a given layer and that consists of protocol-control information of the given layer and possibly user data of that layer. For example: Bridge PDU or iSCSI PDU^[1]

PDUs are relevant in relation to one of the first 4 layers of the OSI model as follows:

The Layer 1 PDU is the bit
The Layer 2 PDU is the frame
The Layer 3 PDU is the packet
The Layer 4 PDU is the segment (e.g. TCP segment)

(Layer 5 and above are referred to as data.)

Packet-switched data networks

In the context of packet-switched data networks, a protocol data unit (PDU) is best understood in relation to a service data unit (SDU). The features or services of the network are implemented in distinct "layers". For example, sending ones and zeros across a wire, fiber, etc. is done by the physical layer, organizing the ones and zeros into chunks of data and getting them safely to the right place on the wire is done by the data link layer, passing data chunks over multiple connected networks is done by the network layer and delivery of the data to the right software application at the destination is done by the transport layer. Between the layers (and between the application and the top-most layer), the layers pass service data units across the interfaces. The application or higher layer understands the structure of the data in the SDU, but the lower layer at the interface does not; it treats it as payload, undertaking to get it to the same interface at the destination. In order to do this, the protocol layer will add to the SDU certain data it needs to perform its function. For example, it might add a port number to identify the application, a network address to help with routing, a code to identify the type of data in the packet and error-checking information. All this additional information, plus the original service data unit from the higher layer, constitutes the protocol data unit at this layer. The significance of this is that the PDU is the structured information that is passed to a matching protocol layer further along on the data's journey that allows the layer to deliver its intended function or service. The matching layer, or "peer", decodes the data to extract the original service data unit, decide if it is error-free and where to send it next, etc. Unless we have already arrived at the lowest (physical) layer, the PDU is passed to the peer using services of the next lower layer in the protocol "stack". When the PDU passes over the interface from the layer that constructed it to the layer that merely delivers it (and therefore does not understand its internal structure), it becomes a service data unit to that layer. The addition of addressing and control information (which is called encapsulation) to an SDU to form a PDU and the passing of that PDU to the next lower layer as an SDU repeats until the lowest layer is reached and the data passes over some medium as a physical signal.

MAC layer PDU becomes physical layer SDU

The above process can be likened to the mail system in which a letter (SDU) is placed in an envelope on which is written an address (addressing and control information) making it a PDU. The sending post office might look only at the post code and place the letter in a mail bag so that the address on the envelope can no longer be seen, making it now an SDU. The mail bag is labelled with the destination post code and so becomes a PDU, until it is combined with other bags in a crate, when it is now an SDU, and the crate is labelled with the region to which all the bags are to be sent, making the crate a PDU. When the crate reaches the destination matching its label, it is opened and the bags (SDUs) removed only to become PDUs when someone reads the code of the destination post office. The letters themselves are SDUs when the bags are opened but become PDUs when the address is read for final delivery. When the addressee finally opens the envelope the top-level SDU, the letter itself, emerges.

Spread Spectrum and Multiple Access Technique

Multiple Access Techniques and Cellular CDMA

An important use of the concept of spread spectrum in wireless communication systems is to allow multiple users occupy the same transmission band for simultaneous transmission of signals without considerable interference. The three basic multiple access techniques are briefly mentioned below:

Frequency Division Multiple Access (FDMA):

This classical technique has been in use in conventional telephone systems and satellite communication systems. Every user gets a certain frequency band assigned and can use this part of the spectrum to perform its communication. If only a small number of users is active, not the whole resource (frequency-spectrum) is used. Assignment of the channels can be done centrally or by carrier sensing in a mobile. The latter possibility enables random-access.

Time Division Multiple Access (TDMA):

Every user is assigned one or a set of well-defined time-slots within a ‘Time Frame’. A transmitting user sends its own data only in the designated time-slot(s), and waits for the remaining time-frame duration till it gets another time-slot in the next time frame. Precise time synchronization among all users is an important and necessary feature of TDMA multiple access strategy. Usually, a central unit controls the synchronization and the assignment of time-slots.

Code Division Multiple Access (CDMA) / Spread Spectrum Multiple Access SSMA):

One or more unique spreading codes are assigned to each user for accessing the RF bandwidth simultaneously for transmission and reception of signals. The spreading codes, assigned to all participating users, are carefully chosen to ensure very low cross-correlation among them. This ensures that the signals from undesired transmitters appear as noise (with no or very poor correlation with the desired signal after dispreading operation). CDMA / SSMA does not need very precise time synchronization among the users and hence, random-access is protocols can be implemented relatively easily.

In the following section, a brief account of CDMA scheme, used in cellular mobile communications, is presented.

Cellular CDMA

Mobile telephony, using the concept of cellular architecture, has been very popular world wide. Such systems are built based on accepted standards, such as GSM (Global System for Mobile communication) and IS-95(Intermediate Standard-95). Several standards of present and future generations of mobile communication systems include CDMA as an important component which allows a satisfactorily large number of users to communicate simultaneously over a common radio frequency band.

Cellular CDMA is a promising access technique for supporting multimedia services in a mobile environment as it helps to reduce the multi-path fading effects and interference. It also supports universal frequency reuse, which implies large teletraffic capacity to accommodate new calling subscribers. In a practical system, however, the actual number of users who can simultaneously use the RF band satisfactorily is limited by the amount of interference generated in the air interface. A good feature is that the teletraffic capacity is ‘soft’, i.e. there is no ‘hard’ or fixed value for the maximum capacity. The quality of received signal degrades gracefully with increase in the number of active users at a given point of time.

It is interesting to note that the quality of a radio link in a cellular system is often indicated by the Signal-to-Interference Ratio (SIR), rather than the common metric ‘SNR’. Let us remember that in a practical system, the spreading codes used by all the simultaneous users in a cell have some cross-correlation amongst themselves and also due to other propagation features, the signals received in a handset from all transmitters do not appear orthogonal to each other. Hence, the signals from all users, other than the desired transmitter, manifest as interference. In a practical scenario, the total interference power may even momentarily exceed the power of the desired signal. This happens especially when the received signals fluctuate randomly (fading) due to mobility of the users. Fading is a major factor degrading the performance of a CDMA system. While large-scale fading consists of path loss and shadowing, small-scale fading refers to rapid changes in signal amplitude and phase over a small spatial separation.

The desired signal at a receiver is said to be ‘in outage’ (i.e. momentarily lost) when the SIR goes below an acceptable threshold level. An ongoing conversation may get affected adversely if the outage probability is high or if the duration of outage (often called as ‘fade duration’) is considerable. On the other hand, low outage probability and insignificant ‘average fade duration’ in a CDMA system usually implies that more users could be allowed in the system ensuring good quality of signal.

Version 2 ECE IIT, Kharagpur

cryptography

The word cryptography has come from a Greek word, which means secret writing. In the present day context it refers to the tools and techniques used to make messages secure for communication between the participants and make messages immune to attacks by hackers. For private communication through public network, cryptography plays a very crucial role. The role of cryptography can be illustrated with the help a simple model of cryptography as shown in Fig. 8.1.1. The message to be sent through an unreliable medium is known as plaintext, which is encrypted before sending over the medium. The encrypted message is known as ciphertext, which is received at the other end of the medium and decrypted to get back the original plaintext message. In this lesson we shall discuss various cryptography algorithms, which can be divided into two broad categorize - Symmetric key cryptography and Public key cryptography.

Figure 8.1.1.

what is frequency efficiency in gsm..??

Doeacc mantra

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